Delay Spread Measurements and Characterization ... - Semantic Scholar
DELAY SPREAD MEASUREMENTS AND CHARACTERIZATION IN A SPECIAL PROPAGATION ENVIRONMENT FOR PCS MICROCELLS Nektarios Moraitis, Athanasios Kanatas, George Pantos, Philip Constantinou National Technical University of Athens, Mobile RadioCommunictions Laboratory 9 Heroon Polytechniou 15773 Zografou, Athens, Greece, {morai, kanatas}@mobile.ntua.gr
Abstract - This paper reports the measurement and analysis of wideband radio channel at 1900 MHz within a special propagation environment as the Olympic Stadium of Athens. RMS delay spread values are evaluated as well as the coherence bandwidth of the channel is derived by the frequency correlation function. Mean delay spread was found 0.314 µs and 0.731 µs for LoS and NLoS conditions respectively. The mean coherence bandwidth that characterizes the entire area reaches 3.463 MHz providing wide transmission data rates. Correlation bandwidth is found to be inversely proportional to the RMS delay spread and modeled in a minimum mean square error sense. Keywords – wideband measurements, delay spread, coherence bandwidth. I. INTRODUCTION The application of current technology wireless communications systems in environments with special constructions such as stadiums, and the increased demand for high data rates and heavy telecommunication traffic has driven engineers to thoroughly investigate the propagation conditions and to assess typical and worst case scenarios for digital signal transmission. The characterization of the mobile radio channel requires the analytic and thorough investigation of three propagation phenomena, namely: time dispersion (or frequency selectivity), frequency dispersion (or time variance), and angular dispersion (or spatial variance). The mobile radio channel is well represented by a linear filter with randomly time variant characteristics. Time delay or time dispersion is due to the multiple scatterers in the channel, called multipath, and results in a frequency selectivity or frequency variance. There are numerous publications presenting results on the time dispersion phenomenon, most of them with omni and few with directive antennas [1-4], for urban, suburban and rural environments. In this paper we present time and frequency domain parameters extracted by measurements in the Olympic Stadium of Athens. This environment was especially selected in the view of Olympic Games to be held in Athens in 2004, and the expected wireless communications systems to be installed and verified in the wide area of the stadium.
0-7803-7589-0/02/$17.00 ©2002 IEEE
A measure of the delay spread depicted in the channel power delay profile is useful since the inter-symbol interference (ISI) which causes higher bit error rates in a digital system is related to this parameter. Under Rayleigh fading channels having wide-sense stationary uncorrelated scattering (WSSUS) characteristics [6], ISI is related to the root mean square (RMS) delay spread of the channel. Furthermore, one of the key performance indicators of the channel is the knowledge of the coherence bandwidth in different spectral regions over the proposed transmission bandwidth [6]. If the coherence bandwidth of the channel is less than the transmission bandwidth, channel protection techniques, such as coding, diversity or equalization need to be employed. In [8], a relationship between RMS delay spread and coherence bandwidth has been indicated, whereas in [9] a confinement boundary of the coherence bandwidth has been proposed for application to WSSUS systems. The presented results contain information about the delay spread, the coherence bandwidth for alternative antenna positions including line-of-sight (LoS) and non-line-of-sight (NLoS) situations. Furthermore, a relationship between delay spread and coherence bandwidth is proposed by fitting the measured data in a minimum mean square error sense. This paper is organized as follows. Section II deals with the measurement system describing the operation of the transmit/receive set. In Section III, the measurement environment and procedure is analyzed whereas in Section IV the data processing method is introduced and described analytically in order to evaluate the channel parameters. Section V contains results derived from the measurements, extracting the channel parameters such as time delay and correlation bandwidth. Finally, Section VI is devoted to discussion and conclusions. II. MEASUREMENT SYSTEM The equipment used for the measurements was a commercially available transmit/receive set whose operation is based on a variation of the sliding correlator principle [7]. The transmitter produces a user selected spread spectrum digital signal within the PCS band whilst the receiver is a wideband spread spectrum receiver, which can identify and demodulate CDMA signals and its multipath components.
PIMRC 2002
The received signal is down-converted to a 70 MHz IF and the output of the IF amplifier is led to the I/Q demodulator. The output of the demodulator is sampled by a pair of A/D converters with a 20 MHz sampling rate. The digital sampled pair of data stream is fed to four independent correlators for the identification of the multipath components. The receiver processor acts to identify the 13 strongest of the echoes it resolves and to report their powers and delays as its output. This set of power-delay samples constitutes the output data of a single snapshot. The powerdelay data are recorded by the instrument at a rate of 5 snapshots/s and stored to a PCMCIA card for further processing. The measurements performed at a carrier frequency of 1900 MHz. During the measurements the chip rate of the signal was always fixed at 9.83040 MHz, which results in a 0.1 µs time resolution. Initial trial measurements were conducted for different PN lengths in order to select the best length, accommodating all multipath components. The length of the pseudo-noise sequence was set at 51l. Finally, the transmitter output power was fixed at +40 dBm, and omni-directional antennas were used in both transmitter and receiver having a gain of 5 dBi. III. MEASUREMENT ENVIRONMENT The Olympic Stadium of Athens is considered as a special area of interest due to its specific architecture. The measurements took place within the stadium with no rain and without spectators. The transmitter was placed in two different positions as depicted in Fig. 1 at a height of 1.9 m above floor. The first position (P1) is at the upper stage of the stadium at the last row looking at the centerline of the field. The second position (P2) is under the shelter of the upper stage, in front of the VIP section looking also at the centerline of the field.
semicircle of the stadium respectively. Each semicircle is divided in two sections hence the entire stadium is divided into four measured quarters (Q1-4) as shown in Fig. 1. The distance between the corridor of the upper stage and P1 is 23 m. Each measured quarter is approximately 140 m and 1min recordings conducted at 10-m intervals along the corridor. The measurements always started at the centerline of the field S-point as indicated in Fig. 1. Furthermore, measurements collected around the running field (F) of the stadium as shown in Fig. 1, in 10-m intervals covering a total distance of 450 m. At each quarter the measurements started at the location aligned to the centerline of the field. The measurements along the running field started at the location aligned to the matrix of the stadium right to transmitter P1. Finally measurements performed at the entrance of the gates of the stadium. In every measurement point, the receiver was stationary and the recording duration was approximately 1 minute resulting at 300 snapshots to be stored in the memory card. The same measurements performed for both transmitter positions in order to achieve alternative propagation conditions. For every measured quarter, gates, and along the field, for both transmitter positions the time delay and the coherence bandwidth of the channel is evaluated. For both transmitter positions, powerdelay data were collected in 307 different locations including LoS and NLoS conditions. IV. MEASUREMENT ANALYSIS The purpose of the measurement processing is the extraction of statistical parameters that describe the mobile radio channel in the area under consideration. The set of recorded data was preprocessed to make it suitable for our analysis. There were noise level, frequency resolution, and other issues that had to be addressed. Therefore, we performed the following steps prior to data reduction. In each snapshot, the 13 most significant echoes were recorded. Some noise peaks may, by random chance, be strong enough to appear as weak echoes. Therefore, a threshold referenced to the noise floor had to be set above which echoes are counted and below which they are ignored. We chose a threshold of 6 dB above the mean noise floor. The mean noise floor was found by linearly averaging echo-free noise samples over many data records. The most significant parameter derived from the data processing is the received power as a function of the time delay known also as the power delay profile (PDP). The measurement system records the received power at the moment t with a propagation delay τ ( h(t ,τ ) ). The 2
Fig. 1. Measurement environment and measurement locations. The receiver was always on a cart and the antenna was fixed at 1.8 m above the ground. The cart was moving along the corridor of the upper stage in the same and the opposite
power delay profile is obtained from the linear power versus delay, averaged over all the snapshots in a 1-min period (300 snapshots):
{
P(τ ) = E t h(t ,τ )
2
}
where E t {•} declares the time average value.
(1)
The time resolution of the receiver is 0.1 µsec (which corresponds to a length difference of 30 m between potential scatterers). During the data binning process we assigned each echo to the nearest value of delay equal to a multiple of 0.1 µs. The average received power in every bin is normalized to the maximum received power. A significant parameter to be evaluated is the RMS Delay Spread ( τ RMS ), which characterizes the frequency selective behavior of the channel and is given by:
∑ P(τ ) ⋅ τ ∑ P(τ )
∑ P(τ k ) ⋅ τ k τ RMS = k (2) − k k ∑ P(τ k ) k k where k is the number of the bin, τ k is the time delay of the k -bin and P(τ k ) is the average power of the k -bin. The Fourier transform of the normalized PDP gives the normalized frequency correlation function: N −1 2πn∆f (3) R H (∆f ) = ∑ P(τ n ) ⋅ exp − j N n=0 where Ν is the number of bins contained in the normalized PDP. In order to increase the frequency resolution we used a noise padding procedure technique resulting a frequency resolution of 2.44 kHz. k
2 k
1-min recording with relative delays until 3 µs. We observe that the multipath components arrive at the receiver with relative delays of 0.35 µs, 0.75 µs and 1.25 µs. Finally it is clear that the power of the direct component is not constant and exhibits a variation of about 10 dB.
2
It is noteworthy that the frequency correlation function characterizes all the system that intercedes between the transmitted and received signal. In other words, the function is affected also by the RF sections of the system, the connectors and the cables. For this reason it is necessary to calibrate the measurement system. The measurement procedure is repeated with the same settings in transmitter and receiver but connecting the receiver directly to the transmitter via a coaxial cable (back-to-back). Then the recorded data are processed with the same way as the real measured data. The normalized frequency correlation function that we derive, characterizes the measurement system. Therefore, the normalized frequency correlation function, which characterizes the channel itself is derived by dividing the measured function with the normalized function of the system. Based on the real value of R H (∆f ) , we calculate the coherence bandwidth for 90% correlation, in other words: (4) R H (∆f coherencebandwidth ) = 0.9
Fig. 2. Successive snapshots as a function of time. Fig. 3 and 4 depict the average power delay profile for LoS and NLoS condition respectively. In both cases the receiver is located in the corridor of Q1 approximately 20 m away from the starting point. For LoS propagation the transmitter was in P1 whereas for the NLoS situation the transmitter was in P2. We also provide the normalized frequency correlation functions derived by the Fourier transformation of the average PDPs through equation (3). The x-axis in the power delay figures represents the number of the bin with each bin to be 0.1 µs. Hence, bin 20 corresponds to a 2 µs time delay.
Fig. 3. Average PDP and frequency correlation function for LoS condition.
The resulted coherence bandwidth values comprise a sufficient sample to provide valid statistical characteristics. V. RESULTS A. Channel Parameters versus Transmitter Position Fig. 2 shows the result of successive snapshot recordings for a specific location. The transmitter was in P1 while the receiver was in Q1, approximately 37 m away from Tx. For better depiction we present only the first 4.5 seconds of the
Fig. 4. Average PDP and frequency correlation function for NLoS condition.
It is clear that in LoS situation the RMS delay spread is much smaller (0.303 µs) than in the NLoS (0.893 µs). The most significant multipath component in Figure 3 (LoS) arrives with zero delay whilst in Fig. 4 (NLoS) the most significant component arrives with a delay of 2.5 µs. One may observe the frequency correlation function to drop faster with frequency separation in NLoS condition providing worse channel quality having a coherence bandwidth of 162 kHz for 0.9 correlation. In LoS propagation environment the bandwidth is more than double (479 kHz) considering the same Rx position.
as well as its statistics for LoS and NLoS propagation condition respectively. As it is expected the mean RMS delay spread exhibits larger values in NLoS (0.731 µs) than in LoS (0.314 µs) conditions. Furthermore, for the 90th percentile of delay spreads, the value for LoS case is 0.752 µs whereas for NLoS case this value increases significantly to 1.085 µs. It is worthwhile to mention that the CDFs were derived by 282 LoS and 25 NLoS measured locations.
Table 1 shows the results of RMS delay spread and coherence bandwidth for 0.9 correlation (B0.9 in MHz) for the different measurement areas of the stadium taking into account the two alternative transmitter positions. Table 1 Channel parameters for different transmitter positions. P1
P2
τRMS (µs)
B0.9 (MHz)
τRMS (µs)
B0.9 (MHz)
Q1
0.315
2.570
0.370
4.510
Q2
0.199
6.191
0.547
1.690
Q3
0.187
3.881
0.363
1.454
Q4
0.202
4.831
0.414
2.154
F
0.477
1.215
0.315
4.836
Gates
0.573
0.660
0.211
5.777
In average, areas Q1-4 present better channel parameters, when the transmitter is located in P1, since there is better LoS propagation condition. This is more obvious in areas Q3 and 4, comparing the derived bandwidths for P1 and P2. The latter position is under the shelter of the stadium resulting in worse propagation environment with increased clutter around the transmitter. This increases the multipath components with relative delays greater than 2 µs as shown in Fig. 4 resulting in increased values of RMS delay spread and worse channel quality. The opposite happens in the field and at the gates of the stadium (F and Gates areas) where P2 provides better channel characteristics than P1. With transmitter in P2 the measured correlation bandwidth in the gates is up to 5.777 MHz whilst in P1 reaches only 660 kHz. This occurs because P2 provides LoS conditions in the majority of the gates, depressing significantly the multipath phenomena and the RMS delay spread values. In general, if we combine the two positions, each can provide the best channel quality in different areas. Hence, P1 is unique for areas Q1-4 and P2 for areas F and Gates as it is evident in Table 1. In Fig. 5 and Fig. 6 are shown the cumulative distribution functions (CDFs) of the measured RMS delay spread values
Fig. 5. CDF of the measured RMS delay spread for the entire stadium considering LoS condition.
Fig. 6. CDF of the measured RMS delay spread for the entire stadium considering NLoS condition. Table 2 Statistics of the channel parameters for the entire stadium environment. τMAX (µs)
τRMS (µs)
B0.9 (MHz)
Min Value
0.000
0.000
0.103
Max Value
7.700
1.556
>10
Mean Value
2.026
0.348
3.463
Median Value
1.100
0.235
0.921
St. Deviation
1.980
0.308
4.205
90th Percentile
5.400
0.836
10
Finally, Table 2 presents the overall channel parameters and their statistics concerning the entire area of the stadium. The maximum delay spread (τMAX) the RMS delay spread (τRMS) and the 0.9 correlation bandwidth (B0.9) values are presented. The mean values of the mentioned parameters are 2.026 µs, 0.348 µs and 3.463 MHz respectively. We should mention that the overall statistics derived from 306 measured locations. B. Delay Spread versus Coherence Bandwidth Fig. 7 depicts a scatter plot of the measured coherence bandwidth values derived by the frequency correlation function, as a function of the RMS delay spread, derived by the average PDP. A relationship is observed with the coherence bandwidth being inversely proportional to the RMS delay spread.
B c = 0 .9 ≥ 1 13.931 ⋅τ RMS a value well below the one given in equation (6).
(7)
VI. CONCLUSIONS Time delay and coherence bandwidth parameters have been extracted by measurements a specific microcellular environment. Channel parameters have been found to be variable with the transmitter location and the propagation environment including LoS and NLoS cases. Mean delay spread was found 0.314 µs and 0.731 µs for LoS and NLoS conditions respectively. Mean coherence bandwidth is remarkable high in LoS case reaching 3.748 MHz but it reduces to 0.259 MHz in NLoS cases. Additionally, significant differences in the correlation bandwidth values had been observed, for the two antennas positions. Moreover, the modeled inverse relationship given in equation (6) enables prediction of the coherence bandwidth under temporal fading conditions based on the RMS delay spread. A concentration of the RMS delay spread values occurs when the coherence bandwidth is below 2 MHz. REFERENCES [1]
Fig. 7. Coherence bandwidth as a function of the RMS delay spread. Using the values from 220 measured locations and neglecting the coherence bandwidth values, which the channel presents flat fading characteristics (B0.9 > 10 MHz), we fitted the data in a minimum mean square error sense. The mean square error is given by: 1 N (5) )2 σ 2 = ∑ (B0meas − B0pred .9 .9 N i =1 The modeled coherence bandwidth as function of the RMS delay spread follows an inversely proportional function given by: 1 B 0 .9 = (6) 3.98 ⋅τ RMS The derived mean square error fitting B0.9 value in equation (6) is 0.561 kHz. The mean square error for the 1 (50 ⋅ τ RMS ) relationship is 1.872 kHz whilst for the 1 (5 ⋅ τ RMS ) relationship the same value is 0.625 kHz. It is clear then that the best fit to the data is given by equation (6) predicting the coherence bandwidth with the best accuracy and the minimum error. In [9], Fleury has shown that the coherence bandwidth values are lower-bounded by arccos(c ) 2π , where c is the selected coherence level. Hence, in our case the coherence bandwidth is bounded by the relationship:
[2]
[3]
[4]
[5] [6]
[7]
[8]
[9]
R.J.C. Bultitude, G.K. Bedal, “Propagation characteristics on microcellular urban mobile radio channels at 910 MHz”, IEEE J. Select. Areas Commun., vol. 7, no. 1, pp. 31-39, Jan. 1989. J.A. Wepman, J.R. Hoffman, L.H. Loew, “Analysis of impulse response measurements for PCS channel modeling applications,” IEEE Trans. Veh. Technol., vol. 44, no. 3, pp. 613-620, Aug. 1995. V. Erceg et. al., “A model for the multipath delay profile of fixed wireless channels,” IEEE J. Select. Areas Commun., vol. 17, no. 3, pp. 399-410, Mar. 1999. U. Dersch, E. Zollinger, “Physical characteristics of urban micro-cellular propagation,” IEEE Trans. Antennas Propagat., vol. 42, no. 11, pp. 1528-1539, Nov. 1994. W.C.Y. Lee, Mobile Cellular Telecommunication Systems, McGraw Hill Publications, NY, 1989. P.A. Bello, “Characterization of randomly time-variant linear channels,” IEEE Trans. Commun. Syst., vol. CS11, pp. 360-393, Dec. 1963. D.C. Cox, “Distributions of multipath delay spread and average excess delay for 910 MHz urban radio paths,” IEEE Trans. Antennas Propagat., vol. AP-23, pp. 206213, Mar. 1975. D.C. Cox, R. Leck, “Correlation bandwidth and delay spread multipath propagation statistics for 910 MHz urban mobile channels,” IEEE Trans. Commun., vol. COM-23, no. 11, pp. 1271-1280, 1975. B. H. Fleury, “An uncertainty relation for WSS processes and its application to WSSUS systems,” IEEE Trans. Commun., vol. 44, no. 12, Dec. 1996.
Abstract - This paper reports the measurement and analysis of wideband radio channel at 1900 MHz within a special propagation environment as the Olympic Stadium of Athens. RMS delay spread values are evaluated as well as the coherence bandwidth of the channel is derived by the frequency correlation function. Mean delay spread was found 0.314 µs and 0.731 µs for LoS and NLoS conditions respectively. The mean coherence bandwidth that characterizes the entire area reaches 3.463 MHz providing wide transmission data rates. Correlation bandwidth is found to be inversely proportional to the RMS delay spread and modeled in a minimum mean square error sense. Keywords – wideband measurements, delay spread, coherence bandwidth. I. INTRODUCTION The application of current technology wireless communications systems in environments with special constructions such as stadiums, and the increased demand for high data rates and heavy telecommunication traffic has driven engineers to thoroughly investigate the propagation conditions and to assess typical and worst case scenarios for digital signal transmission. The characterization of the mobile radio channel requires the analytic and thorough investigation of three propagation phenomena, namely: time dispersion (or frequency selectivity), frequency dispersion (or time variance), and angular dispersion (or spatial variance). The mobile radio channel is well represented by a linear filter with randomly time variant characteristics. Time delay or time dispersion is due to the multiple scatterers in the channel, called multipath, and results in a frequency selectivity or frequency variance. There are numerous publications presenting results on the time dispersion phenomenon, most of them with omni and few with directive antennas [1-4], for urban, suburban and rural environments. In this paper we present time and frequency domain parameters extracted by measurements in the Olympic Stadium of Athens. This environment was especially selected in the view of Olympic Games to be held in Athens in 2004, and the expected wireless communications systems to be installed and verified in the wide area of the stadium.
0-7803-7589-0/02/$17.00 ©2002 IEEE
A measure of the delay spread depicted in the channel power delay profile is useful since the inter-symbol interference (ISI) which causes higher bit error rates in a digital system is related to this parameter. Under Rayleigh fading channels having wide-sense stationary uncorrelated scattering (WSSUS) characteristics [6], ISI is related to the root mean square (RMS) delay spread of the channel. Furthermore, one of the key performance indicators of the channel is the knowledge of the coherence bandwidth in different spectral regions over the proposed transmission bandwidth [6]. If the coherence bandwidth of the channel is less than the transmission bandwidth, channel protection techniques, such as coding, diversity or equalization need to be employed. In [8], a relationship between RMS delay spread and coherence bandwidth has been indicated, whereas in [9] a confinement boundary of the coherence bandwidth has been proposed for application to WSSUS systems. The presented results contain information about the delay spread, the coherence bandwidth for alternative antenna positions including line-of-sight (LoS) and non-line-of-sight (NLoS) situations. Furthermore, a relationship between delay spread and coherence bandwidth is proposed by fitting the measured data in a minimum mean square error sense. This paper is organized as follows. Section II deals with the measurement system describing the operation of the transmit/receive set. In Section III, the measurement environment and procedure is analyzed whereas in Section IV the data processing method is introduced and described analytically in order to evaluate the channel parameters. Section V contains results derived from the measurements, extracting the channel parameters such as time delay and correlation bandwidth. Finally, Section VI is devoted to discussion and conclusions. II. MEASUREMENT SYSTEM The equipment used for the measurements was a commercially available transmit/receive set whose operation is based on a variation of the sliding correlator principle [7]. The transmitter produces a user selected spread spectrum digital signal within the PCS band whilst the receiver is a wideband spread spectrum receiver, which can identify and demodulate CDMA signals and its multipath components.
PIMRC 2002
The received signal is down-converted to a 70 MHz IF and the output of the IF amplifier is led to the I/Q demodulator. The output of the demodulator is sampled by a pair of A/D converters with a 20 MHz sampling rate. The digital sampled pair of data stream is fed to four independent correlators for the identification of the multipath components. The receiver processor acts to identify the 13 strongest of the echoes it resolves and to report their powers and delays as its output. This set of power-delay samples constitutes the output data of a single snapshot. The powerdelay data are recorded by the instrument at a rate of 5 snapshots/s and stored to a PCMCIA card for further processing. The measurements performed at a carrier frequency of 1900 MHz. During the measurements the chip rate of the signal was always fixed at 9.83040 MHz, which results in a 0.1 µs time resolution. Initial trial measurements were conducted for different PN lengths in order to select the best length, accommodating all multipath components. The length of the pseudo-noise sequence was set at 51l. Finally, the transmitter output power was fixed at +40 dBm, and omni-directional antennas were used in both transmitter and receiver having a gain of 5 dBi. III. MEASUREMENT ENVIRONMENT The Olympic Stadium of Athens is considered as a special area of interest due to its specific architecture. The measurements took place within the stadium with no rain and without spectators. The transmitter was placed in two different positions as depicted in Fig. 1 at a height of 1.9 m above floor. The first position (P1) is at the upper stage of the stadium at the last row looking at the centerline of the field. The second position (P2) is under the shelter of the upper stage, in front of the VIP section looking also at the centerline of the field.
semicircle of the stadium respectively. Each semicircle is divided in two sections hence the entire stadium is divided into four measured quarters (Q1-4) as shown in Fig. 1. The distance between the corridor of the upper stage and P1 is 23 m. Each measured quarter is approximately 140 m and 1min recordings conducted at 10-m intervals along the corridor. The measurements always started at the centerline of the field S-point as indicated in Fig. 1. Furthermore, measurements collected around the running field (F) of the stadium as shown in Fig. 1, in 10-m intervals covering a total distance of 450 m. At each quarter the measurements started at the location aligned to the centerline of the field. The measurements along the running field started at the location aligned to the matrix of the stadium right to transmitter P1. Finally measurements performed at the entrance of the gates of the stadium. In every measurement point, the receiver was stationary and the recording duration was approximately 1 minute resulting at 300 snapshots to be stored in the memory card. The same measurements performed for both transmitter positions in order to achieve alternative propagation conditions. For every measured quarter, gates, and along the field, for both transmitter positions the time delay and the coherence bandwidth of the channel is evaluated. For both transmitter positions, powerdelay data were collected in 307 different locations including LoS and NLoS conditions. IV. MEASUREMENT ANALYSIS The purpose of the measurement processing is the extraction of statistical parameters that describe the mobile radio channel in the area under consideration. The set of recorded data was preprocessed to make it suitable for our analysis. There were noise level, frequency resolution, and other issues that had to be addressed. Therefore, we performed the following steps prior to data reduction. In each snapshot, the 13 most significant echoes were recorded. Some noise peaks may, by random chance, be strong enough to appear as weak echoes. Therefore, a threshold referenced to the noise floor had to be set above which echoes are counted and below which they are ignored. We chose a threshold of 6 dB above the mean noise floor. The mean noise floor was found by linearly averaging echo-free noise samples over many data records. The most significant parameter derived from the data processing is the received power as a function of the time delay known also as the power delay profile (PDP). The measurement system records the received power at the moment t with a propagation delay τ ( h(t ,τ ) ). The 2
Fig. 1. Measurement environment and measurement locations. The receiver was always on a cart and the antenna was fixed at 1.8 m above the ground. The cart was moving along the corridor of the upper stage in the same and the opposite
power delay profile is obtained from the linear power versus delay, averaged over all the snapshots in a 1-min period (300 snapshots):
{
P(τ ) = E t h(t ,τ )
2
}
where E t {•} declares the time average value.
(1)
The time resolution of the receiver is 0.1 µsec (which corresponds to a length difference of 30 m between potential scatterers). During the data binning process we assigned each echo to the nearest value of delay equal to a multiple of 0.1 µs. The average received power in every bin is normalized to the maximum received power. A significant parameter to be evaluated is the RMS Delay Spread ( τ RMS ), which characterizes the frequency selective behavior of the channel and is given by:
∑ P(τ ) ⋅ τ ∑ P(τ )
∑ P(τ k ) ⋅ τ k τ RMS = k (2) − k k ∑ P(τ k ) k k where k is the number of the bin, τ k is the time delay of the k -bin and P(τ k ) is the average power of the k -bin. The Fourier transform of the normalized PDP gives the normalized frequency correlation function: N −1 2πn∆f (3) R H (∆f ) = ∑ P(τ n ) ⋅ exp − j N n=0 where Ν is the number of bins contained in the normalized PDP. In order to increase the frequency resolution we used a noise padding procedure technique resulting a frequency resolution of 2.44 kHz. k
2 k
1-min recording with relative delays until 3 µs. We observe that the multipath components arrive at the receiver with relative delays of 0.35 µs, 0.75 µs and 1.25 µs. Finally it is clear that the power of the direct component is not constant and exhibits a variation of about 10 dB.
2
It is noteworthy that the frequency correlation function characterizes all the system that intercedes between the transmitted and received signal. In other words, the function is affected also by the RF sections of the system, the connectors and the cables. For this reason it is necessary to calibrate the measurement system. The measurement procedure is repeated with the same settings in transmitter and receiver but connecting the receiver directly to the transmitter via a coaxial cable (back-to-back). Then the recorded data are processed with the same way as the real measured data. The normalized frequency correlation function that we derive, characterizes the measurement system. Therefore, the normalized frequency correlation function, which characterizes the channel itself is derived by dividing the measured function with the normalized function of the system. Based on the real value of R H (∆f ) , we calculate the coherence bandwidth for 90% correlation, in other words: (4) R H (∆f coherencebandwidth ) = 0.9
Fig. 2. Successive snapshots as a function of time. Fig. 3 and 4 depict the average power delay profile for LoS and NLoS condition respectively. In both cases the receiver is located in the corridor of Q1 approximately 20 m away from the starting point. For LoS propagation the transmitter was in P1 whereas for the NLoS situation the transmitter was in P2. We also provide the normalized frequency correlation functions derived by the Fourier transformation of the average PDPs through equation (3). The x-axis in the power delay figures represents the number of the bin with each bin to be 0.1 µs. Hence, bin 20 corresponds to a 2 µs time delay.
Fig. 3. Average PDP and frequency correlation function for LoS condition.
The resulted coherence bandwidth values comprise a sufficient sample to provide valid statistical characteristics. V. RESULTS A. Channel Parameters versus Transmitter Position Fig. 2 shows the result of successive snapshot recordings for a specific location. The transmitter was in P1 while the receiver was in Q1, approximately 37 m away from Tx. For better depiction we present only the first 4.5 seconds of the
Fig. 4. Average PDP and frequency correlation function for NLoS condition.
It is clear that in LoS situation the RMS delay spread is much smaller (0.303 µs) than in the NLoS (0.893 µs). The most significant multipath component in Figure 3 (LoS) arrives with zero delay whilst in Fig. 4 (NLoS) the most significant component arrives with a delay of 2.5 µs. One may observe the frequency correlation function to drop faster with frequency separation in NLoS condition providing worse channel quality having a coherence bandwidth of 162 kHz for 0.9 correlation. In LoS propagation environment the bandwidth is more than double (479 kHz) considering the same Rx position.
as well as its statistics for LoS and NLoS propagation condition respectively. As it is expected the mean RMS delay spread exhibits larger values in NLoS (0.731 µs) than in LoS (0.314 µs) conditions. Furthermore, for the 90th percentile of delay spreads, the value for LoS case is 0.752 µs whereas for NLoS case this value increases significantly to 1.085 µs. It is worthwhile to mention that the CDFs were derived by 282 LoS and 25 NLoS measured locations.
Table 1 shows the results of RMS delay spread and coherence bandwidth for 0.9 correlation (B0.9 in MHz) for the different measurement areas of the stadium taking into account the two alternative transmitter positions. Table 1 Channel parameters for different transmitter positions. P1
P2
τRMS (µs)
B0.9 (MHz)
τRMS (µs)
B0.9 (MHz)
Q1
0.315
2.570
0.370
4.510
Q2
0.199
6.191
0.547
1.690
Q3
0.187
3.881
0.363
1.454
Q4
0.202
4.831
0.414
2.154
F
0.477
1.215
0.315
4.836
Gates
0.573
0.660
0.211
5.777
In average, areas Q1-4 present better channel parameters, when the transmitter is located in P1, since there is better LoS propagation condition. This is more obvious in areas Q3 and 4, comparing the derived bandwidths for P1 and P2. The latter position is under the shelter of the stadium resulting in worse propagation environment with increased clutter around the transmitter. This increases the multipath components with relative delays greater than 2 µs as shown in Fig. 4 resulting in increased values of RMS delay spread and worse channel quality. The opposite happens in the field and at the gates of the stadium (F and Gates areas) where P2 provides better channel characteristics than P1. With transmitter in P2 the measured correlation bandwidth in the gates is up to 5.777 MHz whilst in P1 reaches only 660 kHz. This occurs because P2 provides LoS conditions in the majority of the gates, depressing significantly the multipath phenomena and the RMS delay spread values. In general, if we combine the two positions, each can provide the best channel quality in different areas. Hence, P1 is unique for areas Q1-4 and P2 for areas F and Gates as it is evident in Table 1. In Fig. 5 and Fig. 6 are shown the cumulative distribution functions (CDFs) of the measured RMS delay spread values
Fig. 5. CDF of the measured RMS delay spread for the entire stadium considering LoS condition.
Fig. 6. CDF of the measured RMS delay spread for the entire stadium considering NLoS condition. Table 2 Statistics of the channel parameters for the entire stadium environment. τMAX (µs)
τRMS (µs)
B0.9 (MHz)
Min Value
0.000
0.000
0.103
Max Value
7.700
1.556
>10
Mean Value
2.026
0.348
3.463
Median Value
1.100
0.235
0.921
St. Deviation
1.980
0.308
4.205
90th Percentile
5.400
0.836
10
Finally, Table 2 presents the overall channel parameters and their statistics concerning the entire area of the stadium. The maximum delay spread (τMAX) the RMS delay spread (τRMS) and the 0.9 correlation bandwidth (B0.9) values are presented. The mean values of the mentioned parameters are 2.026 µs, 0.348 µs and 3.463 MHz respectively. We should mention that the overall statistics derived from 306 measured locations. B. Delay Spread versus Coherence Bandwidth Fig. 7 depicts a scatter plot of the measured coherence bandwidth values derived by the frequency correlation function, as a function of the RMS delay spread, derived by the average PDP. A relationship is observed with the coherence bandwidth being inversely proportional to the RMS delay spread.
B c = 0 .9 ≥ 1 13.931 ⋅τ RMS a value well below the one given in equation (6).
(7)
VI. CONCLUSIONS Time delay and coherence bandwidth parameters have been extracted by measurements a specific microcellular environment. Channel parameters have been found to be variable with the transmitter location and the propagation environment including LoS and NLoS cases. Mean delay spread was found 0.314 µs and 0.731 µs for LoS and NLoS conditions respectively. Mean coherence bandwidth is remarkable high in LoS case reaching 3.748 MHz but it reduces to 0.259 MHz in NLoS cases. Additionally, significant differences in the correlation bandwidth values had been observed, for the two antennas positions. Moreover, the modeled inverse relationship given in equation (6) enables prediction of the coherence bandwidth under temporal fading conditions based on the RMS delay spread. A concentration of the RMS delay spread values occurs when the coherence bandwidth is below 2 MHz. REFERENCES [1]
Fig. 7. Coherence bandwidth as a function of the RMS delay spread. Using the values from 220 measured locations and neglecting the coherence bandwidth values, which the channel presents flat fading characteristics (B0.9 > 10 MHz), we fitted the data in a minimum mean square error sense. The mean square error is given by: 1 N (5) )2 σ 2 = ∑ (B0meas − B0pred .9 .9 N i =1 The modeled coherence bandwidth as function of the RMS delay spread follows an inversely proportional function given by: 1 B 0 .9 = (6) 3.98 ⋅τ RMS The derived mean square error fitting B0.9 value in equation (6) is 0.561 kHz. The mean square error for the 1 (50 ⋅ τ RMS ) relationship is 1.872 kHz whilst for the 1 (5 ⋅ τ RMS ) relationship the same value is 0.625 kHz. It is clear then that the best fit to the data is given by equation (6) predicting the coherence bandwidth with the best accuracy and the minimum error. In [9], Fleury has shown that the coherence bandwidth values are lower-bounded by arccos(c ) 2π , where c is the selected coherence level. Hence, in our case the coherence bandwidth is bounded by the relationship:
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