NTIA Report 95-324 

Impulse Response Measurements 

Over Space-Earth Paths Using the 

GPS Coarse/Acquisition Codes 

John J. Lemmon 

Peter B. Papazian 

U.S. DEPARTMENT OF COMMERCE 

Ronald H. Brown, Secretary 

Larry Irving, Assistant Secretary 

for Communications and Information 

September 1995 

iii

PREFACE 

Certain commercial equipment, instruments, and software are identified in this report to specify 

adequately the experimental procedure. In no case does such identification imply recommendation 

or endorsement by the National Telecommunications and Information Administration, nor does it 

imply that the material or equipment identified is necessarily the best available for the purpose. 

v 

CONTENTS 

PREFACE .........................................................................................................................................iii 

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

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

2. DATA ACQUISITION SYSTEM .................................................................................................3 

3. SIGNAL PROCESSING................................................................................................................5 

4. EXAMPLES OF IMPULE RESPONSE MEASUREMENTS.....................................................6 

5. RECOMMENDATIONS FOR FUTURE WORK......................................................................13 

6. CONCLUSIONS ..........................................................................................................................15 

 

7. ACKNOWLEDGMENTS............................................................................................................16 

8. REFERENCES .............................................................................................................................16 

IMPULSE RESPONSE MEASUREMENTS OVER SPACE-EARTH PATHS 

USING THE GPS COARSE/ACQUISITION CODES 

John J. Lemmon and Peter B. Papazian1

The impulse responses of radio transmission channels over space-earth paths were 

measured using the coarse/acquisition code signals from the Global Positioning 

System of satellites. The data acquisition system and signal processing techniques 

used to develop the impulse responses are described. Examples of impulse response 

measurements are presented. The results indicate that this measurement approach 

enables detection of multipath signals that are 20 dB or more below the power of the 

direct arrival. Channel characteristics that could be investigated with additional 

measurements and analyses are discussed. 

Key words: impulse response function; Global Positioning System (GPS); radio transmission 

channel; pseudorandom noise (PN) codes 

1. INTRODUCTION 

This report discusses measurements of the impulse response of radio transmission channels over 

space-earth paths. The measurements were performed using signals from the Global Positioning 

System (GPS) of satellites. The possibility of using GPS signals to perform such measurements was 

initially considered in 1985, when the Institute for Telecommunication Sciences (ITS) was asked to 

perform a feasibility study in support of the NASA Propagation Program. The study concluded that 

the structure of the GPS signals, consisting of L-band carriers that are biphase modulated with 

pseudorandom noise (PN) codes, would enable impulse response measurements to be made by 

correlating a received signal with a locally generated replica of the transmitted signal [1]. Analyses of 

the signal-to-noise (S/N) ratio indicated that adequate S/N ratios could be achieved to characterize 

the multipath, and it was recommended that a measurement campaign be conducted. 

Two different kinds of PN codes are used in the GPS signals: the coarse/acquisition (C/A) codes and 

the precision (P) codes. The C/A codes are Gold codes of length 1023 with a chipping rate of 1.023 

MHz; thus, each code word has a duration of exactly 1 ms. The P codes are extremely long codes 

(approximately 37 weeks) that are reset once per week and have a chipping rate of 10.23 MHz. The 

resolution (in time delay) of the measured impulse response is approximately one code bit duration, 

resulting in measurement resolutions of approximately 100 ns and 1 μs for the P codes and the C/A 

codes, respectively. 

 1

The authors are with the Institute for Telecommunication Sciences, National 

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

CO 80303-3328. 
2

A proposal was made to perform impulse response measurements using the P codes rather than the 

C/A codes to obtain greater measurement resolution. Accordingly, upon receipt of NASA funding, 

ITS attempted to contract the development of an appropriately modified P-code receiver, as 

described in [2]. The proposed system was a dual-channel P-code receiver, in which the first channel 

would acquire and lock on to the P code. The current P-code epoch time and Doppler shift would be 

passed on to the second channel, in which the received signal would be correlated with a delayed, 

locally generated P code, enabling the development of the channel impulse response as a function of 

relative time delay. Unfortunately, insufficient funds precluded the development of the system, and 

this approach was abandoned. 

An alternate approach was then proposed [3], whereby a "codeless" P-code receiver would be 

developed at the University of Colorado, Boulder, CO. Using a codeless approach, a single-channel 

receiver would be used to perform a correlation between signals received by two different antennas: a 

high-gain reference antenna that would not receive multipath signals and a low-gain "antenna under 

test" that would receive multipath signals, if any were present. Thus, the PN code received by the 

reference antenna would be used in place of a locally generated code in the correlation processing. 

An advantage of the codeless approach is that time delay and Doppler effects on the signals received 

by the two antennas are identical, obviating a need to know the current P-code epoch and Doppler 

shift; a disadvantage is the need for a high-gain antenna with the capability to track GPS satellites. 

The complexity of the codeless approach and funding difficulties impeded the system development, 

and this approach, like the dual-channel approach discussed above, was abandoned. As an alternative 

to these rather complex P-code approaches, ITS investigated the feasibility of performing multipath 

measurements using the C/A codes. The idea was to use existing hardware to record GPS signals and 

perform the correlation processing in software. Because the C/A codes are known codes of 1-ms 

duration, they can be generated and correlated with received signals in software, so that a high-gain 

reference antenna and most of the hardware required in a modified GPS P-code receiver are no 

longer necessary. This approach therefore results in a vast simplification in hardware. 

The disadvantage of using the C/A codes is the decreased resolution in time delay relative to the P 

codes. A resolution of 1 μs corresponds to a path difference of approximately 300 m; multipath may 

be present in some environments in which the path differences between the multipath and direct 

arrivals are much less than 300 m. On the other hand, impulse response data developed with the C/A

codes can adequately characterize transmission channels whose bandwidths do not exceed those of 

the C/A-code signals (approximately 2 MHz). Thus, this data would be relevant to numerous 

applications of satellite communications and navigation. 

Uncertainties in S/N ratios and the noise figures of the receiver and recording systems, as well as 

variables in the processing, made it difficult to assess the viability of this approach a priori. For 

example, the processing gain is a function of the integration time in the correlation processing; the 

integration time is in turn limited by the amount of memory in the recording system and the time 

scale over which the transmission channel is reasonably stationary. The objective of this work was
3

to investigate whether this approach can generate useful results and to determine the values of S/N 

that can be achieved using various processing techniques. 

Section 2 describes the hardware that was used to collect the raw data. The data processing that was 

performed in software is described in Section 3. In Section 4, example impulse responses developed 

with this method are presented and discussed. Additional processing that could be performed and 

improvements to the measurement system that could be made are described in Section 5. Concluding 

remarks and recommendations for additional measurements and processing are made in Section 6. 

2. DATA ACQUISITION SYSTEM 

Figure 1 shows a block diagram of the data acquisition system. The GPS signals have right-hand 

circular polarization at an L-band frequency of 1575.42 MHz in the absence of Doppler effects 

(spacecraft motion can generate several kHz of Doppler shift). The signals are received by a righthand circular MicroPulse GPS antenna mounted on the roof of the Boulder Laboratories, Boulder, 

CO. The antenna is low-gain (between +4.5 dBiC and -4.5 dBiC, depending on elevation angle) and 

therefore does not discriminate severely against multipath. The RF signals received by the antenna 

are preamplified and passed through 100 feet of RG 58 cable from the roof to the laboratory, where 

they are further amplified and downconverted to IF by an HP 8563A spectrum analyzer. 

The second IF from the analyzer is tuned to 301.027 MHz and is mixed with the 300-MHz 

calibration signal after it is padded for signal conditioning, amplified, and low-pass filtered for 

harmonic suppression. The resulting signal spectrum is centered at 1.027 MHz (in the absence of 

Doppler effects). This frequency was chosen because the bandwidth (defined as the width of the 

central spectral lobe) of the C/A-code signals is twice the chipping rate of 1.023 MHz. Thus, the 

signal spectrum has been translated to as low a frequency as possible (to minimize the Nyquist 

requirement) without folding from negative frequencies, after allowing for as much as 4 kHz of 

Doppler shift. The signal is low-pass filtered for harmonic suppression and anti-aliasing, amplified, 

and sampled by a Lecroy 9450A digital oscilloscope. The scope is clocked and triggered by an HP 

8640B signal generator. 

Each sample is an eight-bit integer, and the memory in the scope allows a data file comprising 

50,000 samples to be collected. The sample rate is 8.192 MHz, and was determined as follows. The 

highest frequency in the signal spectrum (allowing for 4 kHz of Doppler shift) is 2.054 MHz. The 

Nyquist rate for the channel is therefore 4.108 MHz. The digital signal processing (discussed in 

Section 3 below) uses Fast Fourier Transform (FFT) algorithms, which require that the number of 

samples in each record be equal to a power of two. Each record corresponds to a single C/A-code 

word, which has a duration of 1 ms. Thus, the smallest power of two, which when divided by 1 ms is 

greater than 4.108 MHz, is 8192. This corresponds to a sample rate of 8.192 MHz. The IF and 

sample rate are precisely maintained by phase locking the spectrum analyzer and signal generator to 

a stable 10 MHz Rubidium frequency reference. The spectrum analyzer and scope are controlled by a 

personal computer, which is used to store and process the data. 
4
5

3. SIGNAL PROCESSING 

The complex, equivalent low-pass impulse response of the transmission channel was developed 

using the well-known technique of correlating the received signal with a locally generated replica of 

the transmitted signal. The correlation processing was done in the frequency domain; that is, rather 

than computing the cross-correlation function of the transmitted and received signals, the crossspectral density (product of the Fourier transforms) of the signals was computed, and the result was 

inverse Fourier transformed back into the time domain. 

To make this precise, let f(t) denote the received signal at the center frequency (ωIF +ωDS), where ωIF

corresponds to the 1.027-MHz IF and ωDS is the Doppler shift. The received signal is to be correlated 

with a replica of the transmitted signal pn(t), which is a pseudonoise Gold code with a binary value 

of ±1. Before computing the cross-correlation, the received and transmitted signals must be 

converted to the same center frequency, or the relative (time-dependent) phase between the signals 

will cause the cross-correlation to vanish. (Equivalently, in the frequency domain, the spectra of the 

signals must be centered at the same frequency or the lack of spectral overlap will cause the product 

of the spectra to vanish.) Because pn(t) is a baseband signal (zero center frequency), it should be 

correlated with the quantity 

( ) e f (t) j DS t − ωIF +ω , (1) 

which is the received signal at baseband. The impulse response was computed as the inverse discrete 

Fourier transform of the cross-spectral density of the transmitted and received signals at baseband. 

Thus, in terms of f(t) and pn(t), the impulse response at time t0 is 

( ) e pn t e dt f t e dt dw t T

t

j t t T

t

j j t R

R

IF DS S

S ⎭

⎬

⎫

⎩

⎨

⎧

⎥⎦

⎤ ⎢⎣⎡ ∫ ∫ ∫

+ − + + + + − +

−

0 0

0

0 0

0

( ) ( )

*

ωτ ω ω ω ω π

π , (2) 

where τ denotes time delay, RS is the sample rate (8.192 MHz), and T0 is the period of a code word 

(1 ms). The transforms are computed using FFT algorithms with time blocks equal to T0. 

The value of ωDS could, in principle, have been determined from the ephemeral data of the various 

satellites. However, to eliminate errors due to uncertainties in the ephemerides, ωDS was determined 

by computing the impulse response for all values of ωDS between +4 kHz and -4 kHz in steps of 15 

Hz and using the value of ωDS for which the peak of the power delay profile (absolute square of the 

complex impulse response) is a maximum. 
6

4. EXAMPLES OF IMPULSE RESPONSE MEASUREMENTS 

The equipment described in Section 2 was used to collect data at approximately 10:00 a.m. local 

time (17:00 UTC) on March 24, 1994. Two data files of 50,000 samples each were recorded at a 

sample rate of 8.192 MHz. The first data file was recorded with an IF of 1.027 MHz, as described in 

Section 2. The second data file was recorded with an IF of 1.5 MHz to investigate the effect (if any) 

of the IF on the impulse response measurement (the Nyquist requirement for the 1.5 MHz IF is well 

within the 8.192 MHz sample rate). 

The GPS satellite schedule for the date and location that the data were collected was generated using 

public domain software (the InstantTrack program, written by Franklin Antonio), and is shown in 

Figure 2. Local time is indicated across the top of the diagram, and satellite numbers are listed in the 

vertical column at the left. The schedule indicates that as many as nine satellites may have been in 

view when the data were collected. 

 Figure 2. GPS satellite schedule for Boulder, CO on March 24, 1994. The asterisks correspond to 

times when the satellites were above 0° elevation angle. 
7

The data were processed using the technique discussed in Section 3. The C/A codes for the nine 

satellites were generated in accordance with [4]. Peaks in the cross correlation functions stand out 

clearly above the noise floor in five of the nine cases. The failure to detect peaks in the other four 

cases was presumably caused by obstructions due to low elevation angles. This was corroborated by 

generating the approximate azimuth and elevation angles for the nine satellites, and for the time, date, 

and location that the data were collected, using the aforementioned public domain software. The 

results are shown in Table 1. Correlation peaks were detected for those satellites at elevation angles 

greater than or equal to 20°, and were not detected for those satellites at elevation angles less than or 

equal to 15°. 

Table 1. GPS Satellite Positions as Seen from Boulder, CO at 17:00 UTC on March 24, 1994 

Satellite Azimuth Elevation Correlation Peak 

Detected? 

BI -11 45° 7° No 

BII-1 198° 40° Yes 

BII-4 263° 20° Yes 

BII-6 310° 45° Yes 

BIIA-13 127° 15° No 

BIIA-15 260° 0° No 

BIIA-17 342° 79° Yes 

BIIA-18 71° 61° Yes 

BIIA-19 158° 2° No 

At the 8.192 MHz sample rate, 8192 samples were contained in each time block corresponding to 

a C/A code word (1 ms). Thus, the 50,000-sample data files enabled six consecutive impulse 

response functions to be developed for each visible satellite. To improve the S/N ratios of the 

impulse responses, the six consecutive impulse responses for each satellite were combined as 

follows. First, the impulse responses were shifted in time delay (by no more than ±1 time sample) to 

align the peaks of the power delay profiles in relative time delay. Then the impulse responses were 

multiplied by phase factors defined so that each of the resulting impulse responses had zero degrees 

of phase at the peak of the power delay profile to align the phases of the impulse responses. The 

impulse responses were then added coherently. 
8

Figure 3. Correlation peak power (in arbitrary units) versus Doppler shift. 

Typical results are shown in Figures 3, 4, and 5, using an IF of 1.5 MHz and the code for the BIIA18 satellite. Figure 3 is a plot of the peak of the power delay profile (corresponding to the first code 

word in the data file) versus Doppler shift in Hz. A sequence of six consecutive impulse responses 

was developed, using the value of Doppler shift for which the correlation peak is a maximum. 

The inphase (I) and quadrature (Q) components of the impulse response corresponding to the first 

code word are plotted in Figure 4(a) and 4(b), respectively. The units on the vertical scales are 

arbitrary, because the received signal level of the data acquisition system was not calibrated 

(although this could be done). The units on the horizontal scales are sample number; for a sample 

rate of 8.192 MHz the sample time is 0.122 μs and the entire horizontal scale (8192 samples) 

corresponds to 1 ms of relative time delay. 
9

Figure 4. Plots of the (a) inphase and (b) quadrature components of an impulse response function, 

(c) the corresponding power delay profile, and (d) the power delay profile of the sum of 

six consecutive impulse responses (in arbitrary units). 

The power delay profile (I2+Q2) corresponding to Figures 4(a) and 4(b) is plotted in Figure 4(c). 

Figure 4(d) shows the power delay profile obtained by coherently combining the six consecutive 

impulse responses. A plot of this latter power delay profile (in dB units of relative power) is shown 

on magnified scales in Figure 5. The improvement in S/N ratio achieved by combining the impulse 

responses is clearly evident. 
10

Figure 5. Plot of the impulse response function in Figure 4(d) on magnified scales. 

None of the impulse responses developed from the data files shows any indication of multipath. This 

is not surprising, given the location of the receive antenna on a rooftop where multipath reflections 

from nearby terrain and buildings are unlikely to be visible. However, the results do indicate that this 

technique yields S/N ratios that are sufficient to reveal multipath signals that are as much as 20 dB 

below the power of the direct arrival. 

The S/N ratios of all the impulse responses developed from the data files are summarized in Table 2. 

Although noise power generally refers to an average power (NA), it is also of interest to know the 

peak noise power (NP) in each impulse response in order to estimate the power level below which 

multipath signals cannot be distinguished from spurious noise peaks. Therefore, the ratios of the 

signal power to both the average noise power (S/NA) and the peak noise power (S/NP) were 

computed using the following technique. 
11

The measured value of the impulse response at the correlation peak is the sum of the desired signal 

and the noise. Thus, if the noise is treated as a zero-mean random process that is uncorrelated with 

the signal, 

Q S NA I + = +

0

2 2 , (3) 

where 〈I

2

+Q2〉0 denotes the expected value of the power delay profile at the correlation peak, and S 

and NA denote the expected values of the signal power and noise power, respectively. At values of 

time delay far away from the correlation peak, where no signal is expected, the measured value of the 

impulse response is pure noise. Thus, 

A A

I + Q = N 2 2 , (4) 

where 〈I

2

+Q2〉A denotes the average value of the power delay profile at values of time delay far from 

the correlation peak. Only samples of the power delay profile more than 50 samples (approximately 

6 μs) away from the correlation peak were used to compute the average noise power. Dividing (3) by 

(4), the signal-to-noise ratio (S/NA) is 

1

2 2

0

2 2

− +

+ =

A A I Q

I Q

N

S . (5) 

Similarly, for the peak noise power, 

P P

I + Q = N 2 2 , (6) 

where 〈I

2

+Q2〉P denotes the peak value of the power delay profile more than 50 samples away from 

the correlation peak and NP is the peak noise power. Dividing (3) by (6) gives 

P

A

P P N

N

I Q

I Q

N

S − +

+ = 2 2

0

2 2

. (7) 

since NA< NP, replacing NA/ NP by unity in (7) results in the inequality 

1

2 2

0

2 2

− +

+

>

P P I Q

I Q

N

S , (8) 

which can be used to obtain a lower bound for S/NP. 
12

Strictly speaking, 〈I

2

+Q2〉 is an expected value and can only be obtained from an ensemble of 

impulse response records. However, this was precluded by the limited size of the database. 

Therefore, (5) and (8) were used to estimate the S/N ratios for each of the individual impulse 

response records, and the results were averaged for the six consecutive records corresponding to each 

satellite. In addition, (5) and (8) were used to estimate the S/N ratios for the impulse responses 

obtained by coherently combining the six consecutive records for each satellite. 

Table 2 lists the average values of S/NA and S/NP for two IFs (1.027 MHz and 1.5 MHz) and for two 

Doppler resolutions (15 Hz and 250 Hz), resulting in four values for each of the average S/N ratios 

for each satellite. The S/N ratios for the combined records were only computed for the 1.5-MHz IF 

and a Doppler resolution of 15 Hz. As can be seen from the table, using different IFs and/or different 

Doppler resolutions has little effect on the S/N ratios. For the two different IFs, the S/N ratios can 

differ by as much as a dB or more, but typically by a few tenths of a dB. The effect of changing the 

Doppler resolution from 15 Hz to 250 Hz is even less significant, typically on the order of a tenth of 

a dB. The S/N ratios show a slight tendency to increase for higher elevation angles and lower 

Doppler shifts. 

The increases in the S/N ratios as a result of coherently combining the individual impulse responses 

are approximately consistent with expectations. The phases of the individual impulse responses have 

been adjusted so that they all have zero phase at the correlation peak. One therefore expects the peak 

of the coherent sum of N impulse responses to scale like N, and the power to scale like N2

. On the 

other hand, if one assumes the noise is a Gaussian random process, the sum of N independent, 

identically distributed noise processes is a Gaussian process whose variance (which equals the 

expected value of the power) scales like N. Therefore, one expects the S/N ratios to scale like N. For 

N = 6, this corresponds to an increase of 7.8 dB. The average increases in S/NA and S/NP for the five 

sets of impulse responses are 6.3 dB and 8.5 dB, respectively. 

Two possible causes of concern in using the C/A codes for impulse response measurements are the 

autocorrelation sidelobes and the cross-correlation between codes of different satellites. However, 

Gold [5] has shown that relative to the central autocorrelation peak, the magnitudes of the sidelobes 

are bounded by the quantity 

P

n

2 1 2

2

+

⎟

⎠

⎞ ⎜

⎝

⎛ +

, (9)

where n is the number of shift register stages used to generate the codes and P is the length of the 

code. For the C/A codes, n = 10 and P = 1023, so that the sidelobe levels are at least 24 dB down 

from the central peak. For Gold codes of length 1023, it can be shown [6] that the peak crosscorrelation is 23.8 dB down from the autocorrelation peak. Therefore, the autocorrelation sidelobes 

and cross-correlation peaks of the CIA codes are not significant for the measurements discussed 

herein. 
13

Table 2. Signal-to-noise Ratios of Impulse Response Measurements 

Satellite Average 

S/NA (dB) 

Combined 

S/NA (dB) 

Average 

S/NP (dB) 

Combined

S/NP (dB) 

IF 

(MHz) 

Doppler 

Resolution (Hz) 

Doppler 

Shift (Hz)

BII-1 13.3 2.1 1.027 15 3115 

BII-1 12.5 19.2 0.0 10.2 1.5 15 3155 

BII-1 13.5 2.4 1.027 250 3000 

BII-1 11.7 -1.6 1.5 250 3250 

BII-4 11.3 -1.8 1.027 15 -2800 

BII-4 12.4 18.6 0.0 9.7 1.5 15 -2770 

BII-4 11.3 -2.3 1.027 250 -2750 

BII-4 12.5 0.0 1.5 250 -2750 

BII-6 15.0 3.9 1.027 15 -2460 

BII-6 15.5 21.4 4.7 11.4 1.5 15 -2400 

BII-6 14.9 3.8 1.027 250 -2500 

BII-6 15.3 4.5 1.5 250 -2500 

BIIA-17 15.6 4.9 1.027 15 -650 

BIIA-17 15.8 22.1 4.9 11.8 1.5 15 -625 

BIIA-17 15.3 4.3 1.027 250 -750 

BIIA-17 15.6 4.5 1.5 250 -500 

BIIA-18 14.6 2.8 1.027 15 1510 

BIIA-18 14.7 21.0 3.2 12.1 1.5 15 1540 

BIIA-18 14.6 2.8 1.027 250 1500 

BIIA-18 14.8 3.3 1.5 250 1500 

5. RECOMMENDATIONS FOR FUTURE WORK 

The measurement results discussed above indicate that S/N ratios can be achieved that are adequate 

to detect multipath signals many dB below the power of the direct arrival. The absence of multipath 

in the data analyzed thus far can be attributed to the location of the receive antenna at a site where 

multipath is unlikely to be present. However, multipath may be present in some environments, and it 

is important for both navigation and communications applications that such multipath be measured 

and characterized. Aside from multipath, impulse response measurements can provide other 

important information about transmission channels, including received signal levels and channel
14

dynamics. It is therefore recommended that the following research be undertaken: incorporation of 

additional memory into the measurement system, additional measurements, and additional 

processing of the measured data. 

Data files comprising 50,000 samples (at the 8.192 MHz sample rate) allow only six consecutive 

impulse responses to be developed. Some applications, including the computation of the channel 

scattering function (discussed below), require measurements of the impulse response over time 

histories longer than 6 ms. Additional memory could be added to the measurement system with little 

effort and expense. For example, 8.4 million samples would enable 1024 consecutive impulse 

responses to be developed. . 

Installation of the measurement system in a van would enable data to be collected in a variety of 

environments. This is important for two reasons. First, data collected in some environments (for 

example, urban, suburban, and mountainous terrain) may reveal the presence of significant multipath. 

Distributions of delay spread in various environments could be developed and the relationship 

between delay spread and elevation angle investigated. Second, data could be collected while the van 

is moving, so that the channel dynamics could be characterized. This is important for mobile radio 

applications as well as determining the position of moving vehicles. 

The scattering function is a useful quantity for characterizing channel dynamics. It enables the 

display of the time-varying impulse response as a function of both time delay and Doppler shift. If 

one denotes time by t and time delay by τ, the scattering function is defined as the Fourier transform 

(with respect to t) of the autocorrelation function of the impulse response for each value of τ, and is 

therefore the power spectrum of the impulse response for each value of τ. As in the computation of 

the impulse response, it is convenient to compute the correlation integral in the frequency domain. 

Thus, the scattering function can be defined as the square of the Fourier transform (with respect to t) 

of the impulse response: 

( ) ()

2

0

S , h t, e dt j t T

D

ω D τ ω τ −

∫ = , (10) 

where h(t,τ) is the impulse response and T is the length of time over which measurements of the 

impulse response are performed. The Doppler frequency (ωD), not to be confused with the Doppler 

shift (ωDS) due to the motion of the satellite, is the frequency variable in the power spectrum of the 

impulse response. 

In a mobile channel, the direct signal and the multipath signals are generally associated with different 

Doppler shifts, because the different signal components arrive at the receiver via different 

propagation paths. At the L-band frequency of the GPS signals, vehicular motion can generate 

Doppler spreads as large as several hundred Hz in worst case scenarios. For such channels, the 

scattering function should be developed over a Doppler bandwidth on the order of a kHz. If the 

integral in (10) is evaluated as a discrete Fourier transform, the Doppler bandwidth is 1/T and the
15

Doppler frequency resolution is the rate at which the impulse responses are measured in time. Thus, 

the measurement of 1024 consecutive impulse responses at the rate of one impulse response per ms 

would enable the scattering function to be developed over a Doppler bandwidth of 1 kHz with a 

resolution of approximately 1 Hz. Doppler power profiles and distributions of Doppler spread, like 

the corresponding quantities in the time domain (power delay profiles and distributions of delay 

spread), are channel characteristics that are important to system designers. 

Aside from characterizing multipath and channel dynamics, impulse response measurements using 

GPS signals, coupled with knowledge of the elevation angles of the satellites, can provide useful 

information about received signal levels (RSLs) and satellite availability. The RSL for a particular 

satellite is proportional to the magnitude of the correlation peak in the impulse response. Such 

measurements could therefore provide information about the relationship between RSL and elevation 

angle, and could be used to develop distributions of fading rates and fade durations. 

The availability of a particular satellite is determined by the presence or absence of a correlation peak 

corresponding to that satellite. Using impulse response measurements, the relationship between 

availability and elevation angle in various environments can be investigated. This is especially 

important for satellite communication systems that use low earth orbit satellites (LEOS), because the 

satellites that are available to a particular user change on a relatively short-term basis. 

6. CONCLUSIONS 

The results presented in this report clearly establish the feasibility of performing impulse response 

measurements over space-earth paths using the GPS C/A codes. The 1.023-MHz chipping rate of the 

C/A codes provides a time-delay resolution that is probably not adequate to resolve all the multipath 

that may be present in some channels (path differences much less than 300 m). However, this 

measurement resolution should be adequate to characterize the channel for applications that use a 

bandwidth on the order of or less than that of the measurements (2 MHz). Furthermore, the results 

show that the S/N ratios that can be attained are adequate to detect multipath components that are 20 

dB or more below the power of the direct arrival. 

An advantage of using GPS satellites to perform these measurements is that the impulse responses 

from several satellites whose positions are continually varying can be measured simultaneously. 

Thus, distributions of channel characteristics (including delay and Doppler spreads, RSLs, and 

satellite availability) as well as the relationships between these characteristics and satellite position 

(azimuth and elevation angle) can be investigated in a variety of environments. The development of 

such a database would provide a valuable resource for system designers in both the communications 

and navigation communities. 
16

7. ACKNOWLEDGMENTS 

The authors wish to thank Mr. John Kiebler of NASA Headquarters for funding that partially 

supported the work reported herein, and Dr. Faramaz Davarian for several helpful suggestions. 

8. REFERENCES 

[1] J.J. Lemmon and R.W. Hubbard, "Multipath measurements for the land mobile satellite radio 

channel," MSAT-X Report No. 126, Jet Propulsion Laboratory, California Institute of 

Technology, Pasadena, CA, Oct. 1985. 

[2] J.J. Lemmon, "Multipath measurements for land mobile satellite service using Global 

Positioning System Signals," Proceedings of the Mobile Satellite Conference, Pasadena, CA, 

May 1988. 

[3] P.F. MacDoran, R.B. Miller, D. Jenkins, J. Lemmon, K. Gold, W. Schreiner, and G. Snyder, 

"Codeless GPS applications to multipath: CGAMP," Proceedings of the Fourteenth NASA 

Propagation Experimenters Meeting (NAPEX XIV) and the Advanced Communications 

Technology Satellite (ACTS) Propagation Studies Miniworkshop, Austin, TX, May 1990. 

[4] Department of Defense/Department of Transportation, "Global Positioning System Standard 

Positioning Service Signal Specification," Nov. 1993. 

[5] R. Gold, "Optimal binary sequences for spread spectrum multiplexing," IEEE Trans. Info. 

Theory, pp. 619-621, 1967. 

[6] J.J. Spilker, "GPS signal structure and performance characteristics," J. Inst. Navigation, Vol. 

25, No. 2, pp. 121-146, 1978.