CDMA-PPM for UWB Impulse Radio
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 2, MARCH 2008
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CDMA-PPM for UWB Impulse Radio S. H. Song, Member, IEEE, and Q. T. Zhang, Senior Member, IEEE
Abstract—Pulse-position modulation (PPM) is widely used in impulse radio (IR) due to the simplicity of its transceiver structure and signal detection. It is usually used along with time hopping (TH) to support multiple users in IR and to take the advantage of a small collision probability among simultaneous users. This advantage, however, is achieved at the cost of a wider frame length and the concentration of each user’s frame signal energy on a single pulse. Thus, it is likely that the TH-PPM information can totally be damaged whenever a collision occurs. In this paper, we take a different philosophy to evenly distribute the signal energy over the entire frame, ending up with a novel ultrawideband (UWB) IR multiple-access scheme, which is called code division multiple access (CDMA)-PPM, for low-rate wireless-personalarea-network application. The new scheme is superior to the conventional one in terms of error performance, as evidenced by theoretical analysis and simulations. We also examine the power spectrum of CDMA-PPM signals, which is found to be comparable to its TH-PPM counterpart. Index Terms—Code division multiple access pulse-position modulation (CDMA-PPM), impulse radio, multiple access, timehopping PPM (TH-PPM).
I. I NTRODUCTION
I
MPULSE radio (IR) is one of the two short-listed proposals for the IEEE 802.15.4a low-rate communication application. The idea of transmitting digital information by using ultrashort impulse waves was first presented in [1], where the term IR was coined. In [1], the authors stated that “amplitude and frequency/phase modulations are unsuitable for this particular form of impulse communications; the only suitable choice is pulse position modulation.” Subsequently, the pioneering work of Win [2] shows how the IR works with time-hopping pulseposition modulation (TH-PPM). Recently, a multiple-access scheme called direct-sequence ultrawideband (DS-UWB) is proposed for IEEE 802.15.3a high-rate communication application. It resembles the conventional DS code division multiple access (DS-CDMA) system; the only difference is that data modulation is implemented on the polarity of an ultrashort pulse. Although it is not as power efficient as phase modulation, PPM has a simpler transceiver structure and enables noncoherent detection [3], making it very suitable for low-rate and lowcomplexity application. In this paper, we will introduce a new multiple-access scheme for PPM as a possible candidate for the IEEE 502.15.4a low-rate communication application.
Manuscript received March 7, 2005; revised January 7, 2006, October 7, 2006, and May 4, 2007. This work was supported by the City University of Hong Kong under Project 7001856. The review of this paper was coordinated by Prof. R. Qiu. The authors are with the Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TVT.2007.905260
Conventional spread-spectrum (SS) techniques are usually used alongside digital modulation based on phase- (PSK) or frequency-shift keying (FSK). On the contrary, UWB-IR usually employs, instead, PPM to take the advantage of a simple system structure and possible noncoherent detection. Therefore, when extending the concept of SS to allow multiple users to share a UWB channel, one must adopt a different strategy for multiple access. A natural way to achieve this goal is the integration of m-ary PPM with TH, resulting in the wellknown TH-PPM scheme. The TH-PPM, in essence, resembles the classical fast frequency hoping (FFH) in philosophy but is performed in the time domain. In TH-PPM, a symbol interval is partitioned into a number of frames, and an information pulse of each user is repeatedly transmitted over all these frames. Pulse position is randomly hopped over these frames to form the TH pattern under the control of the signature sequence assigned to that user. Accordingly, the TH-PPM can be regarded as the extension of FFH. The difference is that the former is used in the time domain with a seamless combination with PPM, whereas the latter is used in the frequency domain with a seamless integration with FSK. However, we note that, in TH-PPM, the frame duration is much wider than the minimum requirement to accommodate m-PPM in order to leave a room for random TH. The consequence is the reduction of the number of frames in a symbol, thus lowering the diversity gain. Furthermore, the transmitted symbol energy in a TH-PPM system is highly concentrated on a few pulses. Thus, once a pulse collided with that of other users, the error performance will severely drop. Alternatively, one may extend SS techniques to a PPM system along the direction of CDMA. This idea was first adopted in optical communications, ending up with the so-called PPMCDMA system. In PPM-CDMA, each user’s information pulse is first spread by a particular signature sequence before being applied to PPM [4], as shown in Fig. 1(c). The signature sequences are optically implemented through ON–OFF signaling and have a very low weight to prevent user collision. The distinction between users relies on many low weight signature sequences, with a length that is equal to half of the symbol duration. Thus, for a given system bandwidth, the unnecessary reduction in signature length will significantly reduce the number of users that can be supported by the system. This may not be a problem for an optical communication system due to its huge frequency bandwidth but is definitely a problem for wireless UWB communications. A natural question follows: Can we directly spread a user’s PPM symbols so that the transmitted energy can evenly be distributed over the entire SS symbol duration to fully exploit the processing gain, on one hand, and to avoid users’ collisions, as much as possible, on the other hand? The resulting system is CDMA-PPM, which will be addressed in this paper.
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Fig. 1. Examples of the CDMA-PPM, TH-PPM, and PPM-CDMA systems with rectangular pulses. (a) CDMA-PPM. (b) TH-PPM. (c) PPM-CDMA.
The remainder of this paper is organized as follows. The new scheme is described in Section II, followed by the derivation of its error performance and power spectrum in Section III. The performance comparison and discussion are presented in Section IV. The implementation issues of the CDMA-PPM system are briefly addressed in Section V, followed by the conclusion in Section VI.
II. S YSTEM M ODEL To introduce the CDMA-PPM scheme, let us briefly review the TH-PPM system. A typical TH-PPM UWB signal for user k is expressed as (k) st (t)
=
∞ Eb w t − jTft − ckj Tc − dkj/Ns δ Ns j=0
(1)
where Tft and Tc denote the frame length and chip width for TH, respectively, and δ is the PPM modulation depth. The TH code for user k is denoted by {ckj }, where each of its entry is assumed to take on an integer value in the range of [0, Nh − 1], where Nh = Tft /Tc . The j/Ns th information bit from user k is signified by dkj/Ns , where x denotes the largest integer less than x. The basic waveform w(t) is scaled to have a unit norm so that Eb represents the bit energy. Ns is the number of frames per symbol. Multiple access is achieved by assigning each user a particular TH sequence, as
shown in Fig. 1(b), where w(t) is assumed, for convenience, to be a rectangular pulse with a duration that is equal to half of the chip width Tc . All signal energy in a frame is solely transmitted over a single chip interval, and the location of this selected chip changes from frame to frame under the control of a preassigned TH sequence forming a user-specific TH pattern. The pulse position within the transmission chip only depends on the information symbol. With a sufficiently large Nh , the possibility that different users will collide within a frame should be small. However, once such collision occurs, the information of the intended user will severely be damaged. It would therefore be wise to evenly distribute the transmitted energy over all chips within a frame so that the risk of fatal collision can be reduced. The resulting scheme is CDMA-PPM. In the CDMA-PPM scheme that we propose, the spreading sequence for user k ({akm , m = 0, 1, . . . , M − 1}) is used along with its information symbol dkm to generate a new positioninformation sequence for PPM of the basic waveform w(t). Hence, the transmitted signal for user k can be written as s(k) c (t)
=
∞ Eb w t − jTfc − dkj/M ⊕ akmod(j,M ) δ M j=0
(2) where Tfc is the chip duration for the CDMA system and is analogous to the frame length Tft of the TH system, and ⊕ represents the modulo-2 addition. This modulo-2 addition
SONG AND ZHANG: CDMA-PPM FOR UWB IMPULSE RADIO
randomizes the pulse location over each frame, thereby implementing the idea of evenly distributing the transmitted energy in the time domain. The CDMA-PPM signal is shown in Fig. 1(a). In a CDMA-PPM system, it is true that the likelihood for different users to collide over a single chip can increase. However, a partial damage over some chips has no fatal influence on the overall multiple-access performance. At this point, it is interesting to compare CDMA-PPM with the conventional DS-CDMA scheme. In DS-CDMA, the polarity of an information waveform varies over each chip interval through a simple multiplication with a specific spreading sequence. It is clear from Fig. 1 that the CDMA-PPM resembles its DS-CDMA counterpart in that both systems spread an information symbol as a binary sequence. The difference lies in the way to generate these sequences and the way to represent each bit over a chip interval. A bit over a chip is represented by a bipolar waveform in DS-CDMA but is represented by PPM in CDMA-PPM. In CDMA-PPM, spreading is implemented by using the signature sequence {ak0 , ak1 , . . . , akM −1 } to generate a new random position sequence, through the relation {xj } = {dkj/M ⊕ akmod(j,M ) }, for the PPM of w(t). The difference between TH-PPM and CDMA-PPM lies in the multiple-access scheme, while CDMA-PPM differs from DS-CDMA by the data modulation method. Data modulation is usually chosen according to different application environments. For example, PSK is power efficient and is utilized for high-rate application, while PPM is widely utilized in the case when phase or amplitude information is difficult to carry, such as optical communication. Other advantages of PPM include its simple transceiver structure and the possible noncoherent detection. Our motivation in this paper is to combine the good multiple-access performance of the CDMA system with the possible simple transceiver structure of PPM for the IEEE 802.15.4a low-rate application.
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pseudonoise (PN) SS sequences for CDMA-PPM and the PN TH codes for TH-PPM will be considered for fair comparison. 1) Time-Hopping PPM (TH-PPM): The BER performance of the TH-PPM system with a matched filter receiver has been derived [6], [7], and we briefly introduce it here for comparison purposes. The received signal of the TH-PPM with Nu asynchronous users and freeing from a near-far problem can be written as rt (t) =
(1)
By assuming that τ1 = 0 and cj with template
Various basic waveforms of w(t) have been proposed for UWB pulse shaping [5] to meet the requirements set by the Federal Communications Council (FCC) and to avoid a directcurrent component. Since the rectangular pulse can provide a good measure of the relative performance between CDMAPPM and TH-PPM, we follow Hamdi and Gu [6] by utilizing the rectangular impulse and orthogonal PPM for a theoretical comparison of the two systems. The analysis can easily be extended to other waveforms and nonorthogonal PPM. The
(3)
= 0, the correlation detector
vj (t) = w(t − jTft ) − w(t − jTft − δ)
(4)
produces the decision variable V =
Ns
r
(Vsj + VIj + Vnj )
(5)
j=1
where the interference VIj comes from Nu − 1 users VIj =
Nu
. VIjk
(6)
k=2
The components inside the summation on the last line can further be represented by the following: jTft
V
Ijk
=
st (t − τk )vj (t)dt (k)
(j−1)Tft
=
III. P ERFORMANCE A NALYSIS
A. BER Analysis for Matched Filter Receiver
(k)
st (t − τk ) + n(t).
k=1
In this section, we will investigate the bit-error rate (BER) performance of the TH-PPM and CDMA-PPM with the matched filter receiver in additive white Gaussian noise (AWGN) channels. The performance of a minimum mean square error (MMSE) detector in both AWGN and frequencyselective fading channels will be analyzed in the next section. Besides BER performance, we also show the power spectral density (PSD) analysis.
Nu
jTft
Eb Ns
w(t − τd )vj (t)dt
(7)
(j−1)Tft
where τd = Mod(τk + ckj Tc + dkj/Ns δ, Tft ) is uniformly distributed in [0, Tft ). We can use the Gaussian approximation and determine the , obtaining variance of VIjk σV2 I = E VI2 jk
jk
=
Eb E Ns
jTft
2 w(t − τd )vj (t)dt
(j−1)Tft
=
Eb . 2Nh Ns
(8)
Thus, for a system with spreading factor Ns , the variance of the total interference is given by the following: σI2 = (Nu − 1)Ns σV2 I = jk
(Nu − 1)Eb 2Nh
(9)
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which implies that the signal-to-interference plus noise ratio (SINR) is equal to (Ns Vsj )2
γt =
2Ns σn2 + σ 2I
=
1 2 2σn Eb
+
(Nu −1) 2Nh Ns
(10)
in the same form as that of [6, eq. (26)]. 2) Code Division Multiple Access PPM (CDMA-PPM): Consider an asynchronous CDMA-PPM system with Nu active users and freeing from a near-far problem. Its received signal is given by the following:
If bit dm = 1 is sent, then an erroneous decision is made if Vr < 0. To determine error probability, we need to characterize the three terms on the right side of (14). Since w(t) is a pulse √ of unit energy, it follows some manipulations, where Vs = Eb M . It also follows that Vn is a zero-mean Gaussian variable with variance 2M σn2 . The interference term VI remains to be characterized. Since different users are asynchronous and independent, we obtain
VI =
Nu
VIk
(16)
k=2
(t − τ1 ) + rc (t) = s(1) c Sc (t)
Nu k=2
s(k) c (t − τk ) + n(t)
(11)
where
M Tfc
Ic (t)
where τk , k = 1, . . . , Nu denotes the time delay of user k, and n(t) is the AWGN of zero mean and variance σn2 . Component (1) sc (t) is the desired signal, which is denoted by Sc (t) for convenience, whereas the remaining Nu − 1 users’ signals are treated as interference Ic (t). Without loss of generality, assume that τ1 = 0, and hence, τk , k = 2, . . . , Nu represents the time delays of other users relative to the desired one. We further assume that the receiver is perfectly synchronized to the desired user and employs a correlation detector with a chip correlation template (1)
vj (t) = (−1)aj [w(t − jTfc ) − w(t − jTfc − δ)] .
(12)
The M -bit symbol correlation template can thus be written as v(t) =
M
vj (t) =
j=0
M j=0
(13) which, when correlated with the received signal, produces the decision variable (14)
The three terms in this expression are signal, interference, and noise components at the correlator’s output, respectively, which are given by the following: M Tfc
Vs =
For further simplification, we adopt the method of Gaussian approximation. To this end, we need to determine the variance of the zero-mean variable VIk , k = 2, . . . , Nu
σV2 I
k
2 M Tfc = E VI2k = E s(k) (18) c (t − τk )v(t)dt 0
where the expectation E[·] is taken over all random sources. We first take the ensemble average over random delay τk , which is uniformly distributed over the range [0, Tfc ), yielding 1 Eτk [VI2k ] = Tfc
T 2 Tfc M fc dτk . s(k) c (t − τk )v(t)dt 0
=M
pa = Tfc w(t) [w(t) − w(t − δ)] dt 0
Ic (t)v(t)dt 0
n(t)v(t)dt. 0
a M −a 1 1 . 2 2
(20)
2 1 Tfc . Pa (t−τ )v(t)dt dτ s(k) E[VI2k ] = k k a Tfc a=0 M
M Tfc
Vn =
M a
Without loss of generality, we assume that all zero sequences are allocated to the desired user, and we let sa (t) denote the signal associated with PN sequence Ca , which has a zeros and (M − a) ones. We have
M Tfc
VI =
0
0
Eb M
(19)
Next, we average (19) over the interference caused by different PN sequences. We assume that PN sequences (each of length M ) are used as signature sequences for users and that sequence Cu is allocated to the desired user. Over the period of Cu , the interfering users’ signature sequences can have different patterns. Let Ca denote an interfering sequence that has a positions identical to Cu while having (M − a) positions that are different. Then, Ca occurs with probability pa
Sc (t)v(t)dt
(17)
0
(1)
(−1)aj [w(t−jTfc )−w(t−jTfc −δ)]
Vr = Vs + VI + Vn .
s(k) c (t − τk )v(t)dt.
VIk =
(15)
0
(21)
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We should also take into account the cases when τk separately falls into [0, Tfc /2) and [Tfc /2, Tfc ); thus M P a Eb E VI2k = T M a=0 fc # Tfc /2 4τk a 1− × Tfc
with FCC regulations. It is therefore interesting to compare the power spectra of TH-PPM and CDMA-PPM UWB systems. We follow the method used in [10] to determine the PSD Sr (f ), as defined by the following: E |RT (f )|2 T →∞ T
(27)
r(t) exp(−j2πf t)dt
(28)
Sr (f ) = lim where
0
+ (M − a)
T
$2 4τk −1 dτk Tfc
RT (f ) = 0
Tfc # 4τk a + −3 Tfc Tfc /2
+ (M − a) 3 −
4τk Tfc
$2
is the truncated Fourier transform of the random process r(t). For analytical simplicity, we assume that the transmitted pulse w(t) is rectangular in shape. 1) TH-PPM System: The TH-PPM signal with M asynchronous users, over K frames, can be represented as
dτk r(t) = (22)
which can further be simplified as [8] σV2 I = E VI2k
M K−1
At w(t − τu − nTft − cun Tc − bun δ)
(29)
u=1 n=0
where At is the pulse amplitude, τu is the delay for user u, and w(t) is the transmitted pulse. The truncated Fourier transform is then given by the following:
k
=
M M Eb M 1 (2a − M )2 3M a 2 a=0
=
Eb . 3
KT ft
RT Tft (f ) =
r(t) exp(−j2πf t)dt 0
(23) = At W (f )
The variance of the total interference is then given by the following: σI2 = (Nu − 1)σV2 I = k
(Nu − 1)Eb . 3
1 2 2σn Eb
+
(Nu −1) 3M
where the bit error probability can be determined as 2 ∞ 1 x √ exp − Pe = Q ( γc ) = dx 2π √γc 2
u=1 n=0
× exp (−j2πf (τu + nTft + cun Tc + bun δ)) (30)
(24)
The Gaussian approximation allows us to determine the SINR, yielding Vs2 = γc = 2M σn2 + σI2
M K−1
where W (f ) is the Fourier transform of waveform w(t). As such |RT Tft (f )|2
(25) = [At W (f )]2
M K−1 M K−1 u=1 v=1 n=0 m=0
× exp (−j2πf ((τu − τv ) + (n − m)Tft + (cun − cvm )Tc + (bun − bvm )δ))
(26)
(31) which is a function of the number of active users Nu . The expression in (25) is similar to the DS-CDMA system (17) [9], except that the noise power is doubled due to the use of orthogonal PPM. B. PSD Analysis The power spectrum is one of the important characteristics of UWB signals since all UWB applications must comply
which, after taking expectation and simplifying, results in E |RT Tft (f )|2 = M [At W (f )]2 {K + K(M − 1)E1 E2 E3 + [(M − 1)E1 + 1] E2 E3 E4 } (32)
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with symbols E defined by the following:
is also taken into consideration, the situation is somewhat different. The locations of discrete spectral lines are dictated by the average signal period. In a TH-PPM system, it is the chip width Tc that determines the average fundamental period. This physical intuition is confirmed in (34). 2) Code Division Multiple Access PPM (CDMA-PPM): For a CDMA-PPM signal, there are no TH codes, and the frame length is much shorter. The K-frame signal for M asynchronous users is
E1 = Eu=v [exp (−j2πf (τu − τv ))] = sinc2 (f Tft ) E2 = En=m [exp (−j2πf (cn − cm )Tc )] =
sin2 (πf Nh Tc ) Nh2 sin2 (πf Tc )
E3 = En=m [exp (−j2πf (bn − bm )δ)] sin2 (πf 2δ) = 4 sin2 (πf δ) E4 =
K−1
r(t) =
exp (−j2πf (n − m)Tft )
sin2 (πf KTft ) − K. sin2 (πf Tft )
(33)
(1 − E2 E3 ) + M [At W (f )]2 Tft +∞ (M − 1)E1 + 1 n × E u f − (34) 3 0 Tft2 Tc n=−∞
SrTH (f ) = M [At W (f )]2
where u0 (f ) is the Dirac delta function. The line spectrum in the second term of (34) is an asymptotic result as K → ∞ after invoking the result due to Robert [10]
sin πf KT sin πf T
2
(37)
where Ac and Tfc are the pulse amplitude and frame length, with other parameters the same as the TH-PPM system. The truncated Fourier transform for the received signal is
It is clear that E1 accounts for the asynchronous arrival of M users’ signals, E2 represents the influence of random TH codes, and E3 comes from the random data modulation. We can use the fact that Tft = Nh Tc to further simplify the aforementioned expressions for E2 and E4 , and we insert the results and (32) into (27) to obtain the following asymptotic PSD expression for multiuser TH-PPM received signals:
1 lim K→∞ KT
Ac w(t − τu − nTfc − bun δ)
u=1 n=0
n,m=0 n=m
=
M K−1
+∞ n 1 . (35) = 2 u0 f − T n=−∞ T
Although it is strictly valid only for an infinite K, (35) provides a good approximation for K of a large value, and the same is true for (34). For the orthogonal-PPM case of practical importance, we have Tc = 2δ. Thus, E3 can further be simplified with E2 and E4 , and the aforementioned PSD expression can be simplified as (1 − E2 E3 ) + M [At W (f )]2 Tft +∞ (M − 1)E1 + 1 2n × u0 f − . (36) Tft2 Tc n=−∞
SrTH (f ) = M [At W (f )]2
The PSD in (34) is composed of two parts, with the first one accounting for the continuous component and the second one representing the discrete spectral lines. In [13], it is shown that the line spectrum spacing for framed TH systems is determined by the TH frame length. If the influence of PPM modulation
RT Tfc(f ) = Ac W(f )
M K−1
exp(−j2πf (τu +nTfc +bun δ)) .
u=1 n=0
Then |RT Tfc (f )|2 = [Ac W (f )]2
M K−1 M K−1 u=1 v=1 n=0 m=0
× exp (−j2πf ((τu − τv ) +(n − m)Tfc + (bun − bvm )δ)) and E |RT Tfc (f )|2 = M [Ac W (f )]2 {K + K(M − 1)E1 E3 + [(M − 1)E1 + 1] E3 E4 }
(38)
where E1 and E4 are the counterparts of E1 and E4 , with Tft replaced by Tfc . The PSD for the multiuser CDMA-PPM received signal is (1 − E3 ) + M [Ac W (f )]2 Tfc +∞ (M − 1)E1 + 1 n × E u f − . 3 0 Tfc2 Tfc n=−∞
SrCDMA (f ) = M [Ac W (f )]2
(39) In case of orthogonal PPM, the result is (1 − E3 ) + M [Ac W (f )]2 Tfc +∞ (M − 1)E1 + 1 2n × u f − . 0 Tfc2 Tfc n=−∞
SrCDMA (f ) = M [Ac W (f )]2
IV. R ESULTS AND D ISCUSSION A. BER Performance Comparison 1) Matched Filter: Let us compare (25) and (10) to see the difference between the two systems. By assuming the same
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Fig. 2. Performance comparison based on Gaussian approximation and simulation.
Fig. 3. Performance comparison utilizing Gaussian monocycle.
the system performance comparison, and the results are shown in Fig. 3. Specifically, the pulse waveform that we use is
TABLE I SYSTEM SETTING FOR THE TH-PPM AND CDMA-PPM
w
transmission rate, for the two systems, we can relate their spreading factors to obtain M = Nh N s
(40)
which, when inserted into (25), leads to γc =
1 2 2σn Eb
+
(Nu −1) 3Nh Ns
.
(41)
By comparing (41) with (10), we find that multiple-access interference is suppressed in the CDMA-PPM system. The TH system achieves a good anticollision performance at the cost of sacrificing its processing gain. The CDMA-PPM system, however, has the capability of maintaining the good tradeoff between the two performance parameters. Theoretical bit-error performance is shown in Fig. 2, where the simulation results are also included for comparison. The system parameters that are used to obtain Fig. 2 are shown in Table I. It is confirmed that the BER of the CDMA-PPM is superior compared to its TH-PPM counterpart. Recall that the method of the Gaussian approximation, although it is good for the CDMA system, is proven [6], [7] to underestimate the BER performance of the TH systems. This phenomenon can easily be seen in Fig. 2 when a small number of users are active. To exclude the possibility that pulse form may influence system performance, we, instead, use a Gaussian monocycle for
t τp
#
= 1 − 4π
t τp
2 $
# exp −2π
t τp
2 $ (42)
which is the same as the one that is used in [7]. Here, τp is a time normalization factor, and the remaining parameter settings, such as the optimum modulation depth for the nonorthogonal PPM, are exactly the same as [7], with Ns = 2. The results again show that with Gaussian pulse shaping, the CDMAPPM outperforms the TH-PPM. It should also be pointed out that since the nonorthogonal PPM is utilized for the Gaussian monocycle, a better performance is achieved, as shown by comparison in Figs. 2 and 3. 2) MMSE Detector: It is shown that low-complexity multiuser detectors can greatly improve the BER performance of the TH-IR system [11]. Thus, it is valuable to compare the performance of the CDMA-PPM and TH-PPM systems with multiuser detection. The general MMSE receiver for the detection of the symbol transmitted by the kth user is of the form [12] ˆbk = sgn
% T & 1 (S S + σn2 A−2 )−1 (S)T r k A(k, k)
(43)
where r is the received symbol; A is a diagonal matrix, with its diagonal entry corresponding to the power of each user; and the collum of S is the user signature sequence for both the CDMA and TH systems. From this point of view, the two systems only differ in the utilized spread sequence. Fig. 4 shows the performance comparison of the synchronous TH-PPM and CDMA-PPM systems using a Gaussian monocycle with matched filter and MMSE receiver over the AWGN channels. The system parameters are set as Ns = 2, Nh = 16, and Nu = 6. It is observed that, in a high SNR environment, the performance of the MMSE receiver for the TH system deteriorates with an error floor. This is because, as
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Fig. 4. Performance comparison of matched filter and MMSE receivers for the TH-PPM and CDMA-PPM.
the SNR goes to infinity, the MMSE linear detector converges to the decorrelating detector [12], whose performance directly depends on (ST S)−1 . In this sense, the performance difference between TH and CDMA lies on the correlation matrix of their respective spread sequences. Being different from the CDMA spread sequence, the TH sequence has an extremely low weight; thus, the correlation matrix is not diagonally dominant, which may cause the matrix to become singular. For example, consider the extreme case of Ns = 1. Once a collision occurs, the correlation matrix is singular, with |ST S| = 0, and the MMSE receiver cannot work. Thus, for the MMSE detection of the TH signal, it is better to choose a larger Ns . 3) Performance Comparison Over Multipath Channels: Multipath propagation is a critical problem that is faced by UWB high-rate communications such as the 802.15.3a application. Fortunately, the proposed scheme is for low-rate communications with about several hundreds of chips per second [14]. Thus, orthogonal PPM is enough to support the load, even for the CM4 case [15]. We show in Fig. 5 the performance comparison of the TH-PPM and CDMA-PPM systems using a Gaussian monocycle with matched filter and MMSE receivers over lognormal slow-fading channels [15]. The system parameters are set as Ns = 2, Nh = 16, and Nu = 6, with L = 3 paths. We have observed that the CDMA-PPM has an obvious advantage at a high SNR environment. With orthogonal PPM, multipath fading will no longer introduce ISI but only influence the averaged SNR. It is, thus, interesting to see how multipath channels influence performance. Fig. 6 shows the performance comparison of the TH-PPM and CDMA-PPM systems using a Gaussian monocycle over lognormal multipath channels with different number of paths (L = 3 and 5 ), where the total channel gain is normalized. The diversity gain with a larger number of paths, as shown in Fig. 6, is obtained at the cost of the receiver’s complexity and low data rate. 4) Comparison of Possible Combinations: Besides the THPPM and CDMA-PPM, there are other possible combinations of data modulation (PPM and BPSK) and multiple-access
Fig. 5. Performance comparison between the TH-PPM and CDMA-PPM over slow lognormal fading.
Fig. 6. Performance comparison between the TH-PPM and CDMA-PPM over slow lognormal fading with different number of paths.
schemes (TH and CDMA). Throughout this paper, we have focused on the comparison of the TH-PPM with CDMA-PPM because they are utilizing the same data modulation PPM, which is suitable for low-rate and low-complexity UWB-IR applications. For a complete comparison, we then investigate the performance of all the possible combinations and assume that the same type of random TH and CDMA spread sequences are utilized. The BER performance comparison for these systems over the AWGN channels with matched filter receivers can be seen by comparing (41) and (10). The advantage of the CDMA system over TH comes from the second term in the denominator, which is SIR, whereas the difference between BPSK and PPM lies in the first SNR term. In Fig. 7, the performance comparison of the MMSE receiver for synchronous TH-PPM/TH-BPSK/CDMAPPM/DS-UWB systems using a Gaussian monocycle in slow multipath lognormal channels, with L = 3 paths, Ns = 2,
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Fig. 7. Performance comparison of TH-PPM/CDMA-PPM/TH-BPSK/ DS-UWB over lognormal fading.
Fig. 8. PSD comparison between the TH-PPM and CDMA-PPM systems by simulation.
Nh = 16, and Nu = 6, is illustrated. We have observed that, for the same data modulation, CDMA has an obvious advantage over the TH system at high SNR, whereas for the same multiple-access scheme, BPSK has a clear advantage over PPM. The gain of BPSK over PPM comes from the fact that, in PPM, double noise energy is collected. However, position modulation has a simple transceiver structure, and it enables the noncoherent detection [3] for low-complexity and lowrate application. The performance comparison of the TH-PPM and CDMA-PPM systems with a noncoherent receiver requires further investigation.
as opposed to
B. PSD Comparison As shown in (34) and (40), the spectra for the CDMA-PPM and TH-PPM have a similar functional form. The difference in the CDMA-PPM expression is the replacement of E2 E3 in its TH-PPM counterpart with E3 and the replacement of At and Tft with Ac and Tfc , respectively. For a fair comparison, we must impose a constraint wherein the two systems, on average, have identical transmitted energy over the same time period or, equivalently, the same average power. For simplicity and without loss of generality, we assume that the rectangular pulses used in the two systems are of the same time duration, e.g., Tp . Then, the identical average power requirement implies that A2t Tp /Tft = A2c Tp /Tfc , which leads to A2t A2 = c. Tft Tfc
(44)
Insert this relation into (40) and (34) and simplify. The result is (1 − E3 ) + M [At W (f )]2 Nh Tft +∞ (M − 1)E1 + 1 n × E3 u0 f − Tft2 Tc n=−∞
(1 − E2 E3 ) + M [At W (f )]2 Tft +∞ (M − 1)E1 + 1 n × E u f − . 3 0 Tft2 Tc n=−∞
SrTH (f ) = M [At W (f )]2
Recall that 0 ≤ E2 ≤ 1, as indicated in (33). We can therefore assert that the CDMA-PPM has a smaller continuous spectral component than its TH-PPM counterpart. It is also observed that the line spectra of the two systems have the same frequency locations but certainly different power. For orthogonal PPM with rectangular pulse shaping of length Tc /2, the continuous spectrum W (f ) has its nulls located at multiples of 2/Tc , except for f = 0. The spectral lines are located at multiples of 2/Tc , falling into the troughs of the continuous spectrum and thus being cancelled. In this sense, the CDMA-PPM system has a slight advantage over the TH-PPM system allowing for more line spectrum components to be cancelled by an appropriate pulse design. Simulation results with ten active users are shown in Fig. 8, where the binary orthogonal PPM is used with a rectangular pulse of width Tc /2 = 1 ns. It is clear that the pulseshape design is an important issue. An appropriate design can ensure that the continuous spectral component W (f ) meets the FCC’s PSD specification on UWB signals on one hand and provides room for the cancellation of the line spectral component on the other hand. If the polarity randomization method is utilized, no spectral lines will occur, and the two systems will have the same PSD. Under this circumstance, it is better to utilize a noncoherent receiver, which can simply disregard the randomization process and take advantage of the simple receiver structure brought by PPM.
SrCDMA (f ) = M [At W (f )]2
V. S YSTEM I MPLEMENTATION Besides its good performance, the CDMA-PPM system has several advantages in implementation. The first advantage is
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its ease of synchronization. The good autocorrelation structure of the SS code makes it easier to keep track of the signal. Usually, partial correlation suffices for synchronization. On the contrary, searching for the correlation peak of the TH code is more complicated, which normally consists of both frame and TH code synchronization. Second, the CDMA-PPM allows for an easy system expansion. When the system is nearly saturated, the CDMA-PPM system simply needs the addition of spread code length. This is in contrast with the TH-PPM system, which often requires the reconstruction of the frame structure (Tft , Th ). At the same time, we also want to emphasize the advantages of TH system, including the reduced near-far effects, high peak power that might lower the requirements on receiver sensitivity, etc. Based on the aforementioned analysis and performance comparison, we have observed that all these schemes (TH-PPM/TH-BPSK/CDMA-PPM/DS-UWB) have their own advantage and suitable application environment. The DSUWB is a promising candidate for high-rate communications, whereas the CDMA-PPM and TH-PPM have their future in low-complexity and low-rate communications and ranging applications. Besides these systems with single multiple-access schemes, some combined TH-CDMA systems have recently been reported [16], [17]. VI. C ONCLUSION In this paper, a CDMA-PPM multiple-access scheme is proposed as a possible candidate for the IEEE 802.15.4a lowrate communication application. The superior multiple-access performance of the new scheme over TH-PPM with a matched filter and MMSE detectors was theoretically verified and simulated. We have also shown that the two systems have nearly the same PSD characteristics. Furthermore, compared to the TH-PPM, the CDMA-PPM system is easier to implement. R EFERENCES [1] P. Withington, II and L. W. Fullerton, “An impulse radio communications system,” in Proc. Int. Conf. Ultra-Wide Band, Short-Pulse Electromagn., Brooklyn, NY, Oct. 1992, pp. 113–120. [2] M. Z. Win and R. A. Scholtz, “Impulse radio: How it works,” IEEE Commun. Lett., vol. 2, no. 2, pp. 36–38, Feb. 1998. [3] M. K. Oh, B. Jung, R. Harjani, and D. J. Park, “A new noncoherent UWB impulse radio receiver,” IEEE Commun. Lett., vol. 9, no. 2, pp. 151–153, Feb. 2005. [4] H. M. H. Shalaby, “Maximum achievable number of users in optical PPM-CDMA local area networks,” J. Lightw. Technol., vol. 18, no. 9, pp. 1187–1196, Sep. 2000. [5] X. Chen and S. Kiaei, “Monocycle shapes for ultra wideband system,” in Proc. IEEE Conf. Ultra Wideband Syst. Technol., Baltimore, MD, May 20–23, 2002, pp. 597–600. [6] K. A. Hamdi and X. Gu, “Bit error rate analysis for TH-CDMA/PPM impulse radio networks,” in Proc. WCNC, New Orleans, LA, Mar. 2003, pp. 167–172.
[7] B. Hu and N. C. Beaulieu, “Exact bit error rate analysis of TH-PPM UWB systems in the presence of multiple-access interference,” IEEE Commun. Lett., vol. 7, no. 12, pp. 572–574, Dec. 2003. [8] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products. New York: Academic, 1980. [9] M. B. Pursley, “Performance evaluation for phase-coded spread-spectrum multiple-access communication—Part I: System analysis,” IEEE Trans. Commun., vol. COM-25, no. 8, pp. 795–799, Aug. 1977. [10] R. J. Fontana, A Note on Power Spectral Density Calculations for Jittered Pulse Trains. Multispectral Solutions, Inc., 2000. [11] E. Fishler and H. V. Poor, “Low-complexity multiuser detectors for timehopping impulse radio systems,” IEEE Trans. Signal Process., vol. 52, no. 9, pp. 2561–2571, Sep. 2004. [12] S. Verdu, Multiuser Detection. Cambridge, U.K.: Cambridge Univ. Press, 1998. [13] M. Z. Win, “Spectral density of random UWB signals,” IEEE Commun. Lett., vol. 6, no. 12, pp. 526–528, Dec. 2002. [14] Part 15.4: Wireless Medium Access Control (MAC) and Physical Layer (PHY) Specifications for Low-Rate Wireless Personal Area Networks (LR-WPANs), IEEE Std. 802.15.4, 2003. [15] J. Foerster, “UWB channel modeling sub-committee report final,” Feb. 2003. IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs). [16] E. Fishler and H. V. Poor, “On the tradeoff between two types of processing gains,” IEEE Trans. Commun., vol. 53, no. 10, pp. 1744–1753, Oct. 2005. [17] S. H. Song and Q. T. Zhang, “Noncoherent detection of TH-CDMA-PPM signals for low rate WPAN,” in Proc. WCNC, Hong Kong, Mar. 2007, pp. 1745–1750.
S. H. Song (M’06) received the B.S. and M.S. degrees in electrical engineering from Tianjin University, Tianjin, China, in 2000 and 2002, respectively, and the Ph.D. degree in electrical engineering from the City University of Hong Kong, Kowloon, Hong Kong, in 2006. He is now a Senior Research Associate with the City University of Hong Kong. His research interests include ultrawideband systems and statistical signal processing for wireless communications.
Q. T. Zhang (SM’95) received the B.Eng. degree in wireless communications from Tsinghua University, Beijing, China, the M.Eng. degree in wireless communications from South China University of Technology, Guangzhou, China, and the Ph.D. degree in electrical engineering from McMaster University, Hamilton, ON, Canada, in 1986. After receiving the Ph.D. degree from McMaster University, he held a research position and Adjunct Assistant Professorship with the same institution. In January 1992, he joined the Satellite and Communication Systems Division, Spar Aerospace Ltd., Montreal, QC, Canada, as a Senior Member of the Technical Staff, where he participated in the development and manufacturing of the Radar Satellite (Radarsat). He joined Ryerson Polytechnic University, Toronto, ON, in 1993, where he became a Professor in 1999. In 1999, he took a one-year sabbatical leave with the National University of Singapore. He is currently a Professor with the City University of Hong Kong, Kowloon, Hong Kong. His research interest includes transmission and reception over fading channels, with current focus on wireless MIMO and UWB systems. Dr. Zhang is currently an Associate Editor of the IEEE COMMUNICATIONS LETTERS.
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CDMA-PPM for UWB Impulse Radio S. H. Song, Member, IEEE, and Q. T. Zhang, Senior Member, IEEE
Abstract—Pulse-position modulation (PPM) is widely used in impulse radio (IR) due to the simplicity of its transceiver structure and signal detection. It is usually used along with time hopping (TH) to support multiple users in IR and to take the advantage of a small collision probability among simultaneous users. This advantage, however, is achieved at the cost of a wider frame length and the concentration of each user’s frame signal energy on a single pulse. Thus, it is likely that the TH-PPM information can totally be damaged whenever a collision occurs. In this paper, we take a different philosophy to evenly distribute the signal energy over the entire frame, ending up with a novel ultrawideband (UWB) IR multiple-access scheme, which is called code division multiple access (CDMA)-PPM, for low-rate wireless-personalarea-network application. The new scheme is superior to the conventional one in terms of error performance, as evidenced by theoretical analysis and simulations. We also examine the power spectrum of CDMA-PPM signals, which is found to be comparable to its TH-PPM counterpart. Index Terms—Code division multiple access pulse-position modulation (CDMA-PPM), impulse radio, multiple access, timehopping PPM (TH-PPM).
I. I NTRODUCTION
I
MPULSE radio (IR) is one of the two short-listed proposals for the IEEE 802.15.4a low-rate communication application. The idea of transmitting digital information by using ultrashort impulse waves was first presented in [1], where the term IR was coined. In [1], the authors stated that “amplitude and frequency/phase modulations are unsuitable for this particular form of impulse communications; the only suitable choice is pulse position modulation.” Subsequently, the pioneering work of Win [2] shows how the IR works with time-hopping pulseposition modulation (TH-PPM). Recently, a multiple-access scheme called direct-sequence ultrawideband (DS-UWB) is proposed for IEEE 802.15.3a high-rate communication application. It resembles the conventional DS code division multiple access (DS-CDMA) system; the only difference is that data modulation is implemented on the polarity of an ultrashort pulse. Although it is not as power efficient as phase modulation, PPM has a simpler transceiver structure and enables noncoherent detection [3], making it very suitable for low-rate and lowcomplexity application. In this paper, we will introduce a new multiple-access scheme for PPM as a possible candidate for the IEEE 502.15.4a low-rate communication application.
Manuscript received March 7, 2005; revised January 7, 2006, October 7, 2006, and May 4, 2007. This work was supported by the City University of Hong Kong under Project 7001856. The review of this paper was coordinated by Prof. R. Qiu. The authors are with the Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TVT.2007.905260
Conventional spread-spectrum (SS) techniques are usually used alongside digital modulation based on phase- (PSK) or frequency-shift keying (FSK). On the contrary, UWB-IR usually employs, instead, PPM to take the advantage of a simple system structure and possible noncoherent detection. Therefore, when extending the concept of SS to allow multiple users to share a UWB channel, one must adopt a different strategy for multiple access. A natural way to achieve this goal is the integration of m-ary PPM with TH, resulting in the wellknown TH-PPM scheme. The TH-PPM, in essence, resembles the classical fast frequency hoping (FFH) in philosophy but is performed in the time domain. In TH-PPM, a symbol interval is partitioned into a number of frames, and an information pulse of each user is repeatedly transmitted over all these frames. Pulse position is randomly hopped over these frames to form the TH pattern under the control of the signature sequence assigned to that user. Accordingly, the TH-PPM can be regarded as the extension of FFH. The difference is that the former is used in the time domain with a seamless combination with PPM, whereas the latter is used in the frequency domain with a seamless integration with FSK. However, we note that, in TH-PPM, the frame duration is much wider than the minimum requirement to accommodate m-PPM in order to leave a room for random TH. The consequence is the reduction of the number of frames in a symbol, thus lowering the diversity gain. Furthermore, the transmitted symbol energy in a TH-PPM system is highly concentrated on a few pulses. Thus, once a pulse collided with that of other users, the error performance will severely drop. Alternatively, one may extend SS techniques to a PPM system along the direction of CDMA. This idea was first adopted in optical communications, ending up with the so-called PPMCDMA system. In PPM-CDMA, each user’s information pulse is first spread by a particular signature sequence before being applied to PPM [4], as shown in Fig. 1(c). The signature sequences are optically implemented through ON–OFF signaling and have a very low weight to prevent user collision. The distinction between users relies on many low weight signature sequences, with a length that is equal to half of the symbol duration. Thus, for a given system bandwidth, the unnecessary reduction in signature length will significantly reduce the number of users that can be supported by the system. This may not be a problem for an optical communication system due to its huge frequency bandwidth but is definitely a problem for wireless UWB communications. A natural question follows: Can we directly spread a user’s PPM symbols so that the transmitted energy can evenly be distributed over the entire SS symbol duration to fully exploit the processing gain, on one hand, and to avoid users’ collisions, as much as possible, on the other hand? The resulting system is CDMA-PPM, which will be addressed in this paper.
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Fig. 1. Examples of the CDMA-PPM, TH-PPM, and PPM-CDMA systems with rectangular pulses. (a) CDMA-PPM. (b) TH-PPM. (c) PPM-CDMA.
The remainder of this paper is organized as follows. The new scheme is described in Section II, followed by the derivation of its error performance and power spectrum in Section III. The performance comparison and discussion are presented in Section IV. The implementation issues of the CDMA-PPM system are briefly addressed in Section V, followed by the conclusion in Section VI.
II. S YSTEM M ODEL To introduce the CDMA-PPM scheme, let us briefly review the TH-PPM system. A typical TH-PPM UWB signal for user k is expressed as (k) st (t)
=
∞ Eb w t − jTft − ckj Tc − dkj/Ns δ Ns j=0
(1)
where Tft and Tc denote the frame length and chip width for TH, respectively, and δ is the PPM modulation depth. The TH code for user k is denoted by {ckj }, where each of its entry is assumed to take on an integer value in the range of [0, Nh − 1], where Nh = Tft /Tc . The j/Ns th information bit from user k is signified by dkj/Ns , where x denotes the largest integer less than x. The basic waveform w(t) is scaled to have a unit norm so that Eb represents the bit energy. Ns is the number of frames per symbol. Multiple access is achieved by assigning each user a particular TH sequence, as
shown in Fig. 1(b), where w(t) is assumed, for convenience, to be a rectangular pulse with a duration that is equal to half of the chip width Tc . All signal energy in a frame is solely transmitted over a single chip interval, and the location of this selected chip changes from frame to frame under the control of a preassigned TH sequence forming a user-specific TH pattern. The pulse position within the transmission chip only depends on the information symbol. With a sufficiently large Nh , the possibility that different users will collide within a frame should be small. However, once such collision occurs, the information of the intended user will severely be damaged. It would therefore be wise to evenly distribute the transmitted energy over all chips within a frame so that the risk of fatal collision can be reduced. The resulting scheme is CDMA-PPM. In the CDMA-PPM scheme that we propose, the spreading sequence for user k ({akm , m = 0, 1, . . . , M − 1}) is used along with its information symbol dkm to generate a new positioninformation sequence for PPM of the basic waveform w(t). Hence, the transmitted signal for user k can be written as s(k) c (t)
=
∞ Eb w t − jTfc − dkj/M ⊕ akmod(j,M ) δ M j=0
(2) where Tfc is the chip duration for the CDMA system and is analogous to the frame length Tft of the TH system, and ⊕ represents the modulo-2 addition. This modulo-2 addition
SONG AND ZHANG: CDMA-PPM FOR UWB IMPULSE RADIO
randomizes the pulse location over each frame, thereby implementing the idea of evenly distributing the transmitted energy in the time domain. The CDMA-PPM signal is shown in Fig. 1(a). In a CDMA-PPM system, it is true that the likelihood for different users to collide over a single chip can increase. However, a partial damage over some chips has no fatal influence on the overall multiple-access performance. At this point, it is interesting to compare CDMA-PPM with the conventional DS-CDMA scheme. In DS-CDMA, the polarity of an information waveform varies over each chip interval through a simple multiplication with a specific spreading sequence. It is clear from Fig. 1 that the CDMA-PPM resembles its DS-CDMA counterpart in that both systems spread an information symbol as a binary sequence. The difference lies in the way to generate these sequences and the way to represent each bit over a chip interval. A bit over a chip is represented by a bipolar waveform in DS-CDMA but is represented by PPM in CDMA-PPM. In CDMA-PPM, spreading is implemented by using the signature sequence {ak0 , ak1 , . . . , akM −1 } to generate a new random position sequence, through the relation {xj } = {dkj/M ⊕ akmod(j,M ) }, for the PPM of w(t). The difference between TH-PPM and CDMA-PPM lies in the multiple-access scheme, while CDMA-PPM differs from DS-CDMA by the data modulation method. Data modulation is usually chosen according to different application environments. For example, PSK is power efficient and is utilized for high-rate application, while PPM is widely utilized in the case when phase or amplitude information is difficult to carry, such as optical communication. Other advantages of PPM include its simple transceiver structure and the possible noncoherent detection. Our motivation in this paper is to combine the good multiple-access performance of the CDMA system with the possible simple transceiver structure of PPM for the IEEE 802.15.4a low-rate application.
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pseudonoise (PN) SS sequences for CDMA-PPM and the PN TH codes for TH-PPM will be considered for fair comparison. 1) Time-Hopping PPM (TH-PPM): The BER performance of the TH-PPM system with a matched filter receiver has been derived [6], [7], and we briefly introduce it here for comparison purposes. The received signal of the TH-PPM with Nu asynchronous users and freeing from a near-far problem can be written as rt (t) =
(1)
By assuming that τ1 = 0 and cj with template
Various basic waveforms of w(t) have been proposed for UWB pulse shaping [5] to meet the requirements set by the Federal Communications Council (FCC) and to avoid a directcurrent component. Since the rectangular pulse can provide a good measure of the relative performance between CDMAPPM and TH-PPM, we follow Hamdi and Gu [6] by utilizing the rectangular impulse and orthogonal PPM for a theoretical comparison of the two systems. The analysis can easily be extended to other waveforms and nonorthogonal PPM. The
(3)
= 0, the correlation detector
vj (t) = w(t − jTft ) − w(t − jTft − δ)
(4)
produces the decision variable V =
Ns
r
(Vsj + VIj + Vnj )
(5)
j=1
where the interference VIj comes from Nu − 1 users VIj =
Nu
. VIjk
(6)
k=2
The components inside the summation on the last line can further be represented by the following: jTft
V
Ijk
=
st (t − τk )vj (t)dt (k)
(j−1)Tft
=
III. P ERFORMANCE A NALYSIS
A. BER Analysis for Matched Filter Receiver
(k)
st (t − τk ) + n(t).
k=1
In this section, we will investigate the bit-error rate (BER) performance of the TH-PPM and CDMA-PPM with the matched filter receiver in additive white Gaussian noise (AWGN) channels. The performance of a minimum mean square error (MMSE) detector in both AWGN and frequencyselective fading channels will be analyzed in the next section. Besides BER performance, we also show the power spectral density (PSD) analysis.
Nu
jTft
Eb Ns
w(t − τd )vj (t)dt
(7)
(j−1)Tft
where τd = Mod(τk + ckj Tc + dkj/Ns δ, Tft ) is uniformly distributed in [0, Tft ). We can use the Gaussian approximation and determine the , obtaining variance of VIjk σV2 I = E VI2 jk
jk
=
Eb E Ns
jTft
2 w(t − τd )vj (t)dt
(j−1)Tft
=
Eb . 2Nh Ns
(8)
Thus, for a system with spreading factor Ns , the variance of the total interference is given by the following: σI2 = (Nu − 1)Ns σV2 I = jk
(Nu − 1)Eb 2Nh
(9)
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which implies that the signal-to-interference plus noise ratio (SINR) is equal to (Ns Vsj )2
γt =
2Ns σn2 + σ 2I
=
1 2 2σn Eb
+
(Nu −1) 2Nh Ns
(10)
in the same form as that of [6, eq. (26)]. 2) Code Division Multiple Access PPM (CDMA-PPM): Consider an asynchronous CDMA-PPM system with Nu active users and freeing from a near-far problem. Its received signal is given by the following:
If bit dm = 1 is sent, then an erroneous decision is made if Vr < 0. To determine error probability, we need to characterize the three terms on the right side of (14). Since w(t) is a pulse √ of unit energy, it follows some manipulations, where Vs = Eb M . It also follows that Vn is a zero-mean Gaussian variable with variance 2M σn2 . The interference term VI remains to be characterized. Since different users are asynchronous and independent, we obtain
VI =
Nu
VIk
(16)
k=2
(t − τ1 ) + rc (t) = s(1) c Sc (t)
Nu k=2
s(k) c (t − τk ) + n(t)
(11)
where
M Tfc
Ic (t)
where τk , k = 1, . . . , Nu denotes the time delay of user k, and n(t) is the AWGN of zero mean and variance σn2 . Component (1) sc (t) is the desired signal, which is denoted by Sc (t) for convenience, whereas the remaining Nu − 1 users’ signals are treated as interference Ic (t). Without loss of generality, assume that τ1 = 0, and hence, τk , k = 2, . . . , Nu represents the time delays of other users relative to the desired one. We further assume that the receiver is perfectly synchronized to the desired user and employs a correlation detector with a chip correlation template (1)
vj (t) = (−1)aj [w(t − jTfc ) − w(t − jTfc − δ)] .
(12)
The M -bit symbol correlation template can thus be written as v(t) =
M
vj (t) =
j=0
M j=0
(13) which, when correlated with the received signal, produces the decision variable (14)
The three terms in this expression are signal, interference, and noise components at the correlator’s output, respectively, which are given by the following: M Tfc
Vs =
For further simplification, we adopt the method of Gaussian approximation. To this end, we need to determine the variance of the zero-mean variable VIk , k = 2, . . . , Nu
σV2 I
k
2 M Tfc = E VI2k = E s(k) (18) c (t − τk )v(t)dt 0
where the expectation E[·] is taken over all random sources. We first take the ensemble average over random delay τk , which is uniformly distributed over the range [0, Tfc ), yielding 1 Eτk [VI2k ] = Tfc
T 2 Tfc M fc dτk . s(k) c (t − τk )v(t)dt 0
=M
pa = Tfc w(t) [w(t) − w(t − δ)] dt 0
Ic (t)v(t)dt 0
n(t)v(t)dt. 0
a M −a 1 1 . 2 2
(20)
2 1 Tfc . Pa (t−τ )v(t)dt dτ s(k) E[VI2k ] = k k a Tfc a=0 M
M Tfc
Vn =
M a
Without loss of generality, we assume that all zero sequences are allocated to the desired user, and we let sa (t) denote the signal associated with PN sequence Ca , which has a zeros and (M − a) ones. We have
M Tfc
VI =
0
0
Eb M
(19)
Next, we average (19) over the interference caused by different PN sequences. We assume that PN sequences (each of length M ) are used as signature sequences for users and that sequence Cu is allocated to the desired user. Over the period of Cu , the interfering users’ signature sequences can have different patterns. Let Ca denote an interfering sequence that has a positions identical to Cu while having (M − a) positions that are different. Then, Ca occurs with probability pa
Sc (t)v(t)dt
(17)
0
(1)
(−1)aj [w(t−jTfc )−w(t−jTfc −δ)]
Vr = Vs + VI + Vn .
s(k) c (t − τk )v(t)dt.
VIk =
(15)
0
(21)
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We should also take into account the cases when τk separately falls into [0, Tfc /2) and [Tfc /2, Tfc ); thus M P a Eb E VI2k = T M a=0 fc # Tfc /2 4τk a 1− × Tfc
with FCC regulations. It is therefore interesting to compare the power spectra of TH-PPM and CDMA-PPM UWB systems. We follow the method used in [10] to determine the PSD Sr (f ), as defined by the following: E |RT (f )|2 T →∞ T
(27)
r(t) exp(−j2πf t)dt
(28)
Sr (f ) = lim where
0
+ (M − a)
T
$2 4τk −1 dτk Tfc
RT (f ) = 0
Tfc # 4τk a + −3 Tfc Tfc /2
+ (M − a) 3 −
4τk Tfc
$2
is the truncated Fourier transform of the random process r(t). For analytical simplicity, we assume that the transmitted pulse w(t) is rectangular in shape. 1) TH-PPM System: The TH-PPM signal with M asynchronous users, over K frames, can be represented as
dτk r(t) = (22)
which can further be simplified as [8] σV2 I = E VI2k
M K−1
At w(t − τu − nTft − cun Tc − bun δ)
(29)
u=1 n=0
where At is the pulse amplitude, τu is the delay for user u, and w(t) is the transmitted pulse. The truncated Fourier transform is then given by the following:
k
=
M M Eb M 1 (2a − M )2 3M a 2 a=0
=
Eb . 3
KT ft
RT Tft (f ) =
r(t) exp(−j2πf t)dt 0
(23) = At W (f )
The variance of the total interference is then given by the following: σI2 = (Nu − 1)σV2 I = k
(Nu − 1)Eb . 3
1 2 2σn Eb
+
(Nu −1) 3M
where the bit error probability can be determined as 2 ∞ 1 x √ exp − Pe = Q ( γc ) = dx 2π √γc 2
u=1 n=0
× exp (−j2πf (τu + nTft + cun Tc + bun δ)) (30)
(24)
The Gaussian approximation allows us to determine the SINR, yielding Vs2 = γc = 2M σn2 + σI2
M K−1
where W (f ) is the Fourier transform of waveform w(t). As such |RT Tft (f )|2
(25) = [At W (f )]2
M K−1 M K−1 u=1 v=1 n=0 m=0
× exp (−j2πf ((τu − τv ) + (n − m)Tft + (cun − cvm )Tc + (bun − bvm )δ))
(26)
(31) which is a function of the number of active users Nu . The expression in (25) is similar to the DS-CDMA system (17) [9], except that the noise power is doubled due to the use of orthogonal PPM. B. PSD Analysis The power spectrum is one of the important characteristics of UWB signals since all UWB applications must comply
which, after taking expectation and simplifying, results in E |RT Tft (f )|2 = M [At W (f )]2 {K + K(M − 1)E1 E2 E3 + [(M − 1)E1 + 1] E2 E3 E4 } (32)
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with symbols E defined by the following:
is also taken into consideration, the situation is somewhat different. The locations of discrete spectral lines are dictated by the average signal period. In a TH-PPM system, it is the chip width Tc that determines the average fundamental period. This physical intuition is confirmed in (34). 2) Code Division Multiple Access PPM (CDMA-PPM): For a CDMA-PPM signal, there are no TH codes, and the frame length is much shorter. The K-frame signal for M asynchronous users is
E1 = Eu=v [exp (−j2πf (τu − τv ))] = sinc2 (f Tft ) E2 = En=m [exp (−j2πf (cn − cm )Tc )] =
sin2 (πf Nh Tc ) Nh2 sin2 (πf Tc )
E3 = En=m [exp (−j2πf (bn − bm )δ)] sin2 (πf 2δ) = 4 sin2 (πf δ) E4 =
K−1
r(t) =
exp (−j2πf (n − m)Tft )
sin2 (πf KTft ) − K. sin2 (πf Tft )
(33)
(1 − E2 E3 ) + M [At W (f )]2 Tft +∞ (M − 1)E1 + 1 n × E u f − (34) 3 0 Tft2 Tc n=−∞
SrTH (f ) = M [At W (f )]2
where u0 (f ) is the Dirac delta function. The line spectrum in the second term of (34) is an asymptotic result as K → ∞ after invoking the result due to Robert [10]
sin πf KT sin πf T
2
(37)
where Ac and Tfc are the pulse amplitude and frame length, with other parameters the same as the TH-PPM system. The truncated Fourier transform for the received signal is
It is clear that E1 accounts for the asynchronous arrival of M users’ signals, E2 represents the influence of random TH codes, and E3 comes from the random data modulation. We can use the fact that Tft = Nh Tc to further simplify the aforementioned expressions for E2 and E4 , and we insert the results and (32) into (27) to obtain the following asymptotic PSD expression for multiuser TH-PPM received signals:
1 lim K→∞ KT
Ac w(t − τu − nTfc − bun δ)
u=1 n=0
n,m=0 n=m
=
M K−1
+∞ n 1 . (35) = 2 u0 f − T n=−∞ T
Although it is strictly valid only for an infinite K, (35) provides a good approximation for K of a large value, and the same is true for (34). For the orthogonal-PPM case of practical importance, we have Tc = 2δ. Thus, E3 can further be simplified with E2 and E4 , and the aforementioned PSD expression can be simplified as (1 − E2 E3 ) + M [At W (f )]2 Tft +∞ (M − 1)E1 + 1 2n × u0 f − . (36) Tft2 Tc n=−∞
SrTH (f ) = M [At W (f )]2
The PSD in (34) is composed of two parts, with the first one accounting for the continuous component and the second one representing the discrete spectral lines. In [13], it is shown that the line spectrum spacing for framed TH systems is determined by the TH frame length. If the influence of PPM modulation
RT Tfc(f ) = Ac W(f )
M K−1
exp(−j2πf (τu +nTfc +bun δ)) .
u=1 n=0
Then |RT Tfc (f )|2 = [Ac W (f )]2
M K−1 M K−1 u=1 v=1 n=0 m=0
× exp (−j2πf ((τu − τv ) +(n − m)Tfc + (bun − bvm )δ)) and E |RT Tfc (f )|2 = M [Ac W (f )]2 {K + K(M − 1)E1 E3 + [(M − 1)E1 + 1] E3 E4 }
(38)
where E1 and E4 are the counterparts of E1 and E4 , with Tft replaced by Tfc . The PSD for the multiuser CDMA-PPM received signal is (1 − E3 ) + M [Ac W (f )]2 Tfc +∞ (M − 1)E1 + 1 n × E u f − . 3 0 Tfc2 Tfc n=−∞
SrCDMA (f ) = M [Ac W (f )]2
(39) In case of orthogonal PPM, the result is (1 − E3 ) + M [Ac W (f )]2 Tfc +∞ (M − 1)E1 + 1 2n × u f − . 0 Tfc2 Tfc n=−∞
SrCDMA (f ) = M [Ac W (f )]2
IV. R ESULTS AND D ISCUSSION A. BER Performance Comparison 1) Matched Filter: Let us compare (25) and (10) to see the difference between the two systems. By assuming the same
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Fig. 2. Performance comparison based on Gaussian approximation and simulation.
Fig. 3. Performance comparison utilizing Gaussian monocycle.
the system performance comparison, and the results are shown in Fig. 3. Specifically, the pulse waveform that we use is
TABLE I SYSTEM SETTING FOR THE TH-PPM AND CDMA-PPM
w
transmission rate, for the two systems, we can relate their spreading factors to obtain M = Nh N s
(40)
which, when inserted into (25), leads to γc =
1 2 2σn Eb
+
(Nu −1) 3Nh Ns
.
(41)
By comparing (41) with (10), we find that multiple-access interference is suppressed in the CDMA-PPM system. The TH system achieves a good anticollision performance at the cost of sacrificing its processing gain. The CDMA-PPM system, however, has the capability of maintaining the good tradeoff between the two performance parameters. Theoretical bit-error performance is shown in Fig. 2, where the simulation results are also included for comparison. The system parameters that are used to obtain Fig. 2 are shown in Table I. It is confirmed that the BER of the CDMA-PPM is superior compared to its TH-PPM counterpart. Recall that the method of the Gaussian approximation, although it is good for the CDMA system, is proven [6], [7] to underestimate the BER performance of the TH systems. This phenomenon can easily be seen in Fig. 2 when a small number of users are active. To exclude the possibility that pulse form may influence system performance, we, instead, use a Gaussian monocycle for
t τp
#
= 1 − 4π
t τp
2 $
# exp −2π
t τp
2 $ (42)
which is the same as the one that is used in [7]. Here, τp is a time normalization factor, and the remaining parameter settings, such as the optimum modulation depth for the nonorthogonal PPM, are exactly the same as [7], with Ns = 2. The results again show that with Gaussian pulse shaping, the CDMAPPM outperforms the TH-PPM. It should also be pointed out that since the nonorthogonal PPM is utilized for the Gaussian monocycle, a better performance is achieved, as shown by comparison in Figs. 2 and 3. 2) MMSE Detector: It is shown that low-complexity multiuser detectors can greatly improve the BER performance of the TH-IR system [11]. Thus, it is valuable to compare the performance of the CDMA-PPM and TH-PPM systems with multiuser detection. The general MMSE receiver for the detection of the symbol transmitted by the kth user is of the form [12] ˆbk = sgn
% T & 1 (S S + σn2 A−2 )−1 (S)T r k A(k, k)
(43)
where r is the received symbol; A is a diagonal matrix, with its diagonal entry corresponding to the power of each user; and the collum of S is the user signature sequence for both the CDMA and TH systems. From this point of view, the two systems only differ in the utilized spread sequence. Fig. 4 shows the performance comparison of the synchronous TH-PPM and CDMA-PPM systems using a Gaussian monocycle with matched filter and MMSE receiver over the AWGN channels. The system parameters are set as Ns = 2, Nh = 16, and Nu = 6. It is observed that, in a high SNR environment, the performance of the MMSE receiver for the TH system deteriorates with an error floor. This is because, as
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Fig. 4. Performance comparison of matched filter and MMSE receivers for the TH-PPM and CDMA-PPM.
the SNR goes to infinity, the MMSE linear detector converges to the decorrelating detector [12], whose performance directly depends on (ST S)−1 . In this sense, the performance difference between TH and CDMA lies on the correlation matrix of their respective spread sequences. Being different from the CDMA spread sequence, the TH sequence has an extremely low weight; thus, the correlation matrix is not diagonally dominant, which may cause the matrix to become singular. For example, consider the extreme case of Ns = 1. Once a collision occurs, the correlation matrix is singular, with |ST S| = 0, and the MMSE receiver cannot work. Thus, for the MMSE detection of the TH signal, it is better to choose a larger Ns . 3) Performance Comparison Over Multipath Channels: Multipath propagation is a critical problem that is faced by UWB high-rate communications such as the 802.15.3a application. Fortunately, the proposed scheme is for low-rate communications with about several hundreds of chips per second [14]. Thus, orthogonal PPM is enough to support the load, even for the CM4 case [15]. We show in Fig. 5 the performance comparison of the TH-PPM and CDMA-PPM systems using a Gaussian monocycle with matched filter and MMSE receivers over lognormal slow-fading channels [15]. The system parameters are set as Ns = 2, Nh = 16, and Nu = 6, with L = 3 paths. We have observed that the CDMA-PPM has an obvious advantage at a high SNR environment. With orthogonal PPM, multipath fading will no longer introduce ISI but only influence the averaged SNR. It is, thus, interesting to see how multipath channels influence performance. Fig. 6 shows the performance comparison of the TH-PPM and CDMA-PPM systems using a Gaussian monocycle over lognormal multipath channels with different number of paths (L = 3 and 5 ), where the total channel gain is normalized. The diversity gain with a larger number of paths, as shown in Fig. 6, is obtained at the cost of the receiver’s complexity and low data rate. 4) Comparison of Possible Combinations: Besides the THPPM and CDMA-PPM, there are other possible combinations of data modulation (PPM and BPSK) and multiple-access
Fig. 5. Performance comparison between the TH-PPM and CDMA-PPM over slow lognormal fading.
Fig. 6. Performance comparison between the TH-PPM and CDMA-PPM over slow lognormal fading with different number of paths.
schemes (TH and CDMA). Throughout this paper, we have focused on the comparison of the TH-PPM with CDMA-PPM because they are utilizing the same data modulation PPM, which is suitable for low-rate and low-complexity UWB-IR applications. For a complete comparison, we then investigate the performance of all the possible combinations and assume that the same type of random TH and CDMA spread sequences are utilized. The BER performance comparison for these systems over the AWGN channels with matched filter receivers can be seen by comparing (41) and (10). The advantage of the CDMA system over TH comes from the second term in the denominator, which is SIR, whereas the difference between BPSK and PPM lies in the first SNR term. In Fig. 7, the performance comparison of the MMSE receiver for synchronous TH-PPM/TH-BPSK/CDMAPPM/DS-UWB systems using a Gaussian monocycle in slow multipath lognormal channels, with L = 3 paths, Ns = 2,
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Fig. 7. Performance comparison of TH-PPM/CDMA-PPM/TH-BPSK/ DS-UWB over lognormal fading.
Fig. 8. PSD comparison between the TH-PPM and CDMA-PPM systems by simulation.
Nh = 16, and Nu = 6, is illustrated. We have observed that, for the same data modulation, CDMA has an obvious advantage over the TH system at high SNR, whereas for the same multiple-access scheme, BPSK has a clear advantage over PPM. The gain of BPSK over PPM comes from the fact that, in PPM, double noise energy is collected. However, position modulation has a simple transceiver structure, and it enables the noncoherent detection [3] for low-complexity and lowrate application. The performance comparison of the TH-PPM and CDMA-PPM systems with a noncoherent receiver requires further investigation.
as opposed to
B. PSD Comparison As shown in (34) and (40), the spectra for the CDMA-PPM and TH-PPM have a similar functional form. The difference in the CDMA-PPM expression is the replacement of E2 E3 in its TH-PPM counterpart with E3 and the replacement of At and Tft with Ac and Tfc , respectively. For a fair comparison, we must impose a constraint wherein the two systems, on average, have identical transmitted energy over the same time period or, equivalently, the same average power. For simplicity and without loss of generality, we assume that the rectangular pulses used in the two systems are of the same time duration, e.g., Tp . Then, the identical average power requirement implies that A2t Tp /Tft = A2c Tp /Tfc , which leads to A2t A2 = c. Tft Tfc
(44)
Insert this relation into (40) and (34) and simplify. The result is (1 − E3 ) + M [At W (f )]2 Nh Tft +∞ (M − 1)E1 + 1 n × E3 u0 f − Tft2 Tc n=−∞
(1 − E2 E3 ) + M [At W (f )]2 Tft +∞ (M − 1)E1 + 1 n × E u f − . 3 0 Tft2 Tc n=−∞
SrTH (f ) = M [At W (f )]2
Recall that 0 ≤ E2 ≤ 1, as indicated in (33). We can therefore assert that the CDMA-PPM has a smaller continuous spectral component than its TH-PPM counterpart. It is also observed that the line spectra of the two systems have the same frequency locations but certainly different power. For orthogonal PPM with rectangular pulse shaping of length Tc /2, the continuous spectrum W (f ) has its nulls located at multiples of 2/Tc , except for f = 0. The spectral lines are located at multiples of 2/Tc , falling into the troughs of the continuous spectrum and thus being cancelled. In this sense, the CDMA-PPM system has a slight advantage over the TH-PPM system allowing for more line spectrum components to be cancelled by an appropriate pulse design. Simulation results with ten active users are shown in Fig. 8, where the binary orthogonal PPM is used with a rectangular pulse of width Tc /2 = 1 ns. It is clear that the pulseshape design is an important issue. An appropriate design can ensure that the continuous spectral component W (f ) meets the FCC’s PSD specification on UWB signals on one hand and provides room for the cancellation of the line spectral component on the other hand. If the polarity randomization method is utilized, no spectral lines will occur, and the two systems will have the same PSD. Under this circumstance, it is better to utilize a noncoherent receiver, which can simply disregard the randomization process and take advantage of the simple receiver structure brought by PPM.
SrCDMA (f ) = M [At W (f )]2
V. S YSTEM I MPLEMENTATION Besides its good performance, the CDMA-PPM system has several advantages in implementation. The first advantage is
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its ease of synchronization. The good autocorrelation structure of the SS code makes it easier to keep track of the signal. Usually, partial correlation suffices for synchronization. On the contrary, searching for the correlation peak of the TH code is more complicated, which normally consists of both frame and TH code synchronization. Second, the CDMA-PPM allows for an easy system expansion. When the system is nearly saturated, the CDMA-PPM system simply needs the addition of spread code length. This is in contrast with the TH-PPM system, which often requires the reconstruction of the frame structure (Tft , Th ). At the same time, we also want to emphasize the advantages of TH system, including the reduced near-far effects, high peak power that might lower the requirements on receiver sensitivity, etc. Based on the aforementioned analysis and performance comparison, we have observed that all these schemes (TH-PPM/TH-BPSK/CDMA-PPM/DS-UWB) have their own advantage and suitable application environment. The DSUWB is a promising candidate for high-rate communications, whereas the CDMA-PPM and TH-PPM have their future in low-complexity and low-rate communications and ranging applications. Besides these systems with single multiple-access schemes, some combined TH-CDMA systems have recently been reported [16], [17]. VI. C ONCLUSION In this paper, a CDMA-PPM multiple-access scheme is proposed as a possible candidate for the IEEE 802.15.4a lowrate communication application. The superior multiple-access performance of the new scheme over TH-PPM with a matched filter and MMSE detectors was theoretically verified and simulated. We have also shown that the two systems have nearly the same PSD characteristics. Furthermore, compared to the TH-PPM, the CDMA-PPM system is easier to implement. R EFERENCES [1] P. Withington, II and L. W. Fullerton, “An impulse radio communications system,” in Proc. Int. Conf. Ultra-Wide Band, Short-Pulse Electromagn., Brooklyn, NY, Oct. 1992, pp. 113–120. [2] M. Z. Win and R. A. Scholtz, “Impulse radio: How it works,” IEEE Commun. Lett., vol. 2, no. 2, pp. 36–38, Feb. 1998. [3] M. K. Oh, B. Jung, R. Harjani, and D. J. Park, “A new noncoherent UWB impulse radio receiver,” IEEE Commun. Lett., vol. 9, no. 2, pp. 151–153, Feb. 2005. [4] H. M. H. Shalaby, “Maximum achievable number of users in optical PPM-CDMA local area networks,” J. Lightw. Technol., vol. 18, no. 9, pp. 1187–1196, Sep. 2000. [5] X. Chen and S. Kiaei, “Monocycle shapes for ultra wideband system,” in Proc. IEEE Conf. Ultra Wideband Syst. Technol., Baltimore, MD, May 20–23, 2002, pp. 597–600. [6] K. A. Hamdi and X. Gu, “Bit error rate analysis for TH-CDMA/PPM impulse radio networks,” in Proc. WCNC, New Orleans, LA, Mar. 2003, pp. 167–172.
[7] B. Hu and N. C. Beaulieu, “Exact bit error rate analysis of TH-PPM UWB systems in the presence of multiple-access interference,” IEEE Commun. Lett., vol. 7, no. 12, pp. 572–574, Dec. 2003. [8] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products. New York: Academic, 1980. [9] M. B. Pursley, “Performance evaluation for phase-coded spread-spectrum multiple-access communication—Part I: System analysis,” IEEE Trans. Commun., vol. COM-25, no. 8, pp. 795–799, Aug. 1977. [10] R. J. Fontana, A Note on Power Spectral Density Calculations for Jittered Pulse Trains. Multispectral Solutions, Inc., 2000. [11] E. Fishler and H. V. Poor, “Low-complexity multiuser detectors for timehopping impulse radio systems,” IEEE Trans. Signal Process., vol. 52, no. 9, pp. 2561–2571, Sep. 2004. [12] S. Verdu, Multiuser Detection. Cambridge, U.K.: Cambridge Univ. Press, 1998. [13] M. Z. Win, “Spectral density of random UWB signals,” IEEE Commun. Lett., vol. 6, no. 12, pp. 526–528, Dec. 2002. [14] Part 15.4: Wireless Medium Access Control (MAC) and Physical Layer (PHY) Specifications for Low-Rate Wireless Personal Area Networks (LR-WPANs), IEEE Std. 802.15.4, 2003. [15] J. Foerster, “UWB channel modeling sub-committee report final,” Feb. 2003. IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs). [16] E. Fishler and H. V. Poor, “On the tradeoff between two types of processing gains,” IEEE Trans. Commun., vol. 53, no. 10, pp. 1744–1753, Oct. 2005. [17] S. H. Song and Q. T. Zhang, “Noncoherent detection of TH-CDMA-PPM signals for low rate WPAN,” in Proc. WCNC, Hong Kong, Mar. 2007, pp. 1745–1750.
S. H. Song (M’06) received the B.S. and M.S. degrees in electrical engineering from Tianjin University, Tianjin, China, in 2000 and 2002, respectively, and the Ph.D. degree in electrical engineering from the City University of Hong Kong, Kowloon, Hong Kong, in 2006. He is now a Senior Research Associate with the City University of Hong Kong. His research interests include ultrawideband systems and statistical signal processing for wireless communications.
Q. T. Zhang (SM’95) received the B.Eng. degree in wireless communications from Tsinghua University, Beijing, China, the M.Eng. degree in wireless communications from South China University of Technology, Guangzhou, China, and the Ph.D. degree in electrical engineering from McMaster University, Hamilton, ON, Canada, in 1986. After receiving the Ph.D. degree from McMaster University, he held a research position and Adjunct Assistant Professorship with the same institution. In January 1992, he joined the Satellite and Communication Systems Division, Spar Aerospace Ltd., Montreal, QC, Canada, as a Senior Member of the Technical Staff, where he participated in the development and manufacturing of the Radar Satellite (Radarsat). He joined Ryerson Polytechnic University, Toronto, ON, in 1993, where he became a Professor in 1999. In 1999, he took a one-year sabbatical leave with the National University of Singapore. He is currently a Professor with the City University of Hong Kong, Kowloon, Hong Kong. His research interest includes transmission and reception over fading channels, with current focus on wireless MIMO and UWB systems. Dr. Zhang is currently an Associate Editor of the IEEE COMMUNICATIONS LETTERS.
