NTIA Report 99-369

Advanced Antenna Test Bed

Characterization for Wideband

Wireless Communications

Perry F. Wilson

Peter B. Papazian

Michael G. Cotton

Yeh Lo

U.S. DEPARTMENT OF COMMERCE

William M. Daley, Secretary

Larry Irving, Assistant Secretary

for Communications and Information

August 1999
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iii

CONTENTS

Page

LIST OF FIGURES ........................................................................................................... ii

LIST OF TABLES ............................................................................................................ iv

ABSTRACT ........................................................................................................................1

1. INTRODUCTION ........................................................................................................1

2. MEASUREMENT SYSTEM DESCRIPTION ............................................................2

3. CELL DESCRIPTION ..................................................................................................6

4. DELAY SPREAD .........................................................................................................7

4.1 APDP Analysis ...............................................................................................7

4.2 Statistics ..........................................................................................................8

4.3 Spatial Diversity .............................................................................................9

5. FAST FADING .............................................................................................................9

5.1 Frequency Selective Fading versus Bandwidth ............................................10

5.2 Spatial Diversity – General Comments ........................................................11

5.3 Fast Fading Statistics and Burst Duration .....................................................11

5.4 Channel Equivalence ....................................................................................13

5.5 Spatial Diversity – Results of Measured Data ..............................................13

6. CONCLUSION ...........................................................................................................14

7. REFERENCES ...........................................................................................................17

8. FIGURES ....................................................................................................................18
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v

LIST OF FIGURES

Page

Figure 1. Four element linear antenna array spaced 2λ, 5λ, 

and 10λ from leftmost element. ........................................................................18

Figure 2. Sample calibration impulse. ............................................................................19

Figure 3. Example of a received impulse and the resulting normalized PSD. ...............20

Figure 4. Drive routes and received signal strength (RSS) for NE 

and SE sectors of the GMM cell. ....................................................................21

Figure 5. Path loss versus distance for the NE sector of the GMM cell. 

The least squares curve fit has a slope of 4.89. ...............................................22

Figure 6. Path loss versus distance for the SE sector of the GMM cell. 

The least squares curve fit has a slope of 4.08. ...............................................23

Figure 7. An example of a raw APDP and corrected APDP (NE drive, 

burst 1, impulse 8, channel 1). The corrected APDP consists 

of the signal within 20 dB of the peak signal time shifted to t = 0. ................24

Figure 8. The peak power for the 8286 valid NE drive APDPs. 

The APDPs are ordered sequentially in time. .................................................25

Figure 9. The peak power for the 8735 valid SE drive APDPs. 

The APDPs are ordered sequentially in time. .................................................26

Figure 10. Delay spread statistics for the NE data set. Shown are maximum 

delay, mean delay, and RMS delay spread probabilities. ...............................27

Figure 11. Delay spread statistics for the SE data set. Shown are maximum 

delay, mean delay, and RMS delay spread probabilities. ...............................28

Figure 12. Diversity delay spread statistics for the NE data set. Plotted 

are the four channel minimum (red) and four channel 

mean (blue) probabilities for the maximum delay, mean delay, 

and RMS delay spread. ...................................................................................29

Figure 13. Diversity delay spread statistics for the SE data set. Plotted

are the four channel minimum (red) and four channel 

mean (blue) probabilities for the maximum delay, mean delay, 

and RMS delay spread. ...................................................................................30
vi

LIST OF FIGURES (cont’d)

Figure 14. The normalized power spectral density for the four bandwidths 

(19.6 kHz-blue, 1.25 MHz-green, 5.0 MHz-red, 10 MHz-cyan) 

and four channels for a typical burst (NE drive, Burst 1). ..............................31

Figure 15. Distribution profiles (combined channel data) for the NE data 

set for the four bandwidths. .............................................................................32

Figure 16. Distribution profiles (combined channel data) for the SE data 

set for the four bandwidths. .............................................................................33

Figure 17. The path length per burst for the NE data set. 118/220 bursts 

are valid (in the 20-50λ range). .......................................................................34

Figure 18. The path length per burst for the SE data set. 132/206 bursts 

are valid (in the 20-50λ range). .......................................................................35

Figure 19. The straight line path length in wavelengths versus vehicle speed 

for burst durations of 0.2 s to 1.0 s in 0.2 s steps (upper curves) 

and the data points per wavelength for a 128 impulse burst for 

the same range of values (lower curves). ........................................................36

Figure 20. CDFs for channels 1-4 versus bandwidth for the NE (upper) 

and SE (lower) data sets. .................................................................................37

Figure 21. Selection diversity CDFs for the NE (upper) 

and SE (lower) data sets. .................................................................................38

Figure 22. Equal gain diversity CDFs for the NE (upper) 

and SE (lower) data sets. .................................................................................39

Figure 23. Maximal ratio combining diversity CDFs for the NE (upper) 

and SE (lower) data sets. .................................................................................40

Figure 24. 2 channel diversity CDFs and SE (lower) data sets. ......................................41

Figure 25. 3 channel diversity CDFs for the NE (upper) and SE (lower) data sets. .......42

Figure 26. 4 channel diversity CDFs for the NE (upper) and SE (lower) data sets. .......43
vii

LIST OF TABLES

Page

Table 1. Data Acquisition and RF Parameters used for Diversity Tests .........................4

Table 2. The 90% Fade Level Diversity Gain (dB) ........................................................15

Table 3. The 99% Fade Level Diversity Gain (dB) ......................................................16
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___________________

* The authors are with the Institute for Telecommunication Sciences, National 

Telecommunications and Information Administration, U.S. Department of Commerce, 

Boulder, CO 80303

ADVANCED ANTENNA TEST BED CHARACTERIZATION FOR 

WIDEBAND WIRELESS COMMUNICATION SYSTEMS

Perry Wilson, Peter Papazian, Michael Cotton, and Yeh Lo*

An advanced antenna test bed for evaluating adaptive antennas and next-generation 

mobile communication systems is described. The key elements of the data acquisition

system are 8 simultaneous channels, broadband impulse channel sounding, high speed

analog to digital data conversion and storage, and flexible post processing. Mobile

channel sounding measurements were made in two sectors at 1920 MHz using 4

receiving antennas. Received signal strength and transmission loss are examined. Path

loss exponents for the two sectors are found to be 4.89 and 4.08. These are typical for

urban to suburban environments. RMS delay spreads for the two sectors are found to be

less than 1.38 μs and 0.65 μs at the 90% probability level and 3.14 μs and 1.35 μs at the 

99% probability level respectively. Fast fading reduction using antenna diversity (up to 4 

antennas) and increased channel bandwidth (19.6 kHz, 1.25 MHz, 5.0 MHz, and 10.0

MHz) is examined. Three signal combining methods are considered: selection diversity,

equal gain combining, and maximal ratio combining. Measured results indicate that

increasing the number of diversity antennas or the channel bandwidth significantly

reduces fading. Maximal ratio combining yields the largest diversity gain exceeding 11.0 

dB and 17.0 dB at the 90% and 99% fast fade depth probability levels respectively when

all four channels are used. 

Key Words: adaptive antennas; advanced antenna test bed; equal gain combining; fast

signal fading; impulse channel sounding; maximal ratio combining; power 

delay profiles; RMS delay spread; selection diversity; transmission loss;

wideband measurements

1. INTRODUCTION

Adaptive, active, or “smart” antennas can continuously change their radiation pattern as

needed for optimum performance. Wideband wireless communication systems can use

adaptive antennas to track a mobile user. Adaptive antennas thus have the potential to

increase service capacity and the performance/cost ratio for a number of land-mobile 

radio systems, including cellular telephone and personal communication service (PCS). A 

number of researchers are working on adaptive antenna technology, and several adaptive

antenna systems are being developed and marketed. However, common, realistic methods 

for testing the comparative performance of systems and signal processing algorithms are
2

not available. A standardized measurement process and test environment is necessary

before the cost benefits of these complex systems can be assessed.

This report describes an advanced antenna test bed (ATB) developed by the Institute for

Telecommunication Sciences (ITS) which can be used for the comparative testing of

adaptive systems and data processing algorithms. Central to the metrology is a realistic,

well defined test cell and a multi-channel, high-bandwidth measurement system. The

ATB uses the Green Mountain Mesa (GMM) cell which is part of the Boulder Industry

Test Bed (BITB). The BITB provided a common environment for the field testing of PCS 

air-interface standards by the Joint Technical Committee (JTC) on Wireless Access. A

summary of these tests has been prepared by Wepman [1]. Measurement results for all

the current PCS standards are available and can be used for comparison with advanced

antenna tests. The wideband measurements reported here also serve as a base line for

measuring the performance of advanced antennas and systems. 

The report is organized as follows. Section 2 gives a brief description of the ATB digital 

channel probe. The channel probe uses a spread spectrum measurement technique to

approximate the impulse response of a radio channel over a large bandwidth. Impulse

response data are used to characterize the propagation environment of the GMM cell, as 

detailed in Section 3. Signal strength (peak impulse power), as a function of position in

the cell, and basic transmission loss, versus transmitter-to-receiver separation, are

examined. Section 4 uses the impulse data to generate delay statistics for the cell.

Minimum delay, mean delay, and delay spread are considered. In addition, diversity gain 

in the form of best channel (least delay spread) versus mean channel performance is

investigated. Section 5 uses the impulse power spectral density (PSD) data to evaluate

fading reduction and diversity gain for a narrowband signal and three wideband signals.

Various antenna combinations (1-4 antennas) are also examined for the four signal

bandwidths. The bandwidths were chosen to match the existing CDMA and wideband 

CDMA standards. Section 6 summarizes the results.

2. MEASUREMENT SYSTEM DESCRIPTION

The ATB uses an upgraded version of the Institute for Telecommunication Sciences

(ITS) digital channel probe (DCP). This probe has been used to make impulse response 

measurements in the 900-MHz cellular and 1900-MHz PCS bands [2-3]. The DCP

transmits a maximal-length pseudo-noise (PN) code. The PN code is used to biphase shift 

key (BPSK) modulate the RF carrier. The transmitter is both frequency and bit-rate agile 

and can produce multiple PN codes and frequencies simultaneously. This is useful for

polarization and spatial diversity studies. 

The transmitted signal, modified by the radio channel, is received, down-converted to an 

intermediate frequency (IF), and then digitized. If desired, the in-phase and quadraturephase components can then be determined via software. A complex impulse response can 

be generated by cross-correlating a copy of the transmitted PN code with the received

signal after down-conversion to baseband using software. Because the DCP digitizes at
3

IF, it can measure an impulse response much faster than an analog sliding correlator. In

particular, the time window for this digital system is the length of one PN code whereas

the time window for an analog sliding correlator is some larger multiple (>1) of the PN

code length [4]. This allows better characterization of a rapidly changing radio channel.

It also avoids problems with nonlinear components when making wideband

measurements and allows accurate wideband amplitude and phase calibration of the

system. This is essential for digital beam-forming applications. 

The probe is currently configured to transmit a 511 bit PN word at 10 Mb/s using a 1.92

GHz carrier. The theoretical impulse signal power to correlation noise power level is 54

dB for the 511 bit PN sequence. The processing gain of the system is 27 dB when the

signal power equals the noise power. Multipath signals separated by 100 ns can be

resolved to a maximum delay of 51 μs using this setup. A nominally flat 12 MHz

bandwidth power spectral density (PSD) spectrum results after normalizing to a

calibration curve. The 12 MHz bandwidth is approximately the –10 dB roll-off of the

calibration PSD. The probe can also be configured for higher bit rates (higher bandwidth 

and time resolution), longer codes (longer maximum delays), different code types and

other RF carriers. Additional features of the system include time of flight and Doppler

measurements. System timing is maintained using rubidium oscillators at the transmitter

and receiver. These clocks synchronize the PN code generators, phase lock all local

oscillators and provide sampling clocks for the digitizers. Multiple digital signal

processors (DSPs) and a host computer system control data acquisition. The DSPs can be 

configured for real time processing or data streaming. 

For these tests, data acquisition was set to the burst mode. In this mode a burst of data is

collected in rapid sequence and stamped with GPS coordinates and time. The next data

burst is acquired after a programmable delay which was set to 3 seconds. Within a burst,

the delay between impulses was set to 3 ms. This high resolution enables Doppler

spectrum measurements. The number of impulses per burst was set to 128, resulting in an 

overall burst duration of approximately 388 ms. For typical vehicle speeds a burst

covered from 20-60 wavelengths. This is important when analyzing narrowband fading.

By using the vehicular velocity from the GPS data, log normal (slow fading) could be

averaged out from the narrowband data leaving only the fast fading components. 

Table 1 below summarizes the data acquisition parameters used for the diversity

measurements as well as the range of permissible values for the ATB system. Block

diagrams for the system can be found in [5].

A mobile transmitting antenna and a fixed receiving antenna array were used. The mobile

transmitter used an omni-directional dipole antenna with 6.7 dBi gain and 17.5° vertical

beamwidth. This antenna was mounted at a height of 2.4 m on a van equipped with a

GPS/dead reckoning system. The maximum transmitter power is 10 W. The receiving array

consisted of four PCS flat panel antennas horizontally spaced 2λ, 3λ, and 5λ apart. The

antenna array is shown in Figure 1. The 3 dB azimuthal beamwidth of each antenna is 86°

and the vertical beamwidth is 8°. The nominal gain for each antenna is 14 dBi.
4

Table 1. Data Acquisition and RF Parameters used for Diversity Tests

Configurable System Parameters

Parameter Diversity Tests ATB System

Receiver Channels 4 1-8

Carrier Frequency 1.92 GHz .45 – 6 GHz

Bit Rate 10 Mb/s .1 – 50 Mb/s

Resolution 100 ns 10 μs – 20 ns

Code Type Maximal Length Programmable

Code Length 511 bits Programmable

Acquisition Mode Burst Continuous or Burst

Positioning GPS/Dead Reckoning GPS/Dead Reckoning

Transmitters 1 Multiple

Data Processing Post Post or Real Time

The range of the system may be estimated using a modification of the free space path loss

equation

2

4













=

d

g g

p

p

r t

t

r

p

l

 , (1)

where pr and pt are the received and transmitted powers, gr and gt are the receive and

transmit antenna gains, and d is the separation. In a real environment the path loss will be

greater than in free space due to obstacles. Path loss (PL) exponents n are typically in the

range 2-4 with 3.5 typical for a suburban environment. The free space equation may be

modified to include a short free space path length d0 to account for the raised receive

antenna followed by a path length d/d0 (assuming d > d0) with a path loss exponent n [6]

n

r t r t r t

t

r

d

d

d

g g

d

d

d

g g

d

g g

p

p





























 →



























 =











=

0

2

0

2

0

2

0

2

4 4 4p

l

p

l

p

l

. (2)

Expressed in dBs (upper cases), (2) can be written as follows

( ) 10 log ( )

( ) 20log (4 / )

( ) ( / )

10

10

0 0

PL d n d

PL d d

PL P P G G PL d PL d d

n

fs

t r t r fs n

=

=

= − + + = +

p l , (3)

where the subscript fs denotes the free space path loss (isotropic antennas) and the subscript 

n indicates an exponent average received signal power decrease. Consider the following

range estimate: Pt = 35 dBm (the transmitter is typically driven below the 40 dBm (10 W)

maximum power to avoid non-linearities), Pr = -90 dBm (the end of the linear receiver 
5

calibration range although –98 dBm is possible), Gt = 3.7 dBi (6.7 dBi antenna gain less 3

dB cable loss), Gr = 12 dBi (14 dBi antenna gain less 2 dB cable loss), d0 = 100 m

(approximate clear line of sight), and n = 3.5 (typical for suburban environments). Inserting 

these and solving for d yields approximately 6 km. This range is consistent with the

measurement results presented here. A pure free space environment (n = 2) would yield a

range on the order of 135 km. 

The variable antenna spacing was chosen so that channel independence as a function of

antenna spacing can be examined. A typical rule in mobile communications is to use at least 

a 10λ spacing to ensure channel independence. In applications where space is limited

narrower separations would be desirable. The array here allows separations of 2λ, 3λ, 5λ, 

8λ, and 10λ to be considered. Channel independence, as a function of antenna spacing, will

be the topic of a separate investigation. Within this report it will be assumed that channels

are approximately independent when combining them for diversity statistics. This may be a 

poor assumption in the 2λ separation case. However, the 10λ separation is always

considered as well and provides a reasonable check.

The system is calibrated in a back-to-back mode during field testing. When calibrating,

the transmitter maximum non-compressed output power is routed via a fixed attenuator,

variable attenuator, directional coupler and a power splitter to each receiver channel. The 

variable attenuator is used to adjust the input power over the dynamic range of the system 

and a power meter is used to monitor input power. The transmitter used a 2.5 W linear

amplifier. The maximum input power was set at –35 dBm per channel and the dynamic

range of the AGC amplifiers is 60 dB. The sensitivity of the system for a 20 MHz

bandwidth is –98 dBm and the processing gain for the 511 bit code is 27 dB, as discussed 

above. By calibrating from –35 to –115 dBm, system performance can be monitored from 

the maximum input signal to noise. Figure 2 shows a sample calibration impulse (no

propagation channel). The impulse well approximates the triangular shape of an ideal

autocorrelated PN code and the 52 dB peak closely approaches the 54 dB theoretical

limit. 

Figure 3 shows an example of a signal after mobile channel propagation. Such received

impulses form the basis for the statistics that follow. For this example the power delay

profile (PDP) shows significant multipath (a). The received signal strength (RSS)

discussed in Section 3 is the PDP peak. The delay statistics in Section 4 are based on the 

PDP spread. It should be noted that the delay statistics presented in Section 4 are based

on the full impulse data and thus the 20 MHz null-to-null bandwidth shown in (b). The

PSD (b) can be normalized by a calibration impulse PSD (c) resulting in a normalized

PSD (d). The apparent frequency selective fading near the +/- 10 MHz edges of the

normalized PSD is due to poor signal-to-noise ratio (S/N) and does not represent usable

data. The usable bandwidth for the configuration used in this report is on the order of 12-

15 MHz. The fading statistics in Section 5 are based on normalized PSDs (NPSDs).
6

3. CELL DESCRIPTION

The ATB utilizes the Green Mountain Mesa (GMM) cell of the BITB. During the BITB

study [1] the GMM cell receiver was located on a hilltop, 120 m above the Boulder Valley

floor, within a large open area in a suburban residential section of Boulder. For the tests

reported here, the receiving antenna site was moved to the roof of wing 4 of the Radio

Building on the Department of Commerce (DOC) Campus. This put the base of the site 14

m above the floor of Boulder Valley. The base elevation for this site is 1651 m and the

antenna array height is 6.7 m above the base. The GMM cell is essentially east of the DOC

location. Measurements to the west are not feasible because the foothills of the Rocky

Mountains rise rapidly to the west of the DOC campus.

The GMM site is a typical suburban environment with moderate delay spreads and

moderate to high path loss. To characterize the test area, the received signal strength

(peak impulse power) and basic transmission loss were measured for two GMM cell

sectors. A map showing the ITS (receiver) location, the two drive routes (sectors), and

the RSS is shown in Figure 4. The drive routes were selected to maximize data quality

and the percentage of data with acceptable S/N, as needed for delay spread and

normalized power spectral density calculations. A main NW-SE artery (US 36) separates

the two drive routes. For the route north of US 36 the antenna array normal was directed 

47° north of east (approximately NE) and for the south route the array normal was

directed 13° south of east. For simplicity the two routes will be designated NE and SE

respectively in the discussion that follows. 

The RSS data were used to calculate the basic transmission loss (Lbt) for the NE and SE

sectors, as shown in Figures 5-6. The transmission loss data shown are based on the local 

mean RSS for each burst (averaged over the 128 impulses). The data are plotted versus

distance on a log scale. Also shown is a linear curve fit (least squares) of the form

y = n10log10 (d ) + b (4)

which represents the non free space path loss in equation (3) above. Using this fit, the

basic transmission loss has a slope n of 4.89 for the NE sector and 4.08 for the SE sector. 

These are typical for low antenna heights in the 1.9 GHz band [6-7].
7

4. DELAY SPREAD

The delay statistics presented in this report are based on averaged power delay profiles

(APDPs)

∑=

=

N

k

i k i PDP t

N

APDP t

1

( )

1

( ) , (5)

where ti is the i-th time step (sampling point), and N is the number of PDPs used to form 

the APDP. APDPs are used to reduce the noise effects. The present ATB burst

configuration software sets the number of impulses in a burst to a power of 2, typically

32, 64, or 128 (overall range 1-256). APDPs are calculated from a group of 8 successive

PDPs similar to the 10 PDPs used in previous studies [2-3]. The choice of 8 as the group 

size makes efficient use of all the burst data. APDPs are computed separately for each

channel. 

4.1 APDP Analysis

Impulses within an APDP group (8 successive PDPs) are first checked for sufficient

power. The impulse with the maximum total signal power is found by integration over

the full time interval. Impulses with total signal powers more than 10 dB below this

group maximum are discarded for the APDP statistics. Groups containing less than 4

usable impulses are discarded as well. Thus, N ranges from 4 to 8 in (5) above. Valid

impulses within a group are next aligned with the maximum impulse. Alignment is

achieved by calculating the cross correlation and then time shifting each valid impulse

accordingly. The aligned impulses are then averaged via (5) to form the APDP.

The interval of discrimination (ID) is here defined as the difference in power levels

between the peak of the intended signal (impulse) and the peak noise. It is desired that an 

APDP have an ID of at least 20 dB to insure that noise is not calculated into the fading

statistics. A 23 dB ID criterion will be used. A difficulty is determining the end of the

intended signal and the beginning of noise only. It is assumed here that the impulse

occurs near the beginning of the 51 μs time interval so that the last 10% of the time

interval captured may be considered noise. Most meaningful multipath signals should

reach the receiver within 20 μs of the shortest path signal. This corresponds to an

increased path length of 6 km. Signals arriving later than 46 μs (final 10%) should be

sufficiently attenuated so as not to be of interest. Absolute time synchronization between 

the transmitter and the receiver allows the impulse trigger of the transmitted signal to be

positioned at the beginning of the captured time interval. Thus, the ID is determined here 

by comparing the APDP peak during the first 90% of the measured time interval to the

APDP peak during the last 10% of the measured time interval. If the ID is less than 23 dB 

the APDP is discarded. 

Although a 23 dB ID criterion has been applied to the APDP, only signal levels within 20 

dB of the APDP peak are included in the delay statistics. Thus, for each valid APDP the
8

signal of interest is determined and then time shifted such that the impulse begins at time 

zero. These corrected APDPs are the basis for all delay spread statistics that follow.

Figure 7 shows an example of a raw and a corrected APDP. For this APDP only the first 

echo beyond the initial signal is retained for the delay statistics.

Data are presented in two groups based on two GMM cell sectors. These are designated

NE and SE, as discussed above (see Figure 4). The sectors were measured using 220 and 

216 bursts respectively. Each burst consisted of 128 impulses on 4 simultaneous

channels. Thus, the two basic data sets consist of 112,640 (SE) and 110,592 (NE)

impulses resulting in 14,080 and 13,824 APDPs respectively. Of these APDPs, 

8286/14,080 (59%) and 8735/13,824 (63%) are found to be valid under the constraints

described above. The valid APDPs’ peak powers for the NE and SE drives are shown in 

Figures 8-9. The NE drive (Figure 8) is basically an out and back route relative to the

receiving antenna. The SE drive data (Figure 9) are somewhat discontinuous with a

larger segment of the drive at a relatively far distance compared to the NE drive. The NE 

drive is largely toward lower elevations (creek valley) and the SE drive is more toward

higher elevations (with respect to the receiving antenna). Thus, we expect more line of

sight paths for the SE drive.

4.2 Statistics

Three delay measures will be considered: maximum delay, mean delay, and RMS delay

spread. These will be based on the corrected APDPs. The data from all 4 channels are

combined together in a single data set for the purpose of the delay statistics. 

The maximum delay is here defined as the time delay between the first and last signals of 

the corrected APDPs. Since the corrected APDPs have been shifted so that the initial 

signal occurs at t = 0, the maximum delay is equivalent to the length of the corrected

APDP (see Figure 7).

The mean delay (d) is the time weighted average, or first moment, of the corrected

APDPs normalized by the average signal power,

∑

∑

∑

∑

=

=

=

= = = = N

k

k

N

k

k k

N

k

k

N

k

k k

P t

t P t

P t

N

t P t

N

mean delay d

1

1

1

1

( )

( )

( )

1

( )

1

 , (6)

where tk is the time delay (in seconds) relative to the start of the corrected APDP (i.e., t = 

0), P is the signal power (W), and N is the index of the final corrected APDP signal point 

considered. 

The RMS delay spread (S) measures the standard deviation of the delay spread of each

corrected APDP about its mean delay (d). It is the second central moment of the corrected 

APDP given by
9

1/ 2

1

1

2

( )

( ) ( )

























−

= =

∑

∑

=

=

N

k

k

N

k

k k

P t

t d P t

RMS delay spread S . (7)

Figures 10-11 show the cumulative probability distributions for the NE amd SE data

maximum delay, mean delay, and RMS delay spread. The NE data show more multipath

than the SE data as expected from the terrain profile discussed above. The data here are

plotted on the same scale as in [3, Figures 5.4-5.6] for comparison, and fall somewhere

between the hilly rural cell and the urban high-rise cell. This is most clear for the NE

sector data set. The NE sector, while primarily suburban, does feature some large

buildings (reflectors) along with undulating terrain. Thus, the result is consistent with the 

previous measurements.

4.3 Spatial Diversity

Spatial diversity may be used to improve the delay statistics by choosing the APDP with

the least delay effect from the 4 available channels. This assumes that at least two of the

APDPs are valid. The best channel can be compared to the individual channels, or to the 

mean of the 4 channels (valid APDPs only). For this study, the latter choice is used. Only 

cases where at least two of the APDPs are valid are included in the statistics.

Figures 12-13 show the cumulative probability distributions for the NE and SE data sets

where the channel with the best (least) delay spread statistics is compared to the mean of 

the valid channels (for each group). The diversity gain is greater for the NE data than for 

the SE data as is expected from the overall delay statistics shown in the previous two

figures.

5. FAST FADING

This section examines the effect of bandwidth and spatial diversity on signal fading. The 

statistics will be based on the normalized power spectral density (NPSD) of the measured 

impulses. The NPSD is here defined as the magnitude squared of the discrete Fourier

transform (DFT) of an impulse signal (or delay profile (DP)) normalized to the

magnitude squared of the DFT of a calibration impulse (CAL_DP). 

[ ]

[ ]

2

2

2

( ) ( )

( _ )

( )

i i PDP t DP t

DFT CAL DP

DFT DP NPSD

=

=

 . (8)
10

The PDPs discussed in the last section are simply the squares of the DPs. An example of

an NPSD is shown in Figure 3(d).

5.1 Frequency Selective Fading versus Bandwidth

Four bandwidths will be considered: 19.6 kHz, 1.25 MHz, 5.0 MHz, and 10 MHz. The

first of these, 19.6 kHz, represents the minimal bandwidth possible for the measurement

system configuration chosen here and will be considered an approximate narrowband 

continuous wave (CW) signal. The three larger bandwidths are representative of

broadband channels used for CDMA. Note that all four bandwidths are based on the same 

measured NPSDs and differ only in the number of data points about the center frequency 

used for the analysis. 

It is expected that fading should be frequency selective. Thus, signal power r over a

broad bandwidth,

∫

+

−

=

/ 2

/ 2

0

0

( ) ( )

f BW

f BW

r BW NPSD f df , (9)

should be less influenced by fading than signal power over a narrow bandwidth. In (9), 

BW is the bandwidth, f0 is the carrier frequency (typically the data have been

demodulated to baseband and f0 may be replaced by 0), and NPSD(f) is the normalized

PSD as a function of frequency. Note that the integral is actually a summation over the

sampled bandwidth.

For the four bandwidths considered here we expect the 19.6 kHz signal to exhibit the

most fading and the 10 MHz signal to exhibit the least fading. Fading reduction should be 

largest for the initial bandwidth increase (e.g., 19.6 kHz to 5.0 MHz).

Figure 14 shows r(BW) for a typical burst (NE Burst 1). The four bandwidths are plotted 

for each of the four channels. As expected, fading is strongest for the 19.6 kHz

narrowband case (blue line). The 5 MHz data (red line) already show considerably less

variation. Reduced fading with increased bandwidth implies that gains from spatial

diversity are exected to be similarly reduced.

An alternate method to view the bandwidth effect on fading is to consider the data

density distribution. Figures 15 and 16 show the distribution of signals about their local

mean (discussed in the next section) expressed in dB (the local mean is used as the 0 dB 

reference level). The data from all four channels are grouped into a single data set. Both

the NE (Figure 15) and SE (Figure 16) data demonstrate that as the bandwidth is

increased the distribution narrows, implying less fading. 
11

5.2 Spatial Diversity – General Comments

Signals from multiple antennas, or “diversity,” can be used to reduce the effects of

fading. Assuming that the signals from multiple antennas are independent, thus

experiencing fade at different times and frequencies, the combined signal should have a

lower probability of a given fade level than the individual signals. The more independent 

channels used, the better the fade reduction. Three common combining schemes are

investigated here, namely, selection diversity (SD), equal gain combining (EG), and

maximal ratio combining (MR). The combining analysis is performed on the post

processed channel signals ri(BW), where i denotes the channel number. We begin with a

brief review of these three techniques.

For any given impulse, the signal voltages vi ( 2| |

i i

r = v ) from the multiple antennas are

combined as follows,

(max | |) max ( )

2

i i i i

r = v = r selection diversity

2

1

1













= ∑=

M

i

i

v

M

r equal gain . (10)

∑ ∑ = =

= =

M

i

M

i

i i

r v r

1 1

2

| | maximal ratio

Thus, selection diversity chooses the strongest signal (only a single signal is used if

identical signal levels occur), equal gain combines the cophased signal voltages with

equal weights, and maximal ratio weights the cophased signal voltage by itself,

equivalent to a sum of the signal powers. Note that maximal ratio combining should

weight signal voltages according to their relative signal to noise ratio [8]; however, as the 

noise may not be known a priori, signal strength alone is used here.

5.3 Fast Fading Statistics and Burst Duration

The fading reduction resulting from the various schemes will be examined as follows. A 

signal r may be expressed as the product of its local mean m and a fast fading

contribution f [8,10],

r = mf , (11)

where r can represent both a signal from an individual channel and a combined signal.

The local mean m varies slowly as a function of terrain and possible time dependent

medium changes (e.g., rain, foliage), but is essentially stationary over short path lengths

and times. The fast fading portion f of the signal includes the rapid variations due to

multipath and other non quasi-static contributions (e.g., moving reflectors). If the local

mean is known then the fast fading portion is simply
12

m

r

f = . (12)

The local mean is found by averaging over some path length about the point of interest,

or equivalently to a time duration for a moving transmitter [11],

∫

=

P

r x dx

P

m ( )

1

 , (13)

where P describes the path length of interest. The choice of P is nontrivial in that if P is

too short then the local mean may not be accurately estimated and if P is too large then

slow fade terrain effects may be incorrectly included in the local average. An accepted

length used for P is 40 λ [8]; however, a range about this value should give good results. 

Lengths of 20-50 λ are suggested in [8]. Assuming the mean is constant over such a path 

(P) implies that

∫ ∫ ∫

= = =

P P P

f x dx

P

mf x dx m

P

r x dx

P

m ( )

1

( )

1

( )

1

 . (14)

Thus, for the definition here the expected value of the fast fade contribution is unity.

Fast fading statistics will be based on f as expressed in dB. The statistics are generated as 

follows. Data were collected in the burst mode. The distance covered during a burst (128 

impulses, approx. 0.4 s duration) is proportional to the velocity of the mobile transmitter

(assumed constant during the burst). Each burst is checked for path length. Bursts

covering path lengths between 20 λ and 50 λ are considered valid and included in the

statistics. Invalid bursts are discarded. Figures 17 and 18 show the path length per burst

for the two data sets (NE, SE). For the NE data 118/220 bursts satisfy the path length

requirement while for the SE data 132/216 bursts do so. Note that few paths exceed 40 λ; 

thus, the 20-50 λ range suggested in [8] is largely adhered to. For each valid path (burst

of 128 impulses) the mean of the signal power (9) over the path is calculated via (14).

This represents the local mean. The burst signal is then normalized to this local mean to

determine the fast fading portion of the signal.

Invalid bursts are typically due to insufficient vehicle speed resulting in a short path.

Figure 19 shows the straight line path length in wavelengths versus vehicle speed for

burst durations from 0.2 s to 1.0 s in 0.2 s steps. Also shown are the data points per

wavelength for a 128 impulse burst for the same range of values. The choice of burst

duration must balance the requirement of a minimum path length (minimum duration)

and sufficient sampling density (maximum duration). The data here were collected

primarily in suburban areas. Thus, typical vehicle speeds were 30-70 kph. Figure 19
13

(upper) indicates that at least a 0.4 s burst duration is necessary; however, burst durations 

above 0.6 s would yield excessive path lengths over much of the expected speed range

(the desired 20-50 λ path length boundaries are plotted on the graph). Figure 19 (lower)

shows that burst durations longer than 0.4 s will yield insufficient sampling density over

much of the expected speed range (the desired 3-5 samples per λ boundaries are plotted

on the graph). Thus, the 0.377 s burst duration is a reasonable choice for the vehicle

speeds typical of a suburban environment.

For usable bursts (valid path length), channels are combined as outlined above (the three 

weighting schemes) and normalized to the local mean of a single channel [9]. Channel 1, 

the leftmost antenna in Figure 1, will be used as the reference channel. Statistics will be

expressed in terms of the fast fading cumulative distribution functions (CDFs), i.e., the

probability that f (in dB) is less than a given level. Gain is then defined as the difference 

in levels for a given probability. The computed gain for the various combining schemes,

channel numbers, and bandwidths will be in reference to channel 1 data.

5.4 Channel Equivalence

Effective fading reduction via spatial diversity assumes that the channels are equivalent

(similar means) and uncorrelated. As stated, the four antennas used here are located at

distances of 2λ, 5λ, and 10λ with reference to antenna 1. Equivalence can be checked by

comparing the CDFs of the four antennas for the four bandwidths. These data are shown

in Figure 20. The channels exhibit similar fading with some minor exceptions, namely,

NE channel 2 (blue) for 19.6 kHz, NE and SE channel 3 (red) for 1.25 MHz, and SE

channel 4 (green) for 10 MHz. Larger bandwidths yield more compressed distributions.

The narrowband data for both the NE and SE data sets are very similar. However, the

broadband data show noticeably more fading for the SE data set.

5.5 Spatial Diversity – Results of Measured Data

Figure 21 shows selection diversity gain for various channel combinations in the form of

CDF plots. In each case, the reference is channel 1 (no diversity, black line). Considered 

are channel 1 combined individually with channels 2, 3, and 4 (2λ, 5λ, 10λ separation 

respectively, blue lines), as well as three (123, 124, 134, red lines) and four (1234, green 

line) channel combinations. The diversity gain is equivalent to the difference between

curves for a given probability (horizontal offset). In the narrowband case, diversity gain

increases as more channels are combined, as expected. The largest increase is from 1 to 2 

channels (black to blue) with lesser gains for further increases. Diversity gain decreases

as bandwidth is increased, also as expected. For the NE data, selection diversity results in 

little gain for the 5 MHz and above bandwidths. The increased fading for the SE data

results in better selection diversity gain; however, the trend is the same. 

Equal gain combining yielded larger gains than did selection diversity, as shown in

Figure 22. Again, the narrowband data show the largest gains. However, wider
14

bandwidths also exhibit notable gain. This is primarily a result of increased signal

strength (multiple channels are summed) relative to the single channel local mean rather

than fast fading reduction. Figure 23 shows the CDFs for signals combined via the

maximal ratio scheme outlined above. The results are very similar to the equal gain case. 

For a narrowband, Rayleigh distributed signal, we expect that maximal ratio combining

should yield larger gains than equal gain combining and selection diversity, in that order

[9], with equal gain and maximal ratio being nearly equivalent. The data here follow this

trend.

Figures 24-26 show the two channel, three channel, and four channel CDFs for the three 

techniques (an alternate representation of the data in Figures 21-23). The figures indicate 

the ordering in combining technique gains. The data are summarized in Tables 2 and 3

which give the gains for the various channel combinations and combining techniques at

the 90% and 99% probabilty levels (the probability that the fade depth exceeds a given

signal level). As discussed, the largest gains are for the narrowband case with 90%

probability maximal ratio combining gains exceeding 11 dB and the 99% probability

maximal ratio combining gains exceeding 17 dB when all four channels are used.

6. CONCLUSION

The ATB system has been used to define propagation conditions in the GMM cell. Two

GMM sectors, designated NE and SE, have been studied. Log-log plot slopes for the

basic transmission loss versus distance are found to be 4.9 and 4.1 in the NE and SE

sectors. NE sector RMS delay spreads are found to be less than 1.38 μs and 3.14 μs at the 

90% and 99% probability levels while SE sector RMS delay spreads are found to be less

than 0.65 μs and 1.35 μs at the 90% and 99% probability levels. Both the basic

transmission loss and RMS delay spread results are consistent with previously published 

PCS data for a suburban to urban environment.

In addition the GMM cell has been characterized using diversity combining techniques at 

multiple bandwidths. As expected, it was found that diversity gain is greatest for

narrowband signals. Increasing the bandwidth (1.25 MHz, 5.0 MHz and 10 MHz were

considered) reduces the diversity gain. These data will aid in the testing of beam forming 

based advanced antenna systems and processing algorithms. 
15

Table 2. The 90% Fade Level Diversity Gain (dB)

90%

NE SE

19.6

kHz

1.25

MHz

5.0

MHz

10.0

MHz

19.5

kHz

1.25

MHz

5.0

MHz

10.0

MHz

2 Channels

SD12 5.3 2.2 1.5 1.3 5.0 2.4 1.6 1.3

EG12 6.3 4.3 3.8 3.6 6.0 4.1 3.7 3.4

MR12 6.8 4.4 3.9 3.7 6.5 4.3 3.8 3.5

SD13 4.9 1.7 1.1 0.9 4.8 2.0 1.5 1.2

EG13 5.8 3.7 3.4 3.3 5.7 3.9 3.5 3.4

MR13 6.4 3.9 3.5 3.4 6.2 4.1 3.6 3.5

SD14 5.2 2.1 1.5 1.2 5.3 2.5 1.8 1.5

EG14 6.1 4.1 3.6 3.4 6.2 4.3 3.9 3.7

MR14 6.4 4.2 3.7 3.5 6.8 4.5 4.1 3.8

3 Channels

SD123 6.7 2.7 1.9 1.6 6.6 3.0 2.2 1.8

EG123 8.7 6.0 5.5 5.4 8.4 6.0 5.4 5.2

MR123 9.4 6.2 5.6 5.5 9.1 6.3 5.6 5.4

SD124 7.2 3.0 2.1 1.7 7.1 3.5 2.6 2.2

EG124 8.9 6.3 5.7 5.4 8.9 6.5 5.9 5.6

MR124 9.7 6.5 5.8 5.5 9.6 6.8 6.1 5.7

SD134 6.7 2.6 1.8 1.4 6.8 3.2 2.3 1.8

EG134 8.4 5.8 5.3 5.1 8.5 6.2 5.6 5.4

MR134 9.2 6.1 5.5 5.3 9.2 6.4 5.8 5.6

4 Channels

SD1234 7.8 3.2 2.2 1.9 7.8 3.9 2.8 2.3

EG1234 10.4 7.4 6.8 6.6 10.3 7.7 7.0 6.7

MR1234 11.2 7.6 7.0 6.7 11.1 8.0 7.2 6.9
16

Table 3. The 99% Fade Level Diversity Gain (dB)

99%

NE SE

19.6

kHz

1.25

MHz

5.0

MHz

10.0

MHz

19.5

kHz

1.25

MHz

5.0

MHz

10.0

MHz

2 Channels

SD12 10.5 2.6 1.8 1.3 9.4 3.7 2.7 2.1

EG12 11.2 4.7 4.1 3.7 10.3 5.5 4.5 3.9

MR12 11.9 4.8 4.2 3.8 10.9 5.8 4.7 4.0

SD13 10.4 2.2 1.5 1.0 9.2 3.6 2.9 2.3

EG13 11.3 4.4 3.9 3.6 10.1 5.3 4.8 4.4

MR13 11.8 4.5 4.0 3.6 10.7 5.5 5.0 4.6

SD14 10.5 2.5 1.7 1.3 10.0 4.1 3.2 2.6

EG14 11.2 4.6 3.9 3.5 10.9 5.9 5.1 4.5

MR14 11.8 4.8 4.0 3.6 11.4 6.1 5.3 4.7

3 Channels

SD123 13.4 3.4 2.3 1.7 12.3 4.9 3.6 3.0

EG123 15.1 6.8 6.0 5.5 14.2 7.6 6.7 6.2

MR123 16.0 7.0 6.1 5.6 14.9 8.0 6.9 6.4

SD124 13.5 3.7 2.6 2.0 12.9 5.5 4.2 3.4

EG124 15.5 7.2 6.1 5.7 14.6 8.4 7.2 6.4

MR124 16.2 7.3 6.2 5.8 15.3 8.7 7.4 6.6

SD134 13.4 3.3 2.1 1.6 12.9 5.3 4.1 3.3

EG134 15.1 6.8 5.9 5.4 14.4 8.1 7.1 6.4

MR134 15.8 7.0 6.0 5.5 15.3 8.4 7.3 6.6

4 Channels

SD1234 15.0 4.0 2.7 2.1 14.1 5.9 4.5 3.7

EG1234 17.4 8.4 7.3 6.8 16.5 9.4 8.4 7.6

MR1234 18.3 8.6 7.4 6.9 17.4 9.9 8.7 7.8
17

7. REFERENCES

[1] J. A. Wepman, “Personal communications services technology field trials,” NTIA 

Report 98-356, Sept. 1998.

[2] J. A. Wepman, J. R. Hoffman, L. Loew and V. S. Lawrence, “Comparison of

wideband propagation in the 902-928 and 1850-1990 MHz bands in various

macrocellular environments,” NTIA Report 93-299, Sept. 1993.

[3] J. A. Wepman, J. R. Hoffman and L. Loew, “Impulse response measurements in

the 1850-1990 MHz band in large outdoor cells,” NTIA Report 94-309, June 

1994.

[4] R. F. Linfield, R. W. Hubbard and L. E. Pratt, “Transmission channel

characterization by impulse response measurements,” OT Report 76-96, Aug.

1976.

[5] P. B. Papazian, K. Allen and M. Cotton, “A test bed for the evaluation of adaptive 

antennas used for mobile communications,” in Proc. IEEE Aerospace

Conference, Snowmass, CO, 1998, paper #161.

[6] J. Gibson, Ed., The Mobile Communications Handbook, Boca Raton, FL: CRC

Press, 1996, Ch. 22.

[7] R. Steele, Ed., Mobile Radio Communications, New York: IEEE Press, 1995, pp.

159-163.

[8] W. C. Y. Lee, “Estimate of local average power of a mobile radio signal,” IEEE 

Transactions on Vehicular Technology, VT-34, No. 1, pp. 22-27, Feb. 1985.

[9] W. Jakes, Ed., Microwave Mobile Communications, New York: Wiley & Sons,

1974, Ch. 5.

[10] J. Colburn, Y. Rahmat-Samii, M. Jensen and G. Pottie, “Evaluation of personal

communications dual-antenna handset diversity performance,” IEEE Transactions 

on Vehicular Technology, VT-47, No. 3, pp. 737-746, Aug. 1998.

[11] P. Perini and C. Holloway, “Angle and space diversity comparisons in different

mobile radio environments,” IEEE Transactions on Antennas and Propagation, 

AP-46, No. 6, pp. 764-775, June 1998.
18

Figure 1. Four element linear antenna array spaced 2λ, 5λ, and 10λ from leftmost element.
19

0 2 4 6 8 10

-20

-10

0

10

20

30

40

50

60

Time (us)

dBm

Figure 2. Sample calibration impulse.
20

0 5 10

-100

-80

-60

-40

-20

0

Time (us)

dBm

(a) Power Delay Profile

-10 -5 0 5 10

-40

-30

-20

-10

0

10

Frequency (MHz)

dB

(b) Power Spectral Density

-10 -5 0 5 10

-40

-30

-20

-10

0

10

Frequency (MHz)

dB

(c) Cal Power Spectral Density

-10 -5 0 5 10

-40

-30

-20

-10

0

10

Frequency (MHz)

dB

(d) Normalized Power Spectral Density

Figure 3. Example of a received impulse and the resulting normalized PSD.
21

Figure 4. Drive routes and received signal strength (RSS) for NE and SE sectors of the 

GMM cell.
22

10

- 1

10

0

10

1

70

80

90

100

110

120

130

140

150

160

170

Distance (km)

Path Loss: Mean Peak Impulse Power

NE Drive

Measured

Free Space

Least Squares Fit

Figure 5. Path loss versus distance for the NE sector of the GMM cell. The least squares 

curve fit has a slope of 4.89.
23

10

- 1

10

0

10

1

70

80

90

100

110

120

130

140

150

160

170

Distance (km)

Path Loss: Mean Peak Impulse Power

SE Drive

Measured

Free space

Least Squares Fit

Figure 6. Path loss versus distance for the SE sector of the GMM cell. The least squares 

curve fit has a slope of 4.08.
24

0 5 10

-80

-70

-60

-50

-40

-30

-20

-10

Time(us)

dBm

corrected impulse

0 5 10

-80

-70

-60

-50

-40

-30

-20

-10

Time(us)

dBm

raw impulse

Figure 7. An example of a raw APDP and corrected APDP (NE drive, burst 1, impulse 8, 

channel 1). The corrected APDP consists of the signal within 20 dB of the 

peak signal time shifted to t = 0.
25

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

-70

-60

-50

-40

-30

-20

-10

0

NE Peak Power

APDP Number

dBm

Figure 8. The peak power for the 8286 valid NE drive APDPs. The APDPs are ordered 

sequentially in time.
26

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

-70

-60

-50

-40

-30

-20

-10

0

SE Peak Power

APDP Number

dBm

Figure 9. The peak power for the 8735 valid SE drive APDPs. The APDPs are ordered 

sequentially in time.
27

0 5 10 15 20

0

0.5

1

NE Data

Maximum Delay (us)

Probability > Abscissa

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

Mean Delay (us)

Probability > Abscissa

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

RMS Delay Spread (us)

Probability > Abscissa

Figure 10. Delay spread statistics for the NE data set. Shown are maximum delay, mean 

delay, and RMS delay spread probabilities.
28

0 5 10 15 20

0

0.5

1

SE Data

Maximum Delay (us)

Probability > Abscissa

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

Mean Delay (us)

Probability > Abscissa

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

RMS Delay Spread (us)

Probability > Abscissa

Figure 11. Delay spread statistics for the SE data set. Shown are maximum delay, mean 

delay, and RMS delay spread probabilities.
29

0 5 10 15 20

0

0.5

1

NE Data

Maximum Delay (us)

Probability > Abscissa

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

Mean Delay (us)

Probability > Abscissa

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

RMS Delay Spread (us)

Probability > Abscissa

Figure 12. Diversity delay spread statistics for the NE data set. Plotted are the four 

channel minimum (red) and four channel mean (blue) probabilities for the 

maximum delay, mean delay, and RMS delay spread. 
30

0 5 10 15 20

0

0.5

1

SE Data

Maximum Delay (us)

Probability > Abscissa

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

Mean Delay (us)

Probability > Abscissa

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

RMS Delay Spread (us)

Probability > Abscissa

Figure 13. Diversity delay spread statistics for the SE data set. Plotted are the four 

channel minimum (red) and four channel mean (blue) probabilities for the 

maximum delay, mean delay, and RMS delay spread. 
31

0 5 10 15 20 25 30

-10

-5

0

5

Distance in Wavelengths over the Burst

Ch1 (dB)

0 5 10 15 20 25 30

-10

-5

0

5

Distance in Wavelengths over the Burst

Ch2 (dB)

0 5 10 15 20 25 30

-10

-5

0

5

Distance in Wavelengths over the Burst

Ch3 (dB)

0 5 10 15 20 25 30

-10

-5

0

5

Distance in Wavelengths over the Burst

Ch4 (dB)

Figure 14. The normalized power spectral density for the four bandwidths (19.6 kHzblue, 1.25 MHz-green, 5.0 MHz-red, 10 MHz-cyan) and four channels for a 

typical burst (NE Drive, Burst 1).
32

Figure 15. Distribution profiles (combined channel data) for the NE data set for the four 

bandwidths.
33

Figure 16. Distribution profiles (combined channel data) for the SE data set for the four 

bandwidths.
34

20 40 60 80 100 120 140 160 180 200 220

0

10

20

30

40

50

60

Burst Number

Burst Duration Path Length in Wavelengths

Figure 17. The path length per burst for the NE data set. 118/220 bursts are valid (in the 

20-50λ range).
35

20 40 60 80 100 120 140 160 180 200

0

10

20

30

40

50

60

Burst Number

Burst Duration Path Length in Wavelengths

Figure 18. The path length per burst for the SE data set. 132/206 bursts are valid (in the 

20-50λ range).
36

0 20 40 60 80 100

0

20

40

60

Vehicle Speed (kph)

Wavelengths Covered

Path Length in Wavelengths

0 20 40 60 80 100

0

2

4

6

8

10

Vehicle Speed (kph)

Data Points Per Wavelength

128-Impulses: Data Points Per Wavelength

Figure 19. The straight line path length in wavelengths versus vehicle speed for burst 

durations of 0.2 s to 1.0 s in 0.2 s steps (upper curves) and the data points per 

wavelength for a 128 impulse burst for the same range of values (lower 

curves).
37

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE Ch1-Ch4 Fading: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE Ch1-Ch4 Fading: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE Ch1-Ch4 Fading: 5.0 MHz

Ch1

Ch2

Ch3

Ch4

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE Ch1-Ch4 Fading: 10.0 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE Ch1-Ch4 Fading: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE Ch1-Ch4 Fading: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE Ch1-Ch4 Fading: 5.0 MHz

Ch1

Ch2

Ch3

Ch4

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE Ch1-Ch4 Fading: 10.0 MHz

Figure 20. CDFs for channels 1-4 versus bandwidth for the NE (upper) and SE (lower) 

data sets.
38

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE Selection Diversity: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE Selection Diversity: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE Selection Diversity: 5.0 MHz

Ch1

2 Chs

3 Chs

4 Chs

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE Selection Diversity: 10.0 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE Selection Diversity: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE Selection Diversity: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE Selection Diversity: 5.0 MHz

Ch1

2 Chs

3 Chs

4 Chs

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE Selection Diversity: 10.0 MHz

Figure 21. Selection diversity CDFs for the NE (upper) and SE (lower) data sets.
39

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE Equal Gain: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE Equal Gain: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE Equal Gain: 5.0 MHz

Ch1

2 Chs

3 Chs

4 Chs

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE Equal Gain: 10.0 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE Equal Gain: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE Equal Gain: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE Equal Gain: 5.0 MHz

Ch1

2 Chs

3 Chs

4 Chs

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE Equal Gain: 10.0 MHz

Figure 22. Equal gain diversity CDFs for the NE (upper) and SE (lower) data sets.
40

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE Maximal Ratio: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE Maximal Ratio: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE Maximal Ratio: 5.0 MHz

Ch1

2 Chs

3 Chs

4 Chs

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE Maximal Ratio: 10.0 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE Maximal Ratio: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE Maximal Ratio: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE Maximal Ratio: 5.0 MHz

Ch1

2 Chs

3 Chs

4 Chs

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE Maximal Ratio: 10.0 MHz

Figure 23. Maximal ratio combining diversity CDFs for the NE (upper) and SE (lower) 

data sets.
41

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE 2 Channel Diversity: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE 2 Channel Diversity: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE 2 Channel Diversity: 5.0 MHz

Ch1

S D

E G

M R

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE 2 Channel Diversity: 10.0 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE 2 Channel Diversity: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE 2 Channel Diversity: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE 2 Channel Diversity: 5.0 MHz

Ch1

S D

E G

M R

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE 2 Channel Diversity: 10.0 MHz

Figure 24. 2 channel diversity CDFs (ch1-blk, SD-blue, EG-r, MR-g) for the NE (upper) 

and SE (lower) data sets.
42

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE 3 Channel Diversity: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE 3 Channel Diversity: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE 3 Channel Diversity: 5.0 MHz

Ch1

S D

E G

M R

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE 3 Channel Diversity: 10.0 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE 3 Channel Diversity: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE 3 Channel Diversity: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE 3 Channel Diversity: 5.0 MHz

Ch1

S D

E G

M R

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE 3 Channel Diversity: 10.0 MHz

Figure 25. 3 channel diversity CDFs (ch1-blk, SD-blue, EG-r, MR-g) for the NE (upper) 

and SE (lower) data sets.
43

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE 4 Channel Diversity: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

NE 4 Channel Diversity: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE 4 Channel Diversity: 5.0 MHz

Ch1

S D

E G

M R

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

NE 4 Channel Diversity: 10.0 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE 4 Channel Diversity: 19.6 kHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Probability < Abscissa

SE 4 Channel Diversity: 1.25 MHz

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE 4 Channel Diversity: 5.0 MHz

Ch1

S D

E G

M R

-20 -10 0 10

10

- 4

10

- 2

10

0

Fade Depth (dB)

Probability < Abscissa

SE 4 Channel Diversity: 10.0 MHz

Figure 26. 4 channel diversity CDFs (ch1-blk, SD-blue, EG-r, MR-g) for the NE (upper) 

and SE (lower) data sets.