Method for evaluating similarity of signals having a carrier frequency offset

A method and apparatus for evaluating the similarity of multi-mode radar pulses detected by a passive ESM receiver. The method consists of fitting a straight line to the differential phase of pairs of received signals, one signal of a pair being a currently received signal pulse and the other a previously received signal pulse, by a best least squares fit method. The slope of that straight line gives the frequency offset between the signals and the mean square error between the actual phase-time data and the straight line indicates the similarity of the signals. A second measure of the similarity of the signals can be obtained by applying statistical tests for serial correlation in the difference between the phase-time data and the straight line.

FIELD OF THE INVENTION 
The present invention is directed to methods and apparatus for 
characterizing, identifying and evaluating the similarity of radar pulses 
and in particular for evaluating the similarity of multi-mode radar pulses 
detected by passive Electronic Support Measures (ESM) systems. 
BACKGROUND TO THE INVENTION 
Present techniques to classify and identify radar pulses received by 
passive Electronic Warfare (EW) detection systems rely primarily on the 
monopulse measured parameters of carrier frequency, angle of arrival and 
pulse width as well as the intrapulse measured parameters of items such as 
pulse repetition interval and scan period. However, modern computer 
controlled multi-mode radars dynamically vary many of those parameters 
such as carrier frequency, pulse repetition interval and scan period in 
any arbitrary manner. Those parameters, as a result, are becoming 
insufficient to unambiguously discriminate between pulses from multi-mode 
radars having similar characteristics. Therefore, satisfactory results 
cannot always be obtained with present approaches to evaluate and classify 
pulses received from multi-mode radars. 
Since it is becoming increasingly difficult to obtain satisfactory results 
with standard techniques, considerable effort is being directed at the 
problem of exploiting intrapulse information concerning the nature of the 
modulation information within radar pulses. Unfortunately, existing 
approaches to exploit information regarding amplitude and frequency/phase 
modulation of radar have various limitations since they are often 
dependent on a particular model of the detected signal. A polynomial model 
of the signal phase with time, for example, is very good for a linear 
chirp frequency modulation (quadrature phase) but poorly suited for 
signals having random discrete frequency modulation. 
The need for a signal model can be avoided by directly comparing signals 
detected by a receiver. Each signal pulse can be compared with previously 
observed reference signals. When a match is found with one of the 
reference signals, this will infer that both of those signals were 
transmitted by the same radar. Otherwise, when a poor match is found 
between any two signals, it is concluded that a detected signal is 
transmitted by a new radar. 
A simple implementation of this concept for directly comparing signals is 
to perform frequency demodulation on each signal being compared and, after 
subtracting the mean of each signal from itself, applying a suitable 
measurement criteria to determine the amount similarity between the 
signals. The amount of similarity between the signals will provide an 
indication of the goodness of the match between signals. The peak of the 
cross-correlation function has been used for this purpose. This approach 
has the advantage that carrier frequency offsets between the signals 
simply result in a shift of the demodulated signals that can easily be 
removed by subtracting the mean. 
The frequency demodulation can be performed by wideband analog frequency 
demodulators which is a highly developed technology. However, frequency 
demodulation involves a differentiation of the signal phase and this 
generally emphasizes noise. A further problem is that signals having 
frequency modulation which is similar but differs by a scale factor may 
not be easily distinguishable using cross-correlation. These problems 
adversely affect the use of frequency demodulators in comparing radar 
pulses. Since many radars use linear frequency modulation, for instance, 
it is important to be able to distinguish small differences in the chirp 
rate. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a method and apparatus 
for identifying and evaluating the similarity of multi-mode radar signal 
pulses detected by a passive ESM receiver which avoids difficulties 
associated with present ESM techniques. 
The method for evaluating the similarity of multi-mode radar signal pulses 
detected by a passive ESM receiver, according to the present invention, 
comprises determining the differential phase of pairs of received signals, 
one signal of each pair being a currently received signal and the other a 
previously received one, and fitting a straight line to the differential 
phase of pairs of signals wherein the slope of the line gives the 
frequency offset between the signals and the mean square error between the 
actual phase-time date and the straight line indicates the similarity of 
the signals. 
An apparatus for evaluating the similarity of multi-mode radar signal 
pulses detected by a passive ESM receiver, according to a further 
embodiment of the present invention, comprises: 
(1) means for estimation of the differential phase between two complex 
baseband radar signals detected by a passive ESM receiver; 
(2) means for providing a least squares estimation of carrier frequency 
offset .DELTA.f.sub.c between received signals from said estimation of the 
differential phase and a weighting parameter .PSI.(nT) ; and 
(3) means for determining a cost function C from the signals, their 
frequency offset .DELTA.f.sub.c and the weighting parameter .PSI.(nT) , 
wherein C is a measure of the similarity between pairs of signals.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
While it is difficult to generate simple and robust models for the 
frequency or phase time history relationship of a signal having incidental 
frequency modulation, this issue can be avoided by comparing the 
accumulated or unwrapped differential phase between two signals. If they 
are accurately aligned in time, the differential phase between two signals 
will have a linear component proportional to carrier frequency offset. Any 
deviations of the differential phase from such a model result from the 
following factors: 
(1) Noise; 
(2) Multipath propagation; 
(3) Differences between the signal phase or frequency modulation of the 
signals; 
(4) Imperfections in the quadrature demodulation system; and 
(5) Phase noise in the receiver local oscillator. 
These will differ in their statistical behaviour with wideband Gaussian 
noise introducing phase errors that are substantially uncorrelated from 
measurement-to-measurement whereas there will be substantial correlation 
of the phase errors produced by the factors (2) to (4). Multipath 
propagation effects, i.e. factor (2), can be further minimized by using a 
time weighting function to restrict processing to the first part of each 
pulse. This gives reduced weight to measurements at the trailing edge of a 
pulse which is the area most likely to be significantly degraded by noise 
or multipath signals. 
It should be noted that doing a linear regression on the unwrapped phase 
difference has the incidental advantage that an accurate measurement of 
the difference in the signal carrier frequencies is obtained. This is 
potentially useful information since some radars using frequency 
synthesizers tune the transmitter carrier frequency in discrete steps. 
The present invention uses a phase comparison algorithm for signal 
identification and a practical implementation of the concept uses the 
following steps: 
1. Thresholding and endpointing; 
2. Estimation of differential phase; 
3. Least squares estimation of carrier frequency offset; and 
4. Signal comparison. 
In Step 1 (thresholding and endpointing), it is essential that the pair of 
signals to be compared are accurately aligned in time and that subsequent 
processing be restricted to a time interval corresponding to the presence 
of useful signal information. This can be performed as a two stage 
process. In the first stage, the amplitude .sqroot.I.sup.2 (t)+Q.sup.2 (t) 
, (I being the In-phase component and Q the Quadrature component of the 
signal) of each signal is compared to a threshold to define the period 
during which significant signal power is present. This threshold is 
typically set to correspond to a signal-to-noise ratio of 20 dB in order 
to provide acceptable performance. Hysteresis can be used to avoid 
problems with pulse waveforms that might cross a single threshold several 
times. 
Endpointing is performed to determine the positions in time of the leading 
and trailing edges of each pulse for the second stage in Step 1. Amplitude 
insensitive criteria, such as the position of the peak slope or the 
crossing of a threshold computed as a fraction of the peak amplitude, 
should be employed in determining the positions of leading and trailing 
edges for each pulse. A simple fixed threshold is unsatisfactory for this 
purpose since variations in the signal amplitude will affect the measured 
pulse width. It is possible to achieve sub-sample period resolution for 
the pulse endpoints by using interpolation, at least in principle. 
However, this would not normally be necessary given the relatively high 
sampling rates and bandwidth required to accommodate receiver tuning 
errors and minimize aliasing errors for waveforms having fast rise and 
fall times. The trailing edge of a pulse may be severely affected by 
multipath propagation. Therefore, the signal information processed may be 
limited to the first part of the pulse which will also minimize processing 
throughput requirements. 
The estimation of differential phase in Step 2 can be performed either by 
subtracting explicit measurements of phases of individual complex baseband 
signals or, alternatively, can be determined from 
##EQU1## 
The quantities Q(nT) and I(nT) in Equation (1) are the quadrature and 
in-phase components, respectively, of the product Z.sub.i (nT) Z.sub.j 
(nT)* where Z.sub.i (nT) and Z.sub.j (nT) are sampled complex baseband 
representations of the two signals. If the arctangent function is used to 
compute phase, it will be necessary to perform quadrant correction and 
phase unwrapping. Quadrant correction is necessary in order to extend the 
range from the interval [-.pi./2,.pi./2] radians to [-.pi.,.pi.] radians. 
This involves adding .pi. radians when Q and I have positive and negative 
signs respectively and subtracting .pi. radians when Q and I both have 
negative signs. This feature can be implemented in the Fortran IV function 
ARCTAN2. Phase unwrapping can be performed very simply if the phase change 
during a sample interval is less than .pi./2 radians by adding 
(subtracting) 2.pi. radians when the sign of Q changes negative (positive) 
and I is negative. 
The least squares estimation of carrier frequency offset in Step 3 can be 
provided by a least squares estimator for carrier frequency offset 
.DELTA.f.sub.c which is given by: 
##EQU2## 
where .PSI.(nT) is a weighting parameter intended to provide additional 
weight on phase difference measurements having low variance and 
.phi..sub.D (nT) is determined from Equation (1). 
Since the variance of phase measurements is inversely proportional to 
signal-to-noise ratio and the signal-to-noise ratios of the signals are 
approximately proportional to the square of their amplitudes, assuming 
constant noise power, reasonable weights are given by: 
##EQU3## 
Simplified approximations of Equation (3) include 
.PSI.(nT)=.vertline.Z.sub.i (nT).uparw..vertline.Z.sub.j (nT).uparw. and, 
for good minimum post-threshold signal-to-noise ratios, .PSI.(nT)=1. The 
processing should be restricted to the duration defined by the signal 
pulse endpoints even when Equation (3) is employed since noise will result 
in non-zero .PSI.(nT) even when no signal is present .PSI.(nT). 
Algorithms involving differential phase implicity assume that the signals 
are accurately aligned in time. In practice it may be desirable to select 
the best results obtained for a small range of relative time shifts to 
minimize the effects of noise on the endpointing. The possible time error 
of .+-.1/2 sample period should not be particularly significant if the 
signals are oversampled. 
The signal comparison performed in Step 4 provides a measure of the 
similarity of the phase or frequency modulation of a pair of signals being 
processed. This measure is given by a cost function C defined as the 
weighted mean square error of the least squares fit. 
##EQU4## 
where .phi..sub.D (0) is the least squares estimate for the initial phase 
given by 
##EQU5## 
The symbol indicates that this parameter is estimated. The cost function 
C reaches its minimum value of zero for infinite signal-to-noise ratios 
and perfectly time aligned signals having identical phase or frequency 
modulation. 
Additional information concerning the nature of the relationship between 
(.phi..sub.D (nT)-.phi..sub.D (0)) and .DELTA.f.sub.c nT can be obtained 
from the correlation of the residuals of the least squares straight line 
fit. A useful test based on theoretical distributions is given by the von 
Neumann ratio (VNR) test in which 
##EQU6## 
If the residuals have independent random Gaussian values, the VNR will 
have an expectation value of 2 for large N. Its value will be lower in the 
presence of significant serial correlation of the phase errors. This would 
be an indication that the residuals and therefore the result of the cost 
function given by Equation (4) are a result of mismatches in the phase or 
frequency modulation of the signals being processed rather than noise. 
The cost function or VNR is used to determine if new signal data matches 
that from previously observed signals. The lowest (highest) cost function 
(VNR) estimate is first determined. Then, secondly, this result is 
compared with a threshold to determine if a match decision should be 
declared. The actual threshold should be determined empirically since it 
will depend on the degree to which radars in the signal environment are 
different. It will also depend on factors such as multipath propagation 
and other sources of error. 
FIG. 1 is a block diagram of a circuit to illustrate a practical 
implementation for evaluating the similarity of multi-mode radar pulses 
according to the present invention. In FIG. 1, a signal received by an 
antenna 10 is amplified and shifted to a fixed intermediate frequency (IF) 
by a tuner 20. The IF signal from tuner 20 is then applied to an in-phase 
and quadrature demodulator 22 where in-phase and quadrature signals are 
generated. Those in-phase and quadrature signals are then digitized in an 
analog-to-digital (A/D) converter 24 which is connected to demodulator 22. 
One type of digital quadrature demodulator circuit which may be used to 
perform both of these operations is described in U.S. Pat. No. 4,090,145 
by Webb. Digitized data from A/D converter 24 meeting a criteria of having 
sufficient signal energy for further processing is then stored in a buffer 
memory 28. 
Newly stored data in the circular buffer array 28 will be compared to older 
data present in the buffer 28 in subsequent processing. Provisions can be 
made to clear or overwrite old signal data which is no longer of interest 
because a radar transmitter is inactive or that more recent data for the 
same radar transmitter is available in the buffer memory 28. This will 
avoid the need for having an excessively large buffer memory. 
The memory 28 can be organized as an array of buffers by suitably 
addressing a large Random Access Memory (RAM). If that memory has 2.sup.N 
address locations, it can be configured as 2.sup.K buffers of 2.sup.N-K 
word data locations. The K most significant address bits would then define 
the buffer selected and the remaining (N-K) address bits would define the 
location of the individual data words within the buffer. By using a 
resettable counter, the sequence of addresses required to either read or 
write the signal samples in the correct order can be generated. A memory 
controller implementing a similar idea has been developed for a different 
application as described by F. Godon et al on pages 646 to 648 of IEEE 
publication "Proceedings of the 33rd Midwest Symposium on Circuits and 
Systems", Aug. 12-15, 1990, Calgary, Alberta, Canada. Alternatively an 
array of First-In First-Out (FIFO) memory components can be used if 
provisions are made to rewrite data as it is read out. 
The digitized in-phase and quadrature signal data from A/D converter 24 is 
thresholded and endpointed in processor 26 to determine sequences of 
signal samples corresponding to individual pulses with that data being 
forwarded to the circular buffer array 28. The thresholded and endpointed 
operations, as previously described in Step 1, can be implemented in a 
pipelined purpose built processor 26 which receives digitized signal data 
from the A/D converter 24 for real-time operation. 
When a new signal is to be compared with one of the reference signals, the 
data for both signals in the circular buffer array 28 is accessed in the 
order in which it is stored and forwarded to the phase estimation 
processor 30. The differential phase data is then computed by the phase 
estimation processor 30 to provide an estimation of differential phase as 
previously described in Step 2. This computation by processor 30 involves 
multiplying the two signal data sequences on an element-by-element basis 
using a complex arithmetic multiplier and calculating the arctangent 
according to Equation (1). Quadrant correction and phase unwrapping are 
then performed by processor 30 as previously described in Step 2. The use 
of a Read Only Memory (ROM) lookup tables to estimate differential phase 
is described by Webb in U.S. Pat. No. 4,090,145. 
The differential phase data from processor 30 is then forwarded to an 
analysis processor 32 which provides a least squares estimation of carrier 
frequency offset. The least squares estimator for carrier frequency offset 
.DELTA.f.sub.c is determined by processor 32 according to Equation (2) 
from .phi..sub.D (nT) and weighting parameters .PSI.(nT) which are 
determined from Equation (3), or simplified approximations of Equation 
(3), as previously described in Step 3. 
The data from the least squares analysis processor 32 is then forwarded to 
a statistical analysis processor 34 where a cost function C according to 
Equation (4) is computed which provides a measure of the similarity of the 
phase or frequency modulation between a pair of signals. The cost function 
C is defined as the weighted mean square error of the least square fit. 
The lowest cost function C value generated, between a new signal and 
reference signals, is then compared in statistical analysis processor 34 
with a threshold to determine if a new signal matches any of the existing 
reference signals. If the new signal matches one of the reference signals, 
either the new signal data or the corresponding reference signal data can 
be overwritten in the buffer memory 28 when the next signal pulse is 
processed. This will save space in the buffer memory 28 and avoid the need 
for having an excessively large buffer memory available. However, when no 
match can be found for a new signal, that new signal data can be retained 
in the memory and used as a reference signal for processing with detected 
signal pulses which are subsequently receive. 
The results of the processing by the statistical analysis processor 34 can 
be made available to a system operator via a video display 36 or 
transferred, via suitable data bus, to an electronic warfare system (EWS) 
to aid in resolving ambiguities in the processing and identification of 
signals. 
The analysis processors, to which the differential phase data from 
processor 30 is transferred, can be implemented using one or more software 
programmable processors. With only one processor, the cost function C 
would be computed for the new signal and each of the reference signals for 
only one reference signal at a time. The use of multiple processors would 
permit the simultaneous, rather than serial, solution of the cost function 
C for a number of reference signals. This would, thereby, improve the 
maximum throughput for the system. 
The control processor for an EWS, which may be implemented as a standard 
single board computer, performs functions such as tuning the tuner to 
receive signals of interest, setting its gain,setting the orientation of 
the antenna if it is directional and setting threshold levels. Any of 
these changes could result from either manual command of an operator or 
from requests by an EWS for additional information concerning signals that 
have been observed. 
Various modifications may be made to the preferred embodiments without 
departing from the spirit and scope for the invention as defined in the 
appended claims.