Acquisition for DS/CDMA systems with multiple ... - IEEE Xplore
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 2, NO. 4, JULY 2003
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Acquisition for DS/CDMA Systems With Multiple Antennas in Frequency-Selective Fading Channels Hui Won Je, Student Member, IEEE, Oh-Soon Shin, Student Member, IEEE, and Kwang Bok (Ed) Lee, Member, IEEE
Abstract—A generalized code acquisition scheme for direct-sequence code-division multiple-access systems with multiple antennas is proposed over frequency-selective fading channels. The proposed scheme is developed on the framework of a generalized configuration of multiple antennas and correlators. The nonconsecutive search method is generalized and extended to multiple antenna systems to exploit multipath signals in improving acquisition performance over frequency-selective fading channels. The proposed scheme also adopts a hybrid decision strategy to make effective decisions on acquisition. The mean acquisition time performance of the proposed acquisition scheme is analyzed and evaluated in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial-fading correlations. The effects of nonconsecutive search on mean acquisition time are investigated for various channel environments, and the optimal choice of decision strategy is discussed. Furthermore, effects of various configurations of multiple antennas and correlators, decision thresholds, and correlation interval on the performance are also investigated. Index Terms—Acquisition, decision strategy, direct-sequence code-division multiple access (DS/CDMA), multiple antennas, nonconsecutive search.
I. INTRODUCTION
R
ECENTLY, the use of multiple antennas in direct-sequence code-division multiple-access (DS/CDMA) systems has come to receive considerable attention in mobile radio communications. Multiple antennas with a spatial processing can enhance a desired signal and suppress interfering signals, thereby improving performance and increasing the capacity of wireless systems [1], [2]. A number of spatial processing techniques have been developed to exploit the attractive features of multiple antennas [2]. In DS/CDMA systems, however, these techniques are useful only after code timing is acquired. In [3], a simple extension of the conventional noncoherent acquisition scheme to multiple antenna systems has been presented. In [4], an improved acquisition scheme has been proposed for DS/CDMA systems with multiple antennas, and the effective use of multiple antennas has been investigated to improve acquisition performance. The performance has been extensively analyzed in frequency-selective fading channels. In frequency-selective fading channels, there exist a number of resolvable paths. In [4], the effects of multipaths on acquisiManuscript received December 27, 2001; revised July 15, 2002; accepted October 26, 2002. The editor coordinating the review of this paper and approving it for publication is D. I. Kim. This work was supported in part by the Brain Korea 21 Project. The authors are with the School of Electrical Engineering, Seoul National University, Seoul 151-742, Korea (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TWC.2003.814340
tion performance have been well addressed. However, effective methods to utilize multipath signals have not been devised in [4]. From the viewpoint of acquisition, the existence of multipaths implies that there are more than one in-phase cells that can be acquired [5]. In next-generation DS/CDMA systems, the use of wideband signals is essential to providing high data rate services, resulting in an increased number of resolvable paths. Hence, it is challenging to develop acquisition schemes that are effective in frequency-selective fading channels. For single antenna systems, there have been some attempts to exploit multipath signals in improving acquisition performance [5]–[7]. The work in [5] is notable among these attempts since it offers a simple but effective method. In [5], a new search scheme, referred to as the nonconsecutive search, has been proposed to improve the conventional acquisition based on consecutive search. The benefits of the nonconsecutive search result from an intentional rearrangement of the positions of in-phase states on the uncertainty region. Results in [5] have shown that the use of nonconsecutive search significantly reduces the mean acquisition time in frequency-selective fading channels with contiguous multipath intensity profiles. In designing an acquisition system, the choice of an appropriate decision strategy is one of important parts. A decision strategy is concerned with a criterion for deciding an in-phase cell among a mixture of in-phase and out-of-phase cells, and with points in time to make decisions. Various decision strategies have been investigated for fast and efficient acquisition [8], which may be placed under the categories of two fundamental strategies. In one fundamental strategy, the decision variable is compared with a threshold to decide whether it is associated with an in-phase cell, whenever a decision variable for a new test cell is obtained. In the other fundamental strategy, the cell corresponding to the largest decision variable is selected as an in-phase cell, when decision variables associated with all the test cells are collected. We combine these two types of decision strategies, in terms of both the decision criterion and the points in time to make decisions, to form a hybrid type of decision strategy. First, two decision criteria are concatenated, so that the decision variable is compared with a threshold after selecting the largest decision variable [9]. As to the points in time to make decisions, a decision is made whenever decision variables associated with a portion of cells are collected [10]. Thus, different combinations of parameters will establish different decision strategies. This hybrid decision strategy may be utilized to find the optimal decision strategy in terms of the decision threshold and the number of test cells involved in making a decision.
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In this paper, we propose a generalized acquisition scheme in DS/CDMA systems with multiple antennas over frequency-selective fading channels. In the proposed acquisition scheme, generalized configurations of multiple antennas are considered, as in [4]. To exploit more than one in-phase cells in improving acquisition performance, the nonconsecutive search is extended to multiple antenna systems. Furthermore, the nonconsecutive search is generalized so that it is applicable to frequency-selective fading channels with general multipath delay profiles. The hybrid decision strategy discussed above is adopted to find optimal decision strategies in various environments. The mean acquisition time performance of the proposed scheme is analyzed in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial correlations, and evaluated in various channel environments. The effects of nonconsecutive search on mean acquisition time are investigated, and optimal choice of parameters related to the decision strategy is discussed. Furthermore, the effects of various configurations of multiple antennas and correlators, decision thresholds, and correlation interval on the performance are investigated. The remainder of this paper is organized as follows. Section II describes the proposed acquisition scheme with multiple antennas. In Section III, the performance analysis of the proposed acquisition scheme is presented in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial-fading correlations. In Section IV, the mean acquisition time performance is evaluated in various environments, and the effects of various elements of the proposed scheme on the performance are discussed. Finally, conclusions are drawn in Section V.
II. PROPOSED ACQUISITION SCHEME The proposed acquisition scheme is a double-dwell noncoherent scheme with search and verification stages, as depicted in Fig. 1. Multiple antennas are employed to receive the transmitted signal, with multiple correlators being equipped at each antenna element. In Section II-A, the configuration of multiple antennas and correlators for the proposed acquisition scheme is described. In Section II-B, the search procedure of nonconsecutive search is described for multiple antenna systems. In Section II-C, we describe how to decide an in-phase cell using the decision variables formed by the correlators. Section II-D illustrates a simple and representative example that clarifies the description of the proposed acquisition scheme. We define, here, some terminologies used throughout this paper. A cell is the smallest element of the uncertainty region, and it represents a code phase to be tested. A section is a portion of the uncertainty region associated with an antenna element and a correlator. A state is a collection of cells that are tested simultaneously, and a subregion is a portion of states formed by the nonconsecutive search. A. Configuration of Multiple Antennas and Correlators The receiving antennas are a uniform linear array of elements with spacing between adjacent antenna elements equal to
. At each antenna element, correlators with correlation inchips are equipped to correlate the received signal terval of with a local code, as depicted in Figs. 1 and 2. As proposed in antenna elements are partitioned into dis[4], antenna elements in each group. The joint groups with correlators in an antenna group perform the same operations as those in the other groups; they simultaneously produce correladifferent phases every correlation results associated with tion interval. Correlation results associated with the same phase from groups are combined to form a decision variable, producing degrees of combining gain. Specifically, the th antenna group consists of antenna el, as depicted in ements local code generators associated with each corFig. 1. The relator update chips of code phase every correlation interval to support the nonconsecutive search, which will be explained in the Section II-B. The code phase updating interval should be appropriately chosen among integers greater than one. In order correlators, the to cover the entire uncertainty region with phase difference between two adjacent correlators in a group cells, where is the number of phase unceris set to . This assumptainties and it is assumed to be divisible by tion is reasonable, since can be set to the smallest integer that and is not smaller than the actual number of uncertainties . The phase differences of correlators allow divisible by correlators in each antenna group to produce correlation different code phases simultaneresults corresponding to cells in the uncertainty ously, which are separated by region. The decision variable for each code phase is obtained by combining correlator outputs from different groups. Note and are design parameters that determine a tradeoff that between the combining gain and the time required to collect correlation results. The smaller or larger produces the greater combining gain, with the longer time interval being required to collect decision variables [4]. With an appropriate choice of and , we can reduce the mean acquisition time. We should also select the number of correlators at each antenna element, considering that the larger provides the shorter time to get correlation results at the expense of complexity. B. Nonconsecutive Search According to the code phase configurations of correlators described in the previous subsection, the uncertainty region is disections, , and thus, vided into each correlator should be capable of extracting correlation redifferent test cells within a section. In the consults for cells are tested in the ventional consecutive search, the sequential order, and the results are passed to the decision block. in-phase cells ( cells) corresponding Note that there exist to resolvable paths in frequency-selective fading channels. In cell, we genorder to exploit the presence of more than one eralize the nonconsecutive search proposed in [5] and extend it to multiple antenna systems. In this search scheme, cells in each section associated with a correlator are tested in a nonconsecuin tive manner with a step of chips. Note that is set to [5], under the assumptions that the multipaths are contiguous in is known to the receiver. The nonconsecutive time and that search proposed in this paper allows being an arbitrary value,
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Fig. 1.
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Proposed acquisition scheme.
eliminating the assumptions. The nonconsecutive search can be implemented by advancing the phases of local code generators
by chips every correlation interval, with additional adjustments being required in the boundaries of code phase sections.
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Fig. 2. Noncoherent correlators for the
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mth antenna element of the nth group.
The benefits of the nonconsecutive search may be described using the circular state diagram in Fig. 3. There are a total of test states , which are artificially disjoint subregions for divided into states. illustrative purpose, with each subregion containing In each test state, a number of cells are tested simultaneously, and the number of cells associated with a state is related to the decision strategy to be described in Section II-C. The state diagram in Fig. 3 is general, since any state can represent an in-phase state or an out-of-phase state. An in-phase state is decell is tested with the rest fined as a state where at least one out-of-phase cells. In an out-of-phase state, on the contrary, all cells). The positions the tested cells are out-of-phase cells ( of in-phase states in the state diagram are determined by the received code phases of multipath signals and the code phase updating interval . When multipath signals have contiguous code phases, as in [5], and the phases are associated with one section of code phases, the in-phase states are distributed uniformly . Then, each subreover the state diagram by setting gion contains one in-phase state. Note that in the conventional consecutive search, cells in each section are tested in a sequencells tial order from the first cell to the last cell, and thus, are tested in one or more neighboring in-phase states. The rearrangement of in-phase states due to the nonconsecutive search provides a chance of achieving faster acquisition compared with the consecutive search, since it effectively reduces the time required to reach an in-phase state from an initial state. In real situations, the multipath signals may be noncontiguous and the receiver generally does not know . In these cases, should be chosen among integers greater than one. Note that corresponds to the conventional consecutive search. Some subregions may contain more than one in-phase state, and some subregions may contain no in-phase states. Nevertheless, the nonconsecutive search may scatter the in-phase states to some extend, achieving some reduction of mean acquisition time. To utilize the benefits of nonconsecutive search effectively, an appropriate decision strategy should be followed after the nonconsecutive search, and this will be described in the next subsection.
C. Decision Strategy The proposed acquisition scheme is a double-dwell scheme with search and verification stages. In the search stage, decorrecision variables are simultaneously obtained from lation results, as described in Section II-A. To form a decision variable for each phase, correlation results for the same phase from different antenna groups are combined noncoherently. that is derived from the th correThe decision variable lators of the th antenna elements in distinct groups can be expressed as
(1) cells Whenever the decision variables associated with correlation intervals, it is decided which are collected during cells. Thus, cells form is an in-phase cell among a state in the circular state diagram of Fig. 3. The cell corresponding to the largest decision variable is first selected, and then it is compared with the first decision threshold . If the largest decision variable is greater than , the verification stage is activated for the selected cell. Otherwise, decision variables cells are collected and the above associated with the next procedures are repeated until the largest decision variable exceeds . In the verification stage, the local code generator associated with the first correlator at each antenna element is adjusted to have the phase selected in the search stage, and a correlation is performed on the phase. The decision variable is constructed from a noncoherent combination of correlation results from the first correlators of different antennas (2) The decision variable is compared with the second decision threshold . If the decision variable exceeds , acquisition
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Fig. 3. Circular state diagram of the proposed acquisition scheme.
is declared and tracking system is enabled. Otherwise, the acquisition system goes back to the search stage. When an cell is erroneously decided to be an in-phase cell, which corresponds to the occurrence of a false alarm, the acquisition process is restarted after chips of penalty time. Note that the decision strategy described above is a hybrid cells form a test form, as described in Section I. In Fig. 3, . This implies that the number state, and thus, of states decreases in proportion to , since the total number of cells is fixed. A decision is made by selecting the largest decision variable and comparing it with a threshold whenever decision variables are collected. Therefore, is a design parameter that determines the degree of parallelism in decisions. The decision thresholds are also important parameters that affect the performance. If we do not consider the verifi, i.e., cation stage, a special case of and , corresponds to the second fundamental decision strategy described in Section I, while another special case of corresponds to the first one if as well. It and decision is expected that there exists optimal values of thresholds that minimize the mean acquisition time for a given should not be greater than condition. It should be noted that
to achieve the benefits of nonconsecutive search. If is not greater than , , and thus, adjacent cells can create separate in-phase states in the state diagram. Othercells may be merged into one in-phase state, rewise, some ducing the effectiveness of the nonconsecutive search. D. Simple and Representative Example The proposed acquisition scheme descried in the previous subsections can be explained using an example in Fig. 4, where , , , , and are assumed for illustrative purposes. As indicated in Fig. 4, three multipath signals are also assumed to locate in contiguous cells: 33–35th cells are in-phase cells. Fig. 4 illustrates the search and decision procedures only for the first antenna group, since the procedures for the other antenna groups are the same as the first group. Rectangles in this figure represent code phases or cells. Horizontal arrows mark out sections of cells associated with each correlator and antenna element. The left time axis represents the elapsed time until correlation results for cells in the denoting corresponding row are extracted, with the unit the correlation interval of each correlator.
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Fig. 4. Representative illustration of the proposed acquisition scheme (U
= 108, M = 3, L = 3, W = 2, = 2).
In Fig. 4, the number of cells in each section of the uncer. The order of testing cells for tainty region is each correlator is not sequential due to nonconsecutive search. For the nonconsecutive search, the local code phase of each chips, with additional adjustcorrelator is updated by ments in the boundaries of adjacent sections. In the first section , for example, the 18 cells are tested in the order of 1-4-7-10-13-16-2-8-11-14-17-3-6-9-12-15-18. Fig. 4 also indicates that the cells in an uncertainty region are divided into distinct subregions according to the test order, so that each subregion contains one and only one cell. Decisions for acquisition are made whenever correlacells are collected, for tion results associated with of correlation time. As depicted in which it takes total cells forms one of Fig. 4, a collection of states in the circular state diagram of Fig. 3, is the number of states in each where subregion.
III. PERFORMANCE ANALYSIS In this section, the performance of the acquisition scheme described in Section II is analyzed in frequency-selective Rayleigh-fading channels with general multipath intensity profiles and spatial correlations. In Section III-A, the received signal model is described. The derivations of the probabilities of detection, miss-detection, and false alarm can be conducted in a similar manner, as in [4], and they are briefly summarized in Section III-B. In Section III-C, an expression for the mean acquisition time is derived using the circular state diagram of Fig. 3.
A. Received Signal Model It is assumed that a DS/CDMA signal is received without data modulation. The complex baseband equivalent of the received signal at the th antenna element may be expressed as (3) is where denotes the average total received signal power, the frequency offset between the transmitter and receiver, is the pseudonoise code waveform with duration , and is the received code phase for the th resolvable path. Without loss of generality, we assume that . Noise plus multiple-access interference, denoted as in (3), is a complex additive white Gaussian noise process with . In (3), the multiplicativeone-sided power spectral density fading channel for the th resolvable path at the th antenna ; , which is a complex Gaussian element is denoted as random process. Assuming that each path experiences indepen; may dent Rayleigh fading, the correlation function of be expressed as [4]
(4) denotes the where [ ] denotes the statistical expectation, power of the th path, [ ] denotes the Kronecker delta function and 0, otherwise), is the Doppler (defined as 1 for represents the zeroth-order Bessel function of spread, and the first kind. Assuming that the angle of arrival of the th path , , the spatial signal is uniformly distributed over [
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correlation , in (4) between the th path signals at the th and th antenna elements is calculated as [4]
between and , which are associated with the same code phase, and it can be calculated as [4]
(5)
where is the carrier wavelength. In (4), note that the power of ; is normalized so that .
(8)
B. Probabilities of Detection, Miss-Detection, and False Alarm The receiver is assumed to be chip-synchronized to the received signal. We assume that acquisition is completed if any resolvable paths, not necessarily the first path, is acof the cells. After sucquired. This implies that there exist cessful acquisition of one path, the searcher determines the rest paths within a search window [11]. Note that only the acquisition process is considered in this paper. For the nonconsecutive chips, the search with the code phase updating interval of cell associated with the th state number that includes the resolvable path can be calculated as (6) denotes the largest integer smaller than or equal to where . Thus, the state ( ) becomes an in-phase cells. Let denote the state that contains one or more cells in the th state ( ), then number of . A state associated with is an in-phase cells and cells are tested sistate, where multaneously. Clearly, the maximum number of in-phase states or . A state asis , which corresponds to the case of is an out-of-phase state, where sociated with cells are tested simultaneously. To calculate the probabilities of detection, miss-detection, and false alarm in each state, the probability density function (pdf) and cumulative distribution function (cdf) of the decision variables in (1) and (2) are required. These functions can easily be derived using the characteristic function method, and detailed procedures are well described in [4]. We briefly summarize the results in [4]. The pdf and cdf equations of a decision variable in the search stage for an cell corresponding to the th resolvable path ( cell) are given as
, and is dewhere fined as signal-to-interference ratio per chip (SIR/chip). When the same eigenvalues exist, the corresponding pdf and cdf equacell, the pdf and cdf equations can also be derived. For an tions are derived as
(9) in (2), denoted as Note that the pdf and cdf equations of and hereafter, are the same as those of with and by 1 and , respectively. the substitutions of Using the pdf and cdf equations, in the search stage, the prob, that of miss-detection , and ability of detection at the th state (s in Fig. 3) can be that of false alarm calculated as
(10) (11) (12) is the first decision threshold, and ( ) denotes the index of path associated with the th in-phase cell of the th state. Note that for out-of-phase states, since for those states. In the verification stage, only a cell selected in the search stage is for the th tested, and thus, the probability of detection can be calculated as resolvable path and that of false alarm where
(13) (7)
(14) where
, and s are where the eigenvalues of the correlation matrix of correlator outputs combined, and they are assumed to be distinct in (7). The ( , ) element of the correlation matrix is the correlation
is the second decision threshold.
C. Mean Acquisition Time The mean acquisition time of the proposed acquisition scheme may be calculated using the flow graph method in [12].
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The branch gains in the circular state diagram of Fig. 3 are expressed as
where
(15)
(16) , , and . and are, respectively, the gain of the branch connecting the state and acquisition (ACQ) state, state. In and that of the branch connecting the state and is the time required for collecting decision (15) and (16), variables to make a decision in each state, is the correlation is the penalty time due to a interval of correlators, and false alarm. From the circular state diagram of Fig. 3, the transfer function from a given initial state to the ACQ state can be calculated as where
(17) where (18)
(19) in (18) is the state-independent loop gain of the circular , , in (19) is the gain of the shortest state diagram, and state , where path from the initial state to the . Under the assumption that the initial state number is unistate numbers, the generating formly distributed over all is found as function
In (22), it should be noted that the total number of states decreases in proportion to , and it takes to collect decision variables for a decision in a state. Therefore, definitely reduces the time required to test all the cells large decreases the comin the uncertainty region. However, large , bining gain of decision variables represented by and large increases the complexity of the receiver. Note that the combining gain is reflected on the probabilities of detection, miss-detection, and false alarm in the above equations. (or ) and can decrease the Hence, appropriate choices of determines the decimean acquisition time. The parameter sion strategy, and can also be optimized to decrease the mean acquisition time. IV. NUMERICAL RESULTS
(20) The corresponding mean acquisition time may be calculated as [12] (21) which yields
(22)
In this section, the mean acquisition time performance of the proposed acquisition scheme is evaluated. The mean acquisition time of the proposed acquisition scheme is calculated using (22) with probabilities in (10)–(14). The mean acquisition time based on the conventional consecutive search is also evaluated for comparisons. The number of actual code phase uncertainties is assumed to be 1024, and is chosen as for a set of given parameters ( , , , and ), where denotes the smallest integer greater than or equal to . The spacing between adjacent antenna elements is assumed to be . For the multipath delay profile or relative delay and of multipaths, we use six-path ITU-R Pedestrian B power (PB), Vehicular A (VA), and Vehicular B (VB) channel models [13] as well as contiguous uniform (CU) model. These channel models are summarized in Table I, where we calculate the relative delays assuming that the chip rate is equal to 3.84 MHz. and angle spread of each path The mean angle of arrival are assumed to be the values in Table I. In the following results,
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TABLE I CHANNEL MODELS
Fig. 5. Comparisons between numerical and simulation results (VA channel, L , ,W , ).
=2 1=8
= 32 = 1
the penalty time is assumed to be 10 chips. Unless explicitly specified, the correlation interval is set to 256 chips, and and frequency offset , the normalized Doppler spread , are assumed to be which are normalized by the chip rate 10 and 0, respectively. To validate the performance analysis, the analytical results are compared with simulation results in Fig. 5 for the VA channel, , , , and . The decision when thresholds for the analytical results are determined such that the mean acquisition time is minimized for each condition. In the simulations, the thresholds are set to the same values as in the analysis. A close agreement between analytical and simulation results verifies that the performance analysis is correct. The following results are obtained using the analysis. Fig. 6 shows how the mean acquisition time varies with deand for the VA channel, when , cision thresholds , , , , , and SIR/chip dB. It is apparent that inappropriate choices of decision thresholds can increase the mean acquisition time several times. If decision thresholds are very small for both search and verification stages, the mean acquisition time increases steeply due to excessive false alarms. If or is greater than some value, and in Fig. 6; however, the mean acabout 20 for both quisition time is seen to be relatively insensitive to the decision
Fig. 6. Effects of decision thresholds and on mean acquisition time (VA channel, L ,M ,N , ,W , , SIR/chip dB).
= 010
=8
=2
=41=8
= 32 = 1
Fig. 7. Effects of correlation interval K on mean acquisition time (VA channel, L ,M ,N , ,W , ).
=8
=2
=4 1=8
= 32 = 1
thresholds. In the subsequent results, we have numerically determined the decision thresholds such that the mean acquisition time is minimized for each condition. Fig. 7 shows the effects of correlation interval on mean acquisition time for several values of normalized Doppler spread
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Fig. 8. Effects of code phase updating interval (L ,M ,N ,W , ).
=8
=2
=4
= 32 = 1
1 on mean acquisition time
, normalized frequency offset , and SIR/chip for the , , , , , VA channel, when . It is observed that there exists optimal choice and that minimizes the mean acquisition time for each conof increases the reliability of decision dition. An increase in variables, unless the signal component varies significantly over chips due to Doppler spread or frequency offset. However, large can incur signal energy loss in the presence of Doppler also results in spread or frequency offset [14], and large long correlation time, which possibly increases the mean acis shown to be smaller for quisition time. In Fig. 7, optimal higher SIR/chip. This is because the effects of correlation time on mean acquisition time become more substantial than those of Doppler spread and frequency offset as the SIR/chip increases. and 10 result in almost the same In Fig. 7, and SIR/chip. mean acquisition time for the given range of This indicates that the effects of Doppler spread are not signifin practical range of Doppler spread, icant in determining corresponds to as large as 384 Hz for since the chip rate of 3.84 MHz. In the presence of frequency offset ( kHz for the chip rate of 3.84 MHz), however, the signal energy loss is significant for large , and the mean acquisition time is shown to severely increase with . Note that the frequency offset can be as large as a few kilohertz in practical situations. The effects of the code phase updating interval on mean acquisition time are depicted in Fig. 8 for four different chan, , , , and . Note nels, when corresponds to the conventional consecutive search. that always provides shorter mean acquiIt is observed that , verifying the effectiveness of the nonsition time than consecutive search. Although the optimal value of depends on the multipath delay profile, a significant reduction in mean acquisition time may be achieved with an appropriate choice of . It may be reasonable to use greater than or equal to the number of paths, six in the case of Fig. 8, since the benefits of nonconsecutive search are from splitting in-phase states in the seems to state diagram. Based on the results of Fig. 8, be an appropriate choice for the six-path channels.
Fig. 9. Effects of decision parameter W and number of correlators acquisition time (VA channel, L ,M ,N , ).
=8
=2
=4 1=8
on mean
Fig. 9 shows the effects of different decision strategies deand the number of correlators on mean actermined by quisition time of the proposed acquisition scheme for the VA , , , and . As previchannel, when cells form a test state. For given and ously mentioned, , a smaller value of makes decisions to be made more frequently with a smaller number of collected decision variables. can decrease Fig. 9 indicates that an appropriate choice of the mean acquisition time to some extent. For the case of in Fig. 9, or 16 is shown to achieve significantly shorter , especially at high SIR mean acquisition time than values. Similar trends can be observed for the case of or as well. When and SIR/chip dB, for and example, the mean acquisition time for is about 30 000 and 37 000 chips, respectively. The mean acquisition time is also shown to decrease as increases. The performance improvement is more significant at high SIR values. This is because the time required to collect decision variables , and the reduction involved in a decision is proportional to of this time is more effective at high SIR values in reducing the mean acquisition time. It should be noted that is directly related to the complexity of an acquisition receiver, and thus, it should be selected with consideration on both the performance and complexity. Fig. 10 shows the effects of antenna configurations and nonconsecutive search on mean acquisition time for the CU , , and . Although channel, when provides the best performance for the nonconin Fig. 10, since is generally secutive search, we set unknown to the receiver. From the performance for different configurations of antenna elements in Fig. 10, it is found that the larger provides the shorter mean acquisition time at low provides the shorter mean SIR values, while the smaller acquisition time at high SIR values, for both schemes. This is because the effect of combining gain is more significant at low SIR values, while that of the total correlation time required to collect decision variables is more significant at high SIR values, as thoroughly investigated in [4]. As expected, the
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Fig. 10. Mean acquisition time with and without nonconsecutive search (CU , ,W , ). channel, L
Fig. 12. Mean acquisition time with and without nonconsecutive search (VA , ). channel, L , ,W
=8 1=8
= 16 = 1
Fig. 11. Mean acquisition time with and without nonconsecutive search (PB , channel, L ,W , ).
=8 1=8
= 16 = 1
nonconsecutive search is shown to provide better performance than the conventional consecutive search for all cases, and that the performance improvement is greater at high SIR values. The reason for this is that in-phase states are more scattered in the state diagram for the nonconsecutive search than for the consecutive search. At a sufficiently high SIR, the probability of detection at any in-phase state is close to unity, whereas the probabilities of miss-detection and false alarm are small enough to be negligible. In this case, the effects of scattered in-phase states are directly reflected to the mean , , and SIR/chip dB acquisition time. When in Fig. 10, the mean acquisition time for the nonconsecutive search is 10 000 chips, which is close to 1/3.5 times that of the consecutive search, 35 000 chips. At low SIR values, on the other hand, the effects of scattered in-phase states become less significant due to nonnegligible probabilities of miss-detection and false alarm. Consequently, the performance difference of the nonconsecutive search and consecutive search becomes small at low SIR values.
=8 1=8
= 32 = 1
Fig. 13. Mean acquisition time with and without nonconsecutive search (VB channel, L , ,W , ).
=8 1=8
= 32 = 1
Figs. 11–13 compare the mean acquisition time performance of the nonconsecutive and consecutive search schemes for the PB, VA, and VB channels, respectively, which have noncontiguous relative delays, as shown in Table I. Similar trends are observed for different channel models. As expected, the nonconsecutive search is shown to significantly outperform the consec, , and SIR/chip dB, utive search. When for example, the reductions of mean acquisition time for the nonconsecutive search compared with the consecutive search are found to be 36% for the PB channel, 26% for the VA channel, and 17% for the VB channel. V. CONCLUSION In this paper, a generalized acquisition scheme has been proposed for DS/CDMA systems with multiple antennas. In the proposed scheme, a generalized configuration of antennas and correlators has been considered. The nonconsecutive search has been generalized and extended to multiple antenna systems
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to exploit multipath signals in reducing mean acquisition time over frequency-selective fading channels. A hybrid decision strategy is adopted to decide an in-phase cell among the cells in the uncertainty region. The mean acquisition time performance of the proposed acquisition scheme has been analyzed in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial correlations. It has been shown that the nonconsecutive search provides significant reduction of mean acquisition time compared with the conventional consecutive search in typical channel environments. Based on the performance evaluation of hybrid decision strategies with various parameters, we have also investigated the optimal choice of decision strategy that reduces the mean acquisition time. Furthermore, the effects of various configurations of multiple antennas and correlators, decision thresholds, and correlation interval on mean acquisition time have been investigated. REFERENCES [1] J. H. Winters, “Smart antennas for wireless systems,” IEEE Pers. Commun., vol. 5, pp. 23–27, Feb. 1998. [2] R. M. Buehrer, A. G. Kogiantis, S.-C. Liu, J.-A. Tsai, and D. Uptegrove, “Intelligent antennas for wireless communications—Uplink,” Bell Labs Tech. J., vol. 4, pp. 73–103, July/Sept. 1999. [3] R. R. Rick and L. B. Milstein, “Parallel acquisition of spread-spectrum signals with antenna diversity,” IEEE Trans. Commun., vol. 45, pp. 903–905, Aug. 1997. [4] O.-S. Shin and K. B. Lee, “Use of multiple antennas for DS/CDMA code acquisition,” IEEE Trans. Wireless Commun., vol. 2, pp. 424–430, May 2003. [5] , “Utilization of multipaths for spread-spectrum code acquisition in frequency-selective Rayleigh fading channels,” IEEE Trans. Commun., vol. 49, pp. 734–743, Apr. 2001. [6] L.-L. Yang and L. Hanzo, “Serial acquisition of DS-CDMA signals in multipath fading mobile channels,” IEEE Trans. Veh. Technol., vol. 50, pp. 617–628, Mar. 2001. [7] R. R. Rick and L. B. Milstein, “Optimal decision strategies for acquisition of spread-spectrum signals in frequency-selective fading channels,” IEEE Trans. Commun., vol. 46, pp. 684–694, May 1998. [8] M. K. Simon, J. K. Omura, R. A. Scholtz, and B. K. Levitt, Spread Spectrum Communications Handbook. New York: McGraw-Hill, 1994. [9] G. E. Corazza, “On the MAX/TC criterion for code acquisition and its application to DS-SSMA systems,” IEEE Trans. Commun., vol. 44, pp. 1173–1182, Sept. 1996. [10] W. Zhuang, “Noncoherent hybrid parallel PN code acquisition for CDMA mobile communications,” IEEE Trans. Veh. Technol., vol. 45, pp. 643–656, Nov. 1996. [11] S. Glisic and M. D. Katz, “Modeling of the code acquisition process for rake receivers in CDMA wireless networks with multipath and transmitter diversity,” IEEE J. Select. Areas Commun., vol. 19, pp. 21–32, Jan. 2001. [12] A. Polydoros and C. L. Weber, “A unified approach to serial search spread-spectrum code acquisition—Part I: General theory,” IEEE Trans. Commun., vol. COM-32, pp. 542–549, May 1984.
[13] “Guidelines for evaluation of radio transmission technologies (RTT) for IMT-2000,” International Telecommunications Union (ITU), Rec. ITU-R M.1225, 1997. [14] E. Sourour and S. C. Gupta, “Direct-sequence spread-spectrum parallel acquisition in a fading mobile channel,” IEEE Trans. Commun., vol. 38, pp. 992–998, July 1990.
Hui Won Je (S’01) received the B.S. degree from Seoul National University, Seoul, Korea, in 2001. He is currently working toward the Ph.D. degree in electrical engineering and computer science at Seoul National University. His current research interests include synchronization, multiple access scheme, and radio resource management for next-generation mobile communication systems.
Oh-Soon Shin (S’00) received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1998 and 2000, respectively. He is currently working toward the Ph.D. degree in electrical engineering and computer science at Seoul National University. His current research interests include mobile communications, spread spectrum communication systems, synchronization, radio resource management, and signal processing for communications. Mr. Shin received the Best Paper Award from the CDMA International Conference 2000 (CIC 2000).
Kwang Bok (Ed) Lee (M’90) received the B.A.Sc. and M.Eng. degrees from the University of Toronto, Toronto, Ontario, Canada, in 1982 and 1986, respectively, and the Ph.D. degree from McMaster University, Hamilton, Ontario, Canada, in 1990. He was with Motorola Canada from 1982 to 1985, and Motorola USA from 1990 to 1996 as a Senior Staff Engineer. At Motorola, he was involved in the research and development of wireless communication systems. He was with Bell-Northern Research, Canada, from 1989 to 1990. In March 1996, he joined the School of Electrical Engineering, Seoul National University, Seoul, Korea. Currently he is an Associate Professor in the School of Electrical Engineering. He was a Vice Chair of the School of Electrical Engineering from 2000 to 2002. He has been serving as a Consultant to a number of wireless industries. His research interests include mobile communications, communication theories, spread spectrum, and signal processing. He holds ten U.S. patents and two Korean patents, and has a number of patents pending. Dr. Lee has been an Editor of the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, WIRELESS SERIES in 2001, and now he is the Editor of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. He received the Best Paper Award from the CDMA International Conference 2000 (CIC 2000).
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Acquisition for DS/CDMA Systems With Multiple Antennas in Frequency-Selective Fading Channels Hui Won Je, Student Member, IEEE, Oh-Soon Shin, Student Member, IEEE, and Kwang Bok (Ed) Lee, Member, IEEE
Abstract—A generalized code acquisition scheme for direct-sequence code-division multiple-access systems with multiple antennas is proposed over frequency-selective fading channels. The proposed scheme is developed on the framework of a generalized configuration of multiple antennas and correlators. The nonconsecutive search method is generalized and extended to multiple antenna systems to exploit multipath signals in improving acquisition performance over frequency-selective fading channels. The proposed scheme also adopts a hybrid decision strategy to make effective decisions on acquisition. The mean acquisition time performance of the proposed acquisition scheme is analyzed and evaluated in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial-fading correlations. The effects of nonconsecutive search on mean acquisition time are investigated for various channel environments, and the optimal choice of decision strategy is discussed. Furthermore, effects of various configurations of multiple antennas and correlators, decision thresholds, and correlation interval on the performance are also investigated. Index Terms—Acquisition, decision strategy, direct-sequence code-division multiple access (DS/CDMA), multiple antennas, nonconsecutive search.
I. INTRODUCTION
R
ECENTLY, the use of multiple antennas in direct-sequence code-division multiple-access (DS/CDMA) systems has come to receive considerable attention in mobile radio communications. Multiple antennas with a spatial processing can enhance a desired signal and suppress interfering signals, thereby improving performance and increasing the capacity of wireless systems [1], [2]. A number of spatial processing techniques have been developed to exploit the attractive features of multiple antennas [2]. In DS/CDMA systems, however, these techniques are useful only after code timing is acquired. In [3], a simple extension of the conventional noncoherent acquisition scheme to multiple antenna systems has been presented. In [4], an improved acquisition scheme has been proposed for DS/CDMA systems with multiple antennas, and the effective use of multiple antennas has been investigated to improve acquisition performance. The performance has been extensively analyzed in frequency-selective fading channels. In frequency-selective fading channels, there exist a number of resolvable paths. In [4], the effects of multipaths on acquisiManuscript received December 27, 2001; revised July 15, 2002; accepted October 26, 2002. The editor coordinating the review of this paper and approving it for publication is D. I. Kim. This work was supported in part by the Brain Korea 21 Project. The authors are with the School of Electrical Engineering, Seoul National University, Seoul 151-742, Korea (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TWC.2003.814340
tion performance have been well addressed. However, effective methods to utilize multipath signals have not been devised in [4]. From the viewpoint of acquisition, the existence of multipaths implies that there are more than one in-phase cells that can be acquired [5]. In next-generation DS/CDMA systems, the use of wideband signals is essential to providing high data rate services, resulting in an increased number of resolvable paths. Hence, it is challenging to develop acquisition schemes that are effective in frequency-selective fading channels. For single antenna systems, there have been some attempts to exploit multipath signals in improving acquisition performance [5]–[7]. The work in [5] is notable among these attempts since it offers a simple but effective method. In [5], a new search scheme, referred to as the nonconsecutive search, has been proposed to improve the conventional acquisition based on consecutive search. The benefits of the nonconsecutive search result from an intentional rearrangement of the positions of in-phase states on the uncertainty region. Results in [5] have shown that the use of nonconsecutive search significantly reduces the mean acquisition time in frequency-selective fading channels with contiguous multipath intensity profiles. In designing an acquisition system, the choice of an appropriate decision strategy is one of important parts. A decision strategy is concerned with a criterion for deciding an in-phase cell among a mixture of in-phase and out-of-phase cells, and with points in time to make decisions. Various decision strategies have been investigated for fast and efficient acquisition [8], which may be placed under the categories of two fundamental strategies. In one fundamental strategy, the decision variable is compared with a threshold to decide whether it is associated with an in-phase cell, whenever a decision variable for a new test cell is obtained. In the other fundamental strategy, the cell corresponding to the largest decision variable is selected as an in-phase cell, when decision variables associated with all the test cells are collected. We combine these two types of decision strategies, in terms of both the decision criterion and the points in time to make decisions, to form a hybrid type of decision strategy. First, two decision criteria are concatenated, so that the decision variable is compared with a threshold after selecting the largest decision variable [9]. As to the points in time to make decisions, a decision is made whenever decision variables associated with a portion of cells are collected [10]. Thus, different combinations of parameters will establish different decision strategies. This hybrid decision strategy may be utilized to find the optimal decision strategy in terms of the decision threshold and the number of test cells involved in making a decision.
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In this paper, we propose a generalized acquisition scheme in DS/CDMA systems with multiple antennas over frequency-selective fading channels. In the proposed acquisition scheme, generalized configurations of multiple antennas are considered, as in [4]. To exploit more than one in-phase cells in improving acquisition performance, the nonconsecutive search is extended to multiple antenna systems. Furthermore, the nonconsecutive search is generalized so that it is applicable to frequency-selective fading channels with general multipath delay profiles. The hybrid decision strategy discussed above is adopted to find optimal decision strategies in various environments. The mean acquisition time performance of the proposed scheme is analyzed in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial correlations, and evaluated in various channel environments. The effects of nonconsecutive search on mean acquisition time are investigated, and optimal choice of parameters related to the decision strategy is discussed. Furthermore, the effects of various configurations of multiple antennas and correlators, decision thresholds, and correlation interval on the performance are investigated. The remainder of this paper is organized as follows. Section II describes the proposed acquisition scheme with multiple antennas. In Section III, the performance analysis of the proposed acquisition scheme is presented in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial-fading correlations. In Section IV, the mean acquisition time performance is evaluated in various environments, and the effects of various elements of the proposed scheme on the performance are discussed. Finally, conclusions are drawn in Section V.
II. PROPOSED ACQUISITION SCHEME The proposed acquisition scheme is a double-dwell noncoherent scheme with search and verification stages, as depicted in Fig. 1. Multiple antennas are employed to receive the transmitted signal, with multiple correlators being equipped at each antenna element. In Section II-A, the configuration of multiple antennas and correlators for the proposed acquisition scheme is described. In Section II-B, the search procedure of nonconsecutive search is described for multiple antenna systems. In Section II-C, we describe how to decide an in-phase cell using the decision variables formed by the correlators. Section II-D illustrates a simple and representative example that clarifies the description of the proposed acquisition scheme. We define, here, some terminologies used throughout this paper. A cell is the smallest element of the uncertainty region, and it represents a code phase to be tested. A section is a portion of the uncertainty region associated with an antenna element and a correlator. A state is a collection of cells that are tested simultaneously, and a subregion is a portion of states formed by the nonconsecutive search. A. Configuration of Multiple Antennas and Correlators The receiving antennas are a uniform linear array of elements with spacing between adjacent antenna elements equal to
. At each antenna element, correlators with correlation inchips are equipped to correlate the received signal terval of with a local code, as depicted in Figs. 1 and 2. As proposed in antenna elements are partitioned into dis[4], antenna elements in each group. The joint groups with correlators in an antenna group perform the same operations as those in the other groups; they simultaneously produce correladifferent phases every correlation results associated with tion interval. Correlation results associated with the same phase from groups are combined to form a decision variable, producing degrees of combining gain. Specifically, the th antenna group consists of antenna el, as depicted in ements local code generators associated with each corFig. 1. The relator update chips of code phase every correlation interval to support the nonconsecutive search, which will be explained in the Section II-B. The code phase updating interval should be appropriately chosen among integers greater than one. In order correlators, the to cover the entire uncertainty region with phase difference between two adjacent correlators in a group cells, where is the number of phase unceris set to . This assumptainties and it is assumed to be divisible by tion is reasonable, since can be set to the smallest integer that and is not smaller than the actual number of uncertainties . The phase differences of correlators allow divisible by correlators in each antenna group to produce correlation different code phases simultaneresults corresponding to cells in the uncertainty ously, which are separated by region. The decision variable for each code phase is obtained by combining correlator outputs from different groups. Note and are design parameters that determine a tradeoff that between the combining gain and the time required to collect correlation results. The smaller or larger produces the greater combining gain, with the longer time interval being required to collect decision variables [4]. With an appropriate choice of and , we can reduce the mean acquisition time. We should also select the number of correlators at each antenna element, considering that the larger provides the shorter time to get correlation results at the expense of complexity. B. Nonconsecutive Search According to the code phase configurations of correlators described in the previous subsection, the uncertainty region is disections, , and thus, vided into each correlator should be capable of extracting correlation redifferent test cells within a section. In the consults for cells are tested in the ventional consecutive search, the sequential order, and the results are passed to the decision block. in-phase cells ( cells) corresponding Note that there exist to resolvable paths in frequency-selective fading channels. In cell, we genorder to exploit the presence of more than one eralize the nonconsecutive search proposed in [5] and extend it to multiple antenna systems. In this search scheme, cells in each section associated with a correlator are tested in a nonconsecuin tive manner with a step of chips. Note that is set to [5], under the assumptions that the multipaths are contiguous in is known to the receiver. The nonconsecutive time and that search proposed in this paper allows being an arbitrary value,
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Fig. 1.
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Proposed acquisition scheme.
eliminating the assumptions. The nonconsecutive search can be implemented by advancing the phases of local code generators
by chips every correlation interval, with additional adjustments being required in the boundaries of code phase sections.
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mth antenna element of the nth group.
The benefits of the nonconsecutive search may be described using the circular state diagram in Fig. 3. There are a total of test states , which are artificially disjoint subregions for divided into states. illustrative purpose, with each subregion containing In each test state, a number of cells are tested simultaneously, and the number of cells associated with a state is related to the decision strategy to be described in Section II-C. The state diagram in Fig. 3 is general, since any state can represent an in-phase state or an out-of-phase state. An in-phase state is decell is tested with the rest fined as a state where at least one out-of-phase cells. In an out-of-phase state, on the contrary, all cells). The positions the tested cells are out-of-phase cells ( of in-phase states in the state diagram are determined by the received code phases of multipath signals and the code phase updating interval . When multipath signals have contiguous code phases, as in [5], and the phases are associated with one section of code phases, the in-phase states are distributed uniformly . Then, each subreover the state diagram by setting gion contains one in-phase state. Note that in the conventional consecutive search, cells in each section are tested in a sequencells tial order from the first cell to the last cell, and thus, are tested in one or more neighboring in-phase states. The rearrangement of in-phase states due to the nonconsecutive search provides a chance of achieving faster acquisition compared with the consecutive search, since it effectively reduces the time required to reach an in-phase state from an initial state. In real situations, the multipath signals may be noncontiguous and the receiver generally does not know . In these cases, should be chosen among integers greater than one. Note that corresponds to the conventional consecutive search. Some subregions may contain more than one in-phase state, and some subregions may contain no in-phase states. Nevertheless, the nonconsecutive search may scatter the in-phase states to some extend, achieving some reduction of mean acquisition time. To utilize the benefits of nonconsecutive search effectively, an appropriate decision strategy should be followed after the nonconsecutive search, and this will be described in the next subsection.
C. Decision Strategy The proposed acquisition scheme is a double-dwell scheme with search and verification stages. In the search stage, decorrecision variables are simultaneously obtained from lation results, as described in Section II-A. To form a decision variable for each phase, correlation results for the same phase from different antenna groups are combined noncoherently. that is derived from the th correThe decision variable lators of the th antenna elements in distinct groups can be expressed as
(1) cells Whenever the decision variables associated with correlation intervals, it is decided which are collected during cells. Thus, cells form is an in-phase cell among a state in the circular state diagram of Fig. 3. The cell corresponding to the largest decision variable is first selected, and then it is compared with the first decision threshold . If the largest decision variable is greater than , the verification stage is activated for the selected cell. Otherwise, decision variables cells are collected and the above associated with the next procedures are repeated until the largest decision variable exceeds . In the verification stage, the local code generator associated with the first correlator at each antenna element is adjusted to have the phase selected in the search stage, and a correlation is performed on the phase. The decision variable is constructed from a noncoherent combination of correlation results from the first correlators of different antennas (2) The decision variable is compared with the second decision threshold . If the decision variable exceeds , acquisition
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Fig. 3. Circular state diagram of the proposed acquisition scheme.
is declared and tracking system is enabled. Otherwise, the acquisition system goes back to the search stage. When an cell is erroneously decided to be an in-phase cell, which corresponds to the occurrence of a false alarm, the acquisition process is restarted after chips of penalty time. Note that the decision strategy described above is a hybrid cells form a test form, as described in Section I. In Fig. 3, . This implies that the number state, and thus, of states decreases in proportion to , since the total number of cells is fixed. A decision is made by selecting the largest decision variable and comparing it with a threshold whenever decision variables are collected. Therefore, is a design parameter that determines the degree of parallelism in decisions. The decision thresholds are also important parameters that affect the performance. If we do not consider the verifi, i.e., cation stage, a special case of and , corresponds to the second fundamental decision strategy described in Section I, while another special case of corresponds to the first one if as well. It and decision is expected that there exists optimal values of thresholds that minimize the mean acquisition time for a given should not be greater than condition. It should be noted that
to achieve the benefits of nonconsecutive search. If is not greater than , , and thus, adjacent cells can create separate in-phase states in the state diagram. Othercells may be merged into one in-phase state, rewise, some ducing the effectiveness of the nonconsecutive search. D. Simple and Representative Example The proposed acquisition scheme descried in the previous subsections can be explained using an example in Fig. 4, where , , , , and are assumed for illustrative purposes. As indicated in Fig. 4, three multipath signals are also assumed to locate in contiguous cells: 33–35th cells are in-phase cells. Fig. 4 illustrates the search and decision procedures only for the first antenna group, since the procedures for the other antenna groups are the same as the first group. Rectangles in this figure represent code phases or cells. Horizontal arrows mark out sections of cells associated with each correlator and antenna element. The left time axis represents the elapsed time until correlation results for cells in the denoting corresponding row are extracted, with the unit the correlation interval of each correlator.
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Fig. 4. Representative illustration of the proposed acquisition scheme (U
= 108, M = 3, L = 3, W = 2, = 2).
In Fig. 4, the number of cells in each section of the uncer. The order of testing cells for tainty region is each correlator is not sequential due to nonconsecutive search. For the nonconsecutive search, the local code phase of each chips, with additional adjustcorrelator is updated by ments in the boundaries of adjacent sections. In the first section , for example, the 18 cells are tested in the order of 1-4-7-10-13-16-2-8-11-14-17-3-6-9-12-15-18. Fig. 4 also indicates that the cells in an uncertainty region are divided into distinct subregions according to the test order, so that each subregion contains one and only one cell. Decisions for acquisition are made whenever correlacells are collected, for tion results associated with of correlation time. As depicted in which it takes total cells forms one of Fig. 4, a collection of states in the circular state diagram of Fig. 3, is the number of states in each where subregion.
III. PERFORMANCE ANALYSIS In this section, the performance of the acquisition scheme described in Section II is analyzed in frequency-selective Rayleigh-fading channels with general multipath intensity profiles and spatial correlations. In Section III-A, the received signal model is described. The derivations of the probabilities of detection, miss-detection, and false alarm can be conducted in a similar manner, as in [4], and they are briefly summarized in Section III-B. In Section III-C, an expression for the mean acquisition time is derived using the circular state diagram of Fig. 3.
A. Received Signal Model It is assumed that a DS/CDMA signal is received without data modulation. The complex baseband equivalent of the received signal at the th antenna element may be expressed as (3) is where denotes the average total received signal power, the frequency offset between the transmitter and receiver, is the pseudonoise code waveform with duration , and is the received code phase for the th resolvable path. Without loss of generality, we assume that . Noise plus multiple-access interference, denoted as in (3), is a complex additive white Gaussian noise process with . In (3), the multiplicativeone-sided power spectral density fading channel for the th resolvable path at the th antenna ; , which is a complex Gaussian element is denoted as random process. Assuming that each path experiences indepen; may dent Rayleigh fading, the correlation function of be expressed as [4]
(4) denotes the where [ ] denotes the statistical expectation, power of the th path, [ ] denotes the Kronecker delta function and 0, otherwise), is the Doppler (defined as 1 for represents the zeroth-order Bessel function of spread, and the first kind. Assuming that the angle of arrival of the th path , , the spatial signal is uniformly distributed over [
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correlation , in (4) between the th path signals at the th and th antenna elements is calculated as [4]
between and , which are associated with the same code phase, and it can be calculated as [4]
(5)
where is the carrier wavelength. In (4), note that the power of ; is normalized so that .
(8)
B. Probabilities of Detection, Miss-Detection, and False Alarm The receiver is assumed to be chip-synchronized to the received signal. We assume that acquisition is completed if any resolvable paths, not necessarily the first path, is acof the cells. After sucquired. This implies that there exist cessful acquisition of one path, the searcher determines the rest paths within a search window [11]. Note that only the acquisition process is considered in this paper. For the nonconsecutive chips, the search with the code phase updating interval of cell associated with the th state number that includes the resolvable path can be calculated as (6) denotes the largest integer smaller than or equal to where . Thus, the state ( ) becomes an in-phase cells. Let denote the state that contains one or more cells in the th state ( ), then number of . A state associated with is an in-phase cells and cells are tested sistate, where multaneously. Clearly, the maximum number of in-phase states or . A state asis , which corresponds to the case of is an out-of-phase state, where sociated with cells are tested simultaneously. To calculate the probabilities of detection, miss-detection, and false alarm in each state, the probability density function (pdf) and cumulative distribution function (cdf) of the decision variables in (1) and (2) are required. These functions can easily be derived using the characteristic function method, and detailed procedures are well described in [4]. We briefly summarize the results in [4]. The pdf and cdf equations of a decision variable in the search stage for an cell corresponding to the th resolvable path ( cell) are given as
, and is dewhere fined as signal-to-interference ratio per chip (SIR/chip). When the same eigenvalues exist, the corresponding pdf and cdf equacell, the pdf and cdf equations can also be derived. For an tions are derived as
(9) in (2), denoted as Note that the pdf and cdf equations of and hereafter, are the same as those of with and by 1 and , respectively. the substitutions of Using the pdf and cdf equations, in the search stage, the prob, that of miss-detection , and ability of detection at the th state (s in Fig. 3) can be that of false alarm calculated as
(10) (11) (12) is the first decision threshold, and ( ) denotes the index of path associated with the th in-phase cell of the th state. Note that for out-of-phase states, since for those states. In the verification stage, only a cell selected in the search stage is for the th tested, and thus, the probability of detection can be calculated as resolvable path and that of false alarm where
(13) (7)
(14) where
, and s are where the eigenvalues of the correlation matrix of correlator outputs combined, and they are assumed to be distinct in (7). The ( , ) element of the correlation matrix is the correlation
is the second decision threshold.
C. Mean Acquisition Time The mean acquisition time of the proposed acquisition scheme may be calculated using the flow graph method in [12].
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The branch gains in the circular state diagram of Fig. 3 are expressed as
where
(15)
(16) , , and . and are, respectively, the gain of the branch connecting the state and acquisition (ACQ) state, state. In and that of the branch connecting the state and is the time required for collecting decision (15) and (16), variables to make a decision in each state, is the correlation is the penalty time due to a interval of correlators, and false alarm. From the circular state diagram of Fig. 3, the transfer function from a given initial state to the ACQ state can be calculated as where
(17) where (18)
(19) in (18) is the state-independent loop gain of the circular , , in (19) is the gain of the shortest state diagram, and state , where path from the initial state to the . Under the assumption that the initial state number is unistate numbers, the generating formly distributed over all is found as function
In (22), it should be noted that the total number of states decreases in proportion to , and it takes to collect decision variables for a decision in a state. Therefore, definitely reduces the time required to test all the cells large decreases the comin the uncertainty region. However, large , bining gain of decision variables represented by and large increases the complexity of the receiver. Note that the combining gain is reflected on the probabilities of detection, miss-detection, and false alarm in the above equations. (or ) and can decrease the Hence, appropriate choices of determines the decimean acquisition time. The parameter sion strategy, and can also be optimized to decrease the mean acquisition time. IV. NUMERICAL RESULTS
(20) The corresponding mean acquisition time may be calculated as [12] (21) which yields
(22)
In this section, the mean acquisition time performance of the proposed acquisition scheme is evaluated. The mean acquisition time of the proposed acquisition scheme is calculated using (22) with probabilities in (10)–(14). The mean acquisition time based on the conventional consecutive search is also evaluated for comparisons. The number of actual code phase uncertainties is assumed to be 1024, and is chosen as for a set of given parameters ( , , , and ), where denotes the smallest integer greater than or equal to . The spacing between adjacent antenna elements is assumed to be . For the multipath delay profile or relative delay and of multipaths, we use six-path ITU-R Pedestrian B power (PB), Vehicular A (VA), and Vehicular B (VB) channel models [13] as well as contiguous uniform (CU) model. These channel models are summarized in Table I, where we calculate the relative delays assuming that the chip rate is equal to 3.84 MHz. and angle spread of each path The mean angle of arrival are assumed to be the values in Table I. In the following results,
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TABLE I CHANNEL MODELS
Fig. 5. Comparisons between numerical and simulation results (VA channel, L , ,W , ).
=2 1=8
= 32 = 1
the penalty time is assumed to be 10 chips. Unless explicitly specified, the correlation interval is set to 256 chips, and and frequency offset , the normalized Doppler spread , are assumed to be which are normalized by the chip rate 10 and 0, respectively. To validate the performance analysis, the analytical results are compared with simulation results in Fig. 5 for the VA channel, , , , and . The decision when thresholds for the analytical results are determined such that the mean acquisition time is minimized for each condition. In the simulations, the thresholds are set to the same values as in the analysis. A close agreement between analytical and simulation results verifies that the performance analysis is correct. The following results are obtained using the analysis. Fig. 6 shows how the mean acquisition time varies with deand for the VA channel, when , cision thresholds , , , , , and SIR/chip dB. It is apparent that inappropriate choices of decision thresholds can increase the mean acquisition time several times. If decision thresholds are very small for both search and verification stages, the mean acquisition time increases steeply due to excessive false alarms. If or is greater than some value, and in Fig. 6; however, the mean acabout 20 for both quisition time is seen to be relatively insensitive to the decision
Fig. 6. Effects of decision thresholds and on mean acquisition time (VA channel, L ,M ,N , ,W , , SIR/chip dB).
= 010
=8
=2
=41=8
= 32 = 1
Fig. 7. Effects of correlation interval K on mean acquisition time (VA channel, L ,M ,N , ,W , ).
=8
=2
=4 1=8
= 32 = 1
thresholds. In the subsequent results, we have numerically determined the decision thresholds such that the mean acquisition time is minimized for each condition. Fig. 7 shows the effects of correlation interval on mean acquisition time for several values of normalized Doppler spread
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Fig. 8. Effects of code phase updating interval (L ,M ,N ,W , ).
=8
=2
=4
= 32 = 1
1 on mean acquisition time
, normalized frequency offset , and SIR/chip for the , , , , , VA channel, when . It is observed that there exists optimal choice and that minimizes the mean acquisition time for each conof increases the reliability of decision dition. An increase in variables, unless the signal component varies significantly over chips due to Doppler spread or frequency offset. However, large can incur signal energy loss in the presence of Doppler also results in spread or frequency offset [14], and large long correlation time, which possibly increases the mean acis shown to be smaller for quisition time. In Fig. 7, optimal higher SIR/chip. This is because the effects of correlation time on mean acquisition time become more substantial than those of Doppler spread and frequency offset as the SIR/chip increases. and 10 result in almost the same In Fig. 7, and SIR/chip. mean acquisition time for the given range of This indicates that the effects of Doppler spread are not signifin practical range of Doppler spread, icant in determining corresponds to as large as 384 Hz for since the chip rate of 3.84 MHz. In the presence of frequency offset ( kHz for the chip rate of 3.84 MHz), however, the signal energy loss is significant for large , and the mean acquisition time is shown to severely increase with . Note that the frequency offset can be as large as a few kilohertz in practical situations. The effects of the code phase updating interval on mean acquisition time are depicted in Fig. 8 for four different chan, , , , and . Note nels, when corresponds to the conventional consecutive search. that always provides shorter mean acquiIt is observed that , verifying the effectiveness of the nonsition time than consecutive search. Although the optimal value of depends on the multipath delay profile, a significant reduction in mean acquisition time may be achieved with an appropriate choice of . It may be reasonable to use greater than or equal to the number of paths, six in the case of Fig. 8, since the benefits of nonconsecutive search are from splitting in-phase states in the seems to state diagram. Based on the results of Fig. 8, be an appropriate choice for the six-path channels.
Fig. 9. Effects of decision parameter W and number of correlators acquisition time (VA channel, L ,M ,N , ).
=8
=2
=4 1=8
on mean
Fig. 9 shows the effects of different decision strategies deand the number of correlators on mean actermined by quisition time of the proposed acquisition scheme for the VA , , , and . As previchannel, when cells form a test state. For given and ously mentioned, , a smaller value of makes decisions to be made more frequently with a smaller number of collected decision variables. can decrease Fig. 9 indicates that an appropriate choice of the mean acquisition time to some extent. For the case of in Fig. 9, or 16 is shown to achieve significantly shorter , especially at high SIR mean acquisition time than values. Similar trends can be observed for the case of or as well. When and SIR/chip dB, for and example, the mean acquisition time for is about 30 000 and 37 000 chips, respectively. The mean acquisition time is also shown to decrease as increases. The performance improvement is more significant at high SIR values. This is because the time required to collect decision variables , and the reduction involved in a decision is proportional to of this time is more effective at high SIR values in reducing the mean acquisition time. It should be noted that is directly related to the complexity of an acquisition receiver, and thus, it should be selected with consideration on both the performance and complexity. Fig. 10 shows the effects of antenna configurations and nonconsecutive search on mean acquisition time for the CU , , and . Although channel, when provides the best performance for the nonconin Fig. 10, since is generally secutive search, we set unknown to the receiver. From the performance for different configurations of antenna elements in Fig. 10, it is found that the larger provides the shorter mean acquisition time at low provides the shorter mean SIR values, while the smaller acquisition time at high SIR values, for both schemes. This is because the effect of combining gain is more significant at low SIR values, while that of the total correlation time required to collect decision variables is more significant at high SIR values, as thoroughly investigated in [4]. As expected, the
JE et al.: ACQUISITION FOR DS/CDMA SYSTEMS WITH MULTIPLE ANTENNAS
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Fig. 10. Mean acquisition time with and without nonconsecutive search (CU , ,W , ). channel, L
Fig. 12. Mean acquisition time with and without nonconsecutive search (VA , ). channel, L , ,W
=8 1=8
= 16 = 1
Fig. 11. Mean acquisition time with and without nonconsecutive search (PB , channel, L ,W , ).
=8 1=8
= 16 = 1
nonconsecutive search is shown to provide better performance than the conventional consecutive search for all cases, and that the performance improvement is greater at high SIR values. The reason for this is that in-phase states are more scattered in the state diagram for the nonconsecutive search than for the consecutive search. At a sufficiently high SIR, the probability of detection at any in-phase state is close to unity, whereas the probabilities of miss-detection and false alarm are small enough to be negligible. In this case, the effects of scattered in-phase states are directly reflected to the mean , , and SIR/chip dB acquisition time. When in Fig. 10, the mean acquisition time for the nonconsecutive search is 10 000 chips, which is close to 1/3.5 times that of the consecutive search, 35 000 chips. At low SIR values, on the other hand, the effects of scattered in-phase states become less significant due to nonnegligible probabilities of miss-detection and false alarm. Consequently, the performance difference of the nonconsecutive search and consecutive search becomes small at low SIR values.
=8 1=8
= 32 = 1
Fig. 13. Mean acquisition time with and without nonconsecutive search (VB channel, L , ,W , ).
=8 1=8
= 32 = 1
Figs. 11–13 compare the mean acquisition time performance of the nonconsecutive and consecutive search schemes for the PB, VA, and VB channels, respectively, which have noncontiguous relative delays, as shown in Table I. Similar trends are observed for different channel models. As expected, the nonconsecutive search is shown to significantly outperform the consec, , and SIR/chip dB, utive search. When for example, the reductions of mean acquisition time for the nonconsecutive search compared with the consecutive search are found to be 36% for the PB channel, 26% for the VA channel, and 17% for the VB channel. V. CONCLUSION In this paper, a generalized acquisition scheme has been proposed for DS/CDMA systems with multiple antennas. In the proposed scheme, a generalized configuration of antennas and correlators has been considered. The nonconsecutive search has been generalized and extended to multiple antenna systems
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to exploit multipath signals in reducing mean acquisition time over frequency-selective fading channels. A hybrid decision strategy is adopted to decide an in-phase cell among the cells in the uncertainty region. The mean acquisition time performance of the proposed acquisition scheme has been analyzed in frequency-selective Rayleigh-fading channels with general multipath delay profiles and spatial correlations. It has been shown that the nonconsecutive search provides significant reduction of mean acquisition time compared with the conventional consecutive search in typical channel environments. Based on the performance evaluation of hybrid decision strategies with various parameters, we have also investigated the optimal choice of decision strategy that reduces the mean acquisition time. Furthermore, the effects of various configurations of multiple antennas and correlators, decision thresholds, and correlation interval on mean acquisition time have been investigated. REFERENCES [1] J. H. Winters, “Smart antennas for wireless systems,” IEEE Pers. Commun., vol. 5, pp. 23–27, Feb. 1998. [2] R. M. Buehrer, A. G. Kogiantis, S.-C. Liu, J.-A. Tsai, and D. Uptegrove, “Intelligent antennas for wireless communications—Uplink,” Bell Labs Tech. J., vol. 4, pp. 73–103, July/Sept. 1999. [3] R. R. Rick and L. B. Milstein, “Parallel acquisition of spread-spectrum signals with antenna diversity,” IEEE Trans. Commun., vol. 45, pp. 903–905, Aug. 1997. [4] O.-S. Shin and K. B. Lee, “Use of multiple antennas for DS/CDMA code acquisition,” IEEE Trans. Wireless Commun., vol. 2, pp. 424–430, May 2003. [5] , “Utilization of multipaths for spread-spectrum code acquisition in frequency-selective Rayleigh fading channels,” IEEE Trans. Commun., vol. 49, pp. 734–743, Apr. 2001. [6] L.-L. Yang and L. Hanzo, “Serial acquisition of DS-CDMA signals in multipath fading mobile channels,” IEEE Trans. Veh. Technol., vol. 50, pp. 617–628, Mar. 2001. [7] R. R. Rick and L. B. Milstein, “Optimal decision strategies for acquisition of spread-spectrum signals in frequency-selective fading channels,” IEEE Trans. Commun., vol. 46, pp. 684–694, May 1998. [8] M. K. Simon, J. K. Omura, R. A. Scholtz, and B. K. Levitt, Spread Spectrum Communications Handbook. New York: McGraw-Hill, 1994. [9] G. E. Corazza, “On the MAX/TC criterion for code acquisition and its application to DS-SSMA systems,” IEEE Trans. Commun., vol. 44, pp. 1173–1182, Sept. 1996. [10] W. Zhuang, “Noncoherent hybrid parallel PN code acquisition for CDMA mobile communications,” IEEE Trans. Veh. Technol., vol. 45, pp. 643–656, Nov. 1996. [11] S. Glisic and M. D. Katz, “Modeling of the code acquisition process for rake receivers in CDMA wireless networks with multipath and transmitter diversity,” IEEE J. Select. Areas Commun., vol. 19, pp. 21–32, Jan. 2001. [12] A. Polydoros and C. L. Weber, “A unified approach to serial search spread-spectrum code acquisition—Part I: General theory,” IEEE Trans. Commun., vol. COM-32, pp. 542–549, May 1984.
[13] “Guidelines for evaluation of radio transmission technologies (RTT) for IMT-2000,” International Telecommunications Union (ITU), Rec. ITU-R M.1225, 1997. [14] E. Sourour and S. C. Gupta, “Direct-sequence spread-spectrum parallel acquisition in a fading mobile channel,” IEEE Trans. Commun., vol. 38, pp. 992–998, July 1990.
Hui Won Je (S’01) received the B.S. degree from Seoul National University, Seoul, Korea, in 2001. He is currently working toward the Ph.D. degree in electrical engineering and computer science at Seoul National University. His current research interests include synchronization, multiple access scheme, and radio resource management for next-generation mobile communication systems.
Oh-Soon Shin (S’00) received the B.S. and M.S. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1998 and 2000, respectively. He is currently working toward the Ph.D. degree in electrical engineering and computer science at Seoul National University. His current research interests include mobile communications, spread spectrum communication systems, synchronization, radio resource management, and signal processing for communications. Mr. Shin received the Best Paper Award from the CDMA International Conference 2000 (CIC 2000).
Kwang Bok (Ed) Lee (M’90) received the B.A.Sc. and M.Eng. degrees from the University of Toronto, Toronto, Ontario, Canada, in 1982 and 1986, respectively, and the Ph.D. degree from McMaster University, Hamilton, Ontario, Canada, in 1990. He was with Motorola Canada from 1982 to 1985, and Motorola USA from 1990 to 1996 as a Senior Staff Engineer. At Motorola, he was involved in the research and development of wireless communication systems. He was with Bell-Northern Research, Canada, from 1989 to 1990. In March 1996, he joined the School of Electrical Engineering, Seoul National University, Seoul, Korea. Currently he is an Associate Professor in the School of Electrical Engineering. He was a Vice Chair of the School of Electrical Engineering from 2000 to 2002. He has been serving as a Consultant to a number of wireless industries. His research interests include mobile communications, communication theories, spread spectrum, and signal processing. He holds ten U.S. patents and two Korean patents, and has a number of patents pending. Dr. Lee has been an Editor of the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, WIRELESS SERIES in 2001, and now he is the Editor of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. He received the Best Paper Award from the CDMA International Conference 2000 (CIC 2000).
