Complementary-sequence pulse radar with matched filtering and Doppler tolerant sidelobe suppression preceding Doppler filtering

A radar transmits dispersed pulses in which the subpulses are modulated by first and second mutually complementary code sequences, the autocorrelation functions of which are selected so that, in the sum of their autocorrelation functions, the main range lobes add, and the range sidelobes cancel. The received pulses with their Doppler sidebands are applied to a plurality of channels, each of which (except one) contains a mixer-oscillator combination that removes a specific Doppler phase shift along the range dimension at a different channel frequency. One channel has no mixer-oscillator because it is centered at a zero channel frequency. Within each channel, the received signals modulated by the first and second codes are matched-filtered by filters matched to the first and second codes, respectively, to produce first and second time-compressed pulses, each including (a) a main lobe representing the target range, and (b) undesirable range sidelobes. The first and second time compressed pulses are added together in each channel, to produce range pulses with suppressed range sidelobes. The channel signals, after pulse compression, delay, and addition, are each applied to one channel of a pulse-to-pulse Doppler filter bank. The outputs from the pulse-to-pulse Doppler filter bank are applied for further radar signal processing.

This invention relates to radar systems generally, and more specifically to 
arrangements for reducing range sidelobes in radar systems transmitting 
mutually complementary codes, and using matched filtering of the codes, 
and summation for cancelling range sidelobes, followed by Doppler 
processing of received echoes. 
The high speed and long range of modern airborne vehicles places increasing 
range demands on radar systems used for tracking. The long-range 
requirement also requires the use of relatively high transmitted power to 
reliably detect small targets. High transmitted power implies a relatively 
higher peak transmitter power or a longer duration transmitter pulse (also 
known as a "wider" pulse). Assuming a maximum available peak power, longer 
range implies a longer duration transmitted pulse. A longer duration pulse 
tends to reduce range resolution, which is the ability to distinguish 
among targets which are at similar ranges. Pulse compression techniques 
can be used to improve range resolution in spite of the longer pulse 
duration, thus eliminating the need for high peak power short pulses, but 
the minimum range at which a target can be detected by a monostatic radar 
system increases with the transmitted pulse length. Thus, if the 
transmitter pulse duration is 100 microseconds (.mu.s), the minimum 
distance at which a target may be detected by a monostatic radar is about 
8 nautical miles (nm). Clearly, a radar using pulses of such a duration 
cannot be used to detect close-in targets, as for example aircraft which 
are landing or taking off from an airport at which the radar is situated. 
An additional problem associated with pulse compression is the appearance 
of range sidelobes (as distinguished from antenna sidelobes) in addition 
to the main range lobe. The time position, or range, of the main lobe is 
the position that is tested for the presence of a target and for 
estimating the parameters of that target (reflected energy or power, 
closing speed, fluctuations in echo power and closing speed, etc.). The 
presence of range sidelobes on the compressed pulse results in interfering 
echoes which originate at ranges other than the range of the main lobe. 
This interference, known as "flooding," can cause erroneous estimates of 
the echo characteristics in the range cell (i.e., range increment) covered 
by the main lobe. Prior art techniques for suppressing range sidelobes 
include the "zero-Doppler" technique, in which the range sidelobe 
suppression scheme is based in part upon the assumption that the 
interfering echoes, as well as the desired echo, have a closing velocity 
that has no significant Doppler phase change or shift over the duration of 
the uncompressed pulse. The Doppler phase shift .phi..sub.DV across the 
uncompressed pulse is 2.pi. times the product of the Doppler frequency 
shift and the uncompressed pulse duration (i.e. .phi..sub.DV =2.pi. 
f.sub.d T.sub.0 radians). When this Doppler phase shift is actually zero 
or very small, moderate sidelobe suppression is achievable with the zero 
Doppler design. However, the zero Doppler design is very sensitive to 
small Doppler frequency shifts, making deep sidelobe suppression 
impossible for radar applications in which very deep sidelobe suppression 
is desired, as for example in weather mapping, clear air turbulence 
detection, and microburst detection. 
An approach to range sidelobe suppression elimination involves the use of 
complementary phase sequences imposed on the transmitted signal. U.S. Pat. 
No. 5,151,702, issued Sep. 29, 1992, in the name of Urkowitz (Urkowitz 
'702), incorporated herein by reference, describes a pulse radar system in 
which pairs of complementary phase sequences are transmitted sequentially, 
as illustrated in FIG. 2. FIG. 2 illustrates a sequence of transmitted 
pulses as described in the aforementioned Urkowitz '702 patent. In FIG. 2, 
the transmitted sequence includes a plurality M/2 of "A" pulses 1310 
transmitted in sequence, switching over at a time T to a similar sequence 
of a like number M/2 of "B" pulses 1312, for a total of M pulses. The A 
and B pulses are mutually complementary, in that, after pulse compression 
by matched filtering, the sidelobes are equal but of opposite sign, while 
the main lobes are of the same sign and thus the sidelobes are cancelled 
while the main lobes add producing an enhanced main lobe with no 
sidelobes. An illustration is given below. Upon reception, Doppler 
processing is used to separate returns into frequency bins representative 
of radial speed. Each bin output undergoes pulse compression resulting in 
a pair of pulse compressed waveforms having mutually complementary (i.e., 
equal magnitude but opposite sign) sidelobes, but main lobes of the same 
sign and magnitude. Upon addition, after suitable delay, the main lobe is 
enhanced, but the sidelobes are cancelled. Mathematical support for the 
properties of complementary sequences and method for their generation are 
given in the references cited in the aforementioned Urkowitz '702 patent. 
FIG. 1 is a simplified block diagram of a radar system as described in the 
abovementioned Urkowitz '702 patent. In FIG. 1, an antenna 18 is connected 
by way of a transmit-receive (T/R) duplexing or multiplexing system 50 to 
a transmit controller (TX) 3. Controller 3 establishes the system pulse 
duration, PRF, frequency and the like, and provides other control 
functions including generation of local oscillator and tuning signals. 
Antenna 18, controller 3 and T/R 50 together cause transmission of 
electromagnetic signals, illustrated as 7, and couple echoes of the 
electromagnetic signals received by antenna 18 by a path 9 to a receiver 
and analog signal processor (ASP) 52 for low-noise amplification, 
frequency downconversion, and the like, with the aid of local oscillator 
(L.O.) signals. In their broadest concept, these are conventional radar 
techniques. The resulting baseband signals may, in general, include 
orthogonal inphase (I) and quadrature (Q) components. The analog portion 
may also contain a subpulse matched filter, as is well-known in the art, 
to maximize the signal to noise ratio of each subpulse of the set of 
subpulses comprising each input sequence. Subpulse matched filters are 
known in the prior art and may be implemented, for example, by a surface 
acoustic wave (SAW) filter. The baseband signals are applied from 
receiver/ASP 52 to an analog-to-digital converter (ADC) associated with a 
block 62, which converts the analog baseband signals to digital form with 
the aid of system timing signals. The "range clock" portion of the timing 
signals establishes the smallest time interval into which the received 
signals are quantized, and therefore establishes the smallest discernible 
target range increment. 
As described in the abovementioned Urkowitz patent, a buffer may be 
associated with ADC 62 of FIG. 1 for purposes unrelated to the present 
application. The digital signals are coupled from ADC 62 (or its buffers, 
if used) to a digital signal processor (DSP) 68. The signals processed by 
DSP 68 may be further processed in known manner, and ultimately are 
provided to a display for displaying information relating to the target. 
FIG. 3 is a simplified block diagram of a portion of the processing which 
might be included in DSP block 68 of FIG. 1 for prior-art range sidelobe 
reduction using complementary sequences. In FIG. 3, an I+jQ signal from 
the complex analog-to-digital converter in block 62 is applied by way of 
an input port (input) 210 to a bank of narrow-band Doppler filters 
illustrated together as a filter bank 216. Each filter element of bank 216 
responds to a particular narrow frequency band f.sub.0, f.sub.1, f.sub.2 . 
. . f.sub.M-1, thereby separating the incoming signal into a plurality of 
frequency bins, the frequencies of which depend upon the Doppler frequency 
attributable to the radial velocity of the target. FIG. 11 illustrates a 
baseband spectrum f.sub.0 and additional spectra f.sub.1, f.sub.2, f.sub.3 
. . . f.sub.M-1, which together represent the output signals from filter 
bank 216. An echo having a given Doppler shift produces a substantial 
output from only one filter output. For best velocity selectivity, the 
bandwidths of filter elements f.sub.0, f.sub.1, f.sub.2 . . . f.sub.M-1, 
of filter bank 216 of FIG. 2 are narrow, in the range of a few Hertz or 
less. The bank of Doppler filters represented as block 216 may be 
implemented by a signal processor performing a discrete Fourier transform 
(DFT) by means of a fast Fourier transform (FFT) algorithm. The output of 
each filter is a range trace which is the sum of a sequence of Doppler 
filtered range traces. A particular filter output, therefore, represents 
target echoes having the particular Doppler frequency shift corresponding 
to its center frequency, and a small range of Doppler shifts about that 
center frequency, which depends upon the bandwidth of the filter. The 
output of each filter is coupled to a corresponding amplitude detector 
(not illustrated), to generate signals which, when arrayed, can be sorted 
according to the velocity of the target by selecting the appropriate 
detector output. Thus, the presence of a target signal at the output of a 
Doppler filter indicates that the target has a particular radial velocity. 
Within each Doppler frequency bin, the target range is known from the time 
of arrival of the signal. The signals produced by the abovementioned 
detectors are coupled to threshold circuits in DSP block 68 of FIG. 1, to 
allow separation of significant returns from noise, and thence for further 
processing. The circuits fed by the various Doppler filter elements 
f.sub.0, f.sub.1, f.sub.2, . . . f.sub.M-1, may each be considered a 
"Doppler channel." Thus, filter element f.sub.0 and detector 218a 
constitute a Doppler channel relating to targets with a low radial 
velocity, while filter element f.sub.2 and detector 218b together 
constitute another Doppler channel relating to targets with a larger 
radial velocity, corresponding to f.sub.2. 
In the context of the Urkowitz '702 patent, DSP block 68 of FIG. 1 may 
perform the functions of (a) pulse-to-pulse Doppler filtering by means of 
a Fast Fourier Transform (FFT) algorithm, with data weighting to control 
signal leakage from neighboring Doppler shifts (frequency leakage); (b) 
digital pulse compression of the complex envelopes of the returns from the 
complementary sequences; (c) summing of such pulse compressed echo to 
eliminate or substantially reduce range sidelobe due to the complementary 
nature of the compressed sidelobes arising from the complementary code 
patterns associated with the pair of transmitted sequences; (d) further 
signal processing including CFAR (constant false alarm rate) processing, 
thresholding for target detection, spectral processing for weather 
mapping, etc. Items (a) and (d) are performed in ways well understood in 
the art, and form no part of the invention. The summing and consequent 
range sidelobe suppression (c) is advantageously Doppler tolerant as 
described below in the aforementioned Urkowitz '702 patent. The results of 
the processing done in block 68 may include (a) target detection reports 
(aircraft); (b) radar track detection reports; (c) weather components for 
each resolvable volume of space, including (c1) echo intensity; (c2) echo 
closing speed, and (c3) spectral spread of the echo, and these components 
of information may be included in Digitized Radar Detection Reports 
(DRDR). The DRDR reports may also include data relating to the signal 
processing. A person skilled in the art of pulse compression will know 
that the radar pulse must be coded in some manner that allows DSP block 68 
to correlate received signals with the known transmitted pulse code. The 
correlation process simultaneously improves the signal-to-noise ratio and 
the range resolution of target echoes. A person skilled in the art knows 
that the pulse compression, delay, and subsequent summation of pulse 
compressed complementary sequences produces cancellation or substantial 
reduction of range sidelobes while enhancing the main lobe of the 
resultant compressed pulse. Prior to the aforementioned Urkowitz '702 
patent, this could not be accomplished in a Doppler tolerant manner and 
therefore resulted in both sidelobe deterioration (i.e., increase in 
sidelobe level) and main lobe reduction in the presence of unknown Doppler 
shifts. 
In accordance with an aspect of the aforementioned Urkowitz '702 patent 
range sidelobes are suppressed in a Doppler tolerant manner by a technique 
which includes separating the target echoes arising from both transmitted 
pulse sequences into a plurality of Doppler or frequency "bins" and then 
applying the removal of Doppler phase shift along the range dimension, 
sequentially pulse compressing the echoes from the two sequences, then 
delaying the earlier pulse compressed sequence and summing with the 
succeeding pulse compressed sequence. 
SUMMARY OF THE INVENTION 
In a radar system, first and second pulse sets are recurrently transmitted, 
either sequentially or simultaneously. The first set of pulses is 
dispersed in time pursuant to a first phase code, and the second set of 
pulses is dispersed in time pursuant to a second phase code which is 
complementary to the first. The echoes from the target are received to 
form received first and second pulse sets. The echoes may be processed by 
a plurality of multipliers, to each of which there is additionally coupled 
a digital oscillator of appropriate frequency to remove Doppler phase 
shift along the range dimension of the echo. Thereupon the echoes are 
processed by filtering matched to the separate code sequences, to thereby 
produce a pair of compressed range pulses in which the main range 
sidelobes are of the same polarity or phase, and in which the range 
sidelobes are of mutually opposite polarity or phase. The pair of 
compressed range pulses are summed to produce range pulses in which the 
sidelobes are suppressed. Following the process of range sidelobe 
suppression by summing the code-matched-filtered, pulse-to-pulse Doppler 
filtering is applied, to effect separation into frequency bins. Thus, the 
code-matched compressed, summed received pulse sets are separated by 
frequency, and also by incremental time of receipt, which corresponds to 
range. 
In a particular embodiment of the invention, the returned pulse sets are 
received sequentially. A first code-matched filter filters the first pulse 
set, and a switch is operated between the end of the first pulse sequence 
and before the beginning of the second pulse set, to decouple the first 
code-matched filter, and to couple in-line a second code-matched filter. 
The second code-matched filter then filters the second pulse set. A delay 
associated with the first code-matched filter delays the matched-filtered 
first pulse sequence until matched filtering of the second pulse set is 
accomplished, whereupon the delayed first set is summed with the second 
set. The plurality of such sums is applied to the several filters of 
pulse-to-pulse Doppler filter bank whose outputs are amplitude detected 
and applied to further processing as is usual in the radar art. In another 
embodiment of the invention, the returned pulse sets are received 
simultaneously.

DESCRIPTION OF THE INVENTION 
The invention pertains specifically to the reception of returns including 
the aforementioned pairs of complementary phase sequences, and to 
processing using matched filtering (i.e., pulse compression) and sidelobe 
cancellation. Elements of FIG. 4 corresponding to those of FIG. 3 are 
designated by the same reference numerals. FIG. 4 is similar to FIG. 3, 
differing in that the frequency conversions and matched filtering precede, 
rather than follow, Doppler filter 216. An aspect of the present invention 
recognizes that the pulse to pulse Doppler filtering and consequent 
removal of Doppler phase shift in the range dimension, pulse compression, 
delay, and summation are independent operations. This independence arises 
from the fact that removal of Doppler phase shift in range, pulse 
compression, delay, and summation are intra-pulse operations while the 
Doppler filtering is an interpulse (i.e., pulse to pulse) operation. 
Therefore, these operations may be reversed. The alternative set of 
operations is a central feature of the present invention and is 
illustrated in FIG. 4. A mathematical demonstration that FIG. 4 is 
equivalent to FIG. 3 appears in the below Appendix. 
The processor of FIG. 4 couples the signal applied to input port (input) 
210 to a plurality of digital mixers or multipliers (i.e., digital mixers) 
320b, 320c, . . . , 320m. The unmixed I+jQ signal applied to input port 
210 is applied directly, without mixing, to the movable or common element 
of switch 1410a, which is associated with contacts 1412a and 1414a. Thus, 
one of the plurality of outputs from (or connections to) input port 210 is 
a direct connection to switch 1410a. This direct connection exists because 
this path represents the zero Doppler frequency. Similarly, the outputs of 
multipliers 320b, . . . , 320m are connected to the common elements of 
corresponding switches 1410b, . . . , 1410m, respectively. For example, 
one connection from signal input port 210 is to the input port of 
multiplier 320b. Multiplier 320b has a second input port coupled to a 
digital oscillation source (not illustrated in FIG. 4) of signal 
EQU exp (-j2.pi.f.sub.ik .tau..sub.o), k=0, 1, . . . (1) 
where 
f.sub.1 is the center frequency of the corresponding filter of filter bank 
216 that is ultimately coupled to the output of multiplier 320b, 
.tau..sub.0 is the range sampling period, and k is an integer time index. 
The oscillator frequency represented by equation (1) in the arrangement of 
FIG. 4 is thus the negative (i.e., same absolute value, but 180.degree. 
out of phase) of the center frequency (f.sub.1) at which the corresponding 
filter element of filter bank 216 is centered. As a further example, the 
oscillator exp (-j2.pi.f.sub.2 k.tau..sub.0) applied to multiplier 320c is 
negative of frequency f.sub.2 at which filter element f.sub.2 of filter 
bank 216 is centered. Similarly, oscillator exp (-j2.pi.f.sub.M 
k.tau..sub.0) applied to multiplier 320m is the negative of frequency 
f.sub.M at which filter element f.sub.M-1 of filter bank 216 is centered. 
No multiplier 320 is necessary to process that portion of the signal 
applied to input port 210 which is coupled to switch element 1410a, 
because the signal is already centered at frequency f.sub.0 to which 
filter element f.sub.0 of filter bank 216 is tuned. Any initial phase 
shift associated with the oscillator signal is unimportant, because 
eventually only the magnitudes of the Doppler channel signals are used. 
Essentially, the outputs of the individual multipliers have been 
heterodyned in range so that the Doppler phase shift along the range 
dimension has been removed so that the Doppler phase shift in each 
multiplier output has been confined to a narrow interval around zero 
frequency, labeled f.sub.0, as far as Doppler frequency phase variation in 
the range dimension is concerned, leaving only the pulse-to-pulse Doppler 
frequency phase shift. This latter Doppler phase shift will ultimately be 
removed in the Doppler filter bank 216. 
Since the Doppler phase shift along the range dimension has been removed at 
the outputs of multipliers 320b, 320c, . . . , 320m of FIG. 4, as well as 
on the path leading to single pole, double throw switch 1410a, any 
filtering in the range dimension can be identical for all such paths. The 
common elements of switches 1410 are ganged or coupled together so that 
all the movable portions switch to contact their respective contacts 1414 
simultaneously. The input to each of the switches 1410a, 1410b, . . . , 
1410m consists of the two sets of signals, sequential in time, as 
illustrated in FIG. 2. Each set is a set of M/2 subpulses comprising one 
transmitted pulse. The first sequence of subpulses is modulated with phase 
sequence A, while the second sequence of subpulses is modulated with phase 
sequence B, complementary to phase sequence A. Complementary sequences are 
described below. 
In a manner similar to that of FIG. 3 and as described in the Urkowitz '702 
patent each contact 1412 of FIG. 4 is connected to the input of a matched 
filter 1416 which is matched to subpulse sequence A of FIG. 2. Thus, 
contact 1412a of FIG. 4 is connected to the input of matched filter 1416a. 
Similarly, switch contact 1412b is coupled to the input of a matched 
filter 1416b which is matched to the same A sequence. Similarly, contact 
1412m is coupled to the input of matched filter 1416m which is matched to 
subpulse sequence A. Each of the single pole, double throw switches 1410a, 
. . . , 1410m of FIG. 4 is illustrated as a mechanical switch which 
includes contacts 1412 and 1414, but those skilled in the art know that 
mechanical switches are not used, and that solid state transmission 
switches suitable for the number of parallel bits in each data path are 
used instead. 
Each terminal 1414 of switches 1410 of FIG. 4 is coupled to a corresponding 
filter 1418, which is matched to subpulse sequence B of FIG. 2. For 
example, switch contact 1414a is coupled to the input of a matched filter 
1418a, which is matched to subpulse sequence B of FIG. 2. Similarly, 
switch contact 1414c of FIG. 4 is coupled to the input of filter 1418c 
which is also matched to subpulse sequence B of FIG. 2. The position of 
movable elements 1410 determine whether the baseband signals derived from 
the multipliers as well as directly, or in an unmultiplied manner, from 
input port 210, are applied to filters matched to the A or B sequences. In 
the illustrated position of movable switch elements 1410, the A-matched 
filters are connected. 
The output signals from A matched filters 1416 of FIG. 4 are coupled to 
corresponding delay elements 1420. For example, the output of matched 
filter 1416b is coupled to the input of a delay element 1420b, and the 
output of a matched filter 1416m is coupled to the input of a delay 
element 1420m. Each A filtered signal is applied from its filter 1416 to a 
delay 1420, which delays for a duration, MT/2, where T is the pulse 
repetition period. The delay of MT/2 is equal to the duration of the A 
pulse sequence or M/2 pulses. The outputs of delay elements 1420 are 
applied to inputs of a corresponding set of adders (+) or summers 1422, 
which also receive the outputs of the associated B matched filters 1418. 
Thus, the output of A matched filter 1416a is applied to a first input 
port of an adder 1422a by way of a delay 1420a, and the output of B 
matched filter 1418a is coupled to a second input port of adder 1422a. 
Similarly, the output of A matched filter 1416c is applied to a first 
input port of an adder 1422c by way of a delay 1420c, and the output of B 
matched filter 1418c is coupled to a second input port of adder 1422c. 
The A matched filters 1416 of FIG. 4 respond to the sequence of A pulses, 
if present, by producing progressively greater response peaks as the 
filters "fill" with matched signal. At the moment when each A matched 
filter 1416 is "full", the filter output is a maximum. Thus, the A matched 
filter produces a time-compressed filtered signal representing, by its 
time of receipt, the target range, and representing, by its deviation from 
a particular Doppler frequency band, the radial speed of the target. The A 
filtered signal undesirably includes a plurality of sidelobes. 
The time at which the switches 1410 switch from the A to the B filters in 
the arrangement of FIG. 4 may be any time during transmission of the first 
pulse following the initial group of M/2 pulses, and during the first 
pulse of each set of M/2 pulses thereafter. During transmission of the 
pulse, nothing can be received anyway, so any time during the pulse is 
satisfactory. 
In the alternate positions (not illustrated) of switches 1410 of FIG. 4, 
the baseband signals in each Doppler channel are each applied to a B 
matched filter 1418. The B sequence (if present) "fills" the B sequence 
matched filter for that channel, and the filter response increases toward 
a maximum value, which occurs when the B matched filter is "full." 
Thereafter, the response of the B matched filter decreases. The outputs of 
the B matched filters are applied to the corresponding adders 1422, with 
the peak B response arriving at the adder at the same time as the peak A 
response from the associated delay element 1420. The peak responses are 
in-phase and of the same polarity, and they add to produce the main range 
lobe; but the sidelobes produced by the A and B sequences are of mutually 
opposite polarity, and tend to cancel in each adder, as described in 
greater detail below. Thus, the range sidelobes are reduced by mutual 
cancellation when complementary pulse sequences are transmitted, without 
the use of separate range sidelobe reduction filters. 
As described above, the range sidelobes tend to cancel. If the input 
Doppler shift is not exactly equal to the center frequency of a Doppler 
filter element of filter bank 216, the range sidelobes may not cancel 
exactly, but the deterioration in the cancellation will not exceed that 
caused by a frequency shift equal to half the bandwidth of a filter 
element. Normally, this equals half the frequency spacing between adjacent 
filters of the filter bank. 
The pulse-compressed, sidelobe suppressed baseband information at the 
output of each summer 1422 of FIG. 4 is applied to a corresponding filter 
of Doppler filter bank 216 of FIG. 4. For example, the output of summer 
1422a is applied to filter element f.sub.0 of Doppler filter bank 216, the 
output of summer 1422b is applied to filter element f.sub.1 of Doppler 
filter bank 216, . . . and the output of summer 1422m is applied to filter 
element f.sub.M-1 of Doppler filter bank 216. This arrangement has the 
salient advantage that the Doppler filter elements of filter bank 216 are 
identical, being all at baseband. A further operational advantage is that 
the effective Doppler center frequencies of the system may be selected 
simply by selecting the frequency of mixer signals applied to multipliers 
320; the oscillator frequency corresponds to the center Doppler frequency 
of that particular channel. 
In operation of the arrangement of FIG. 4, the complex received signal is 
applied to the common element of switch 1410a and, by way of 
frequency-converting multipliers 320b, 320c, . . . 320m to the 
corresponding common elements of switches 1410b, 1410c, . . . 1410m, 
respectively. This effectively converts the Doppler frequency of interest 
to baseband, so that the following matched filters 1416a-1416m are 
mutually identical, matched filters 1418a-1418m are mutually identical, 
and the Doppler filters of Doppler filter bank 216 are mutually identical, 
for cost reduction. 
FIG. 5 illustrates a tapped delay line or transversal filter of the type 
known as a "finite impulse response" (FIR) filter, because a change in the 
input causes a change in the output that extends over a finite time. Such 
a filter may be used as a matched filter signal processor 1416 or as a 
matched filter signal processor 1418 in FIG. 4. For definiteness, FIG. 5 
represents matched filter (i.e., pulse compressor) 1416b for sequence A. 
Downconverted signals from multiplier 320b are applied via terminal 1412b 
of switch 1410b of FIG. 4 to an input port 444a of the filter of FIG. 5. 
Port 444a of FIG. 5 applies the signal to a tapped structure 440 which may 
be a delay line (analog) or shift register (digital) coupled as a 
transversal filter, and allowing signals to propagate to the right. 
Signals propagate past taps illustrated as nodes 444b, 444c, . . . , 444N. 
The temporal spacing (delay) between taps equals the range sampling period 
.tau..sub.0. Each node 444 is coupled to a tap weight multiplier, 
illustrated by a triangular symbol 446a, 446b, . . . 446n, which weights 
the signals applied thereto. The weighted, delayed signals from 
multipliers 446 are applied to a combinatorial summer (.SIGMA.) 450 for 
summing all the weighted signals for producing the desired matched 
filtered signals. The summed signals are applied from the output of summer 
450 of FIG. 5 to delay element 1420b of FIG. 4. The number of taps and the 
weights to be applied are determined by the pattern of subpulses making up 
sequence A. the weights are, in fact, the conjugate, time reverse, of the 
complex envelope values of the A sequence pulse sampled at a sampling 
frequency 1/.tau..sub.0. 
An arrangement like that of FIG. 5, but with taps weights matched to the 
complex envelope samples of sequence B, may be used as matched filter 
1418b of FIG. 4 for sequence B. The output of sequence B matched filter 
1418b of FIG. 5 is applied to adder 1422b, and the sum is formed therein 
with the delayed (through delay 1422b) output of sequence A matched filter 
1416b. The sum formed in summer 1422b is applied to filter f.sub.1 of the 
pulse to pulse Doppler filter bank 216. The outputs of Doppler filter bank 
216 are coupled for further processing to amplitude detectors, as 
described previously, for sorting and further processing. The operation 
described explicitly for matched filters 1416b, 1418b, delay 1420b, and 
summer 1422b also applies to the corresponding other matched filters, 
delays and summers. 
FIG. 6 is a simplified block diagram of another arrangement for performing 
matched filtering of complementary pulse sequences in accordance with the 
invention. Elements of FIG. 6 corresponding to those of FIG. 4 are 
designated by like reference numerals. In FIG. 6, the baseband (f.sub.0) 
signals in each Doppler channel are applied to switched-tap transversal 
filters 1514. For example, the baseband signal from multiplier 320b in the 
f.sub.1 Doppler channel is applied by way of a data path 1512b to a 
switched-tap transversal filter 1514b, and the baseband signal from 
multiplier 320m in the f.sub.M-1 Doppler channels is applied to a similar 
filter 1514m. The f.sub.0 Doppler channel, already being at baseband, does 
not require a multiplier 320. 
FIG. 7 illustrates a representative switched-tap transversal filter 1514. 
For definiteness, FIG. 7 represents filter 1514b of FIG. 6. In FIG. 7, the 
baseband signals are received on data path 1512b and are applied to a 
delay line or shift register 1530, which propagates the signal to the 
right, past a plurality of taps 1532(0), 1532(1) . . . 1532(N-1). Each tap 
is coupled to the inputs of a pair of weighting elements h.sub.A and 
h.sub.B. For example, tap 1532(0) is coupled to the inputs of a pair of 
weighting elements h.sub.A (0) and h.sub.B (0), tap 1532(1) is coupled to 
the inputs of a pair of weighting elements h.sub.A (1) and h.sub.B (1), 
and other taps (not illustrated) are coupled to corresponding pairs of 
weighting elements. Last tap 1532(N-1) is coupled to the inputs of a pair 
of weighting elements h.sub.A (N-1) and h.sub.B (N-1). 
The output of each weighting element h.sub.A of FIG. 7 is coupled to a 
first contact 1534A of a single pole, double throw switch illustrated as a 
movable mechanical element 1536. The output of each h.sub.B weighting 
elements is connected to the other contact, 1534B, of one of switches 
1536. For example, the outputs of weighting element h.sub.A (0) and 
h.sub.B (0) are connected to contacts 1534A(0) and 1534B(0), respectively, 
of switch 1536(0), the outputs of weighting elements h.sub.A (1) and 
h.sub.B (1) are connected to contacts 1534A(1) and 1534B(1) of switch 
1536(1), and the outputs of weighting elements h.sub.A (N-1) and h.sub.B 
(N-1) are connected to contacts 1534A(N-1) and 1534B(N-1), respectively, 
of switch 1536(N-1). Movable switch elements 1536 are all coupled to a 
combinatorial summing network 1538. Switches 1536 are ganged for 
simultaneous operation. 
In operation of the arrangement of FIG. 7, switches 1536 are thrown to the 
positions appropriate to the subpulse sequence of that one of the A and B 
sequences (or other sequences, as appropriate) which currently transverses 
the delay line. This connects the corresponding weighting elements 
(h.sub.A or h.sub.B) in-line, so that the summing element 1538 responds to 
a match to the subpulse sequence. Consequently, a compressed pulse is 
generated on output data path 1540b. At the appropriate time during the 
change-over between A and B received sequences, ganged switches 1536 are 
thrown to the alternate position (the position illustrated), thereby 
placing the h.sub.B weighting in-line. The filter then responds when the B 
sequence is matched, by producing a second compressed pulse on data path 
1540b. Thus, it can be seen that a switched-tap filter produces sequential 
compressed pulses on data path 1540b in response to the two complementary 
sequences. 
Referring once again to FIG. 6, the compressed pulse pair produced by any 
one of, or by more than one of, matched filters 1514, may appear on the 
associated one or more data path 1540 if the target radial velocity 
includes components producing a Doppler shift within the Doppler channel 
bandwidth. The output of each filter 1514 is applied to a single pulse, 
double throw switch illustrated by a mechanical switch symbol 1516. 
Switches 1516 are ganged together, and are illustrated in the position 
selected for routing the first of the two compressed pulses to a delay 
1520. Switches 1516 of FIG. 6 may be ganged with switches 1536 of FIG. 7 
for simultaneous operation therewith. For example, the first (A) 
compressed pulse produced at the output of filter 1514b is routed by 
switch 1516b to a delay element 1520b, which delays for a time MT/2, as 
described in conjunction with FIG. 4. Switch 1516b then switches 
concurrently with arrival of the B pulse sequence at filter 1514b, and 
routes the B compressed pulse to a summing circuit 1522b, for summing with 
the delayed compressed A pulse, as described in conjunction with FIG. 4. 
FIG. 8 is a simplified block diagram of a system for simultaneous 
transmission of two signals, each coded with one of mutually complementary 
codes, as described in more detail in copending patent application Ser. 
No. 08/079,725, filed Jun. 21, 1993 in the name of Urkowitz . In FIG. 8, a 
transmit-receive antenna 810 is coupled to the input-output port 812 of a 
circulator 813 for separating input and output energy. A first 
controllable radio-frequency source, modulator or "transmitter" (TX 1) 
816, operating at a first carrier frequency F1, is coupled, through a 
transmit path 815, to a duplexer or combiner 814, as well known in the 
art. A second controllable radio-frequency electromagnetic signal source, 
modulator or "transmitter" (TX2) 820, operating at a second carrier 
frequency F2, is also coupled to duplexer 814, through a transmit path 
819. A pulse code generator 824 recurrently produces first and second 
pulses or sets of subpulses ("chips") under the control of timing signals 
applied over a control signal path 830 from a radar controller (not 
illustrated), and applies the pulses so produced over paths 826 and 828, 
respectively, to transmitters 816 and 820, respectively. In accordance 
with an aspect of the invention, the first and second sets of pulses are 
each dispersed in time, and are phase coded in a mutually complementary 
manner, so that, after pulse compression by code-matched filtering, 
described below, the main range lobes of the two compressed pulses are of 
the same sign or polarity, and the range sidelobes are of mutually 
opposite sign or polarity. The carrier signals produced by transmitters 
816 and 820 are phase modulated by the first and second pulses (sets of 
subpulses), respectively, during recurrent transmitted pulse intervals 
Thus, each transmitted pulse is occupied by a set of subpulses or chips, 
and both pulses are simultaneously transmitted, each modulated by a 
mutually complementary subpulse set. 
Transmitters 816 and 820 are operated simultaneously at different carrier 
frequencies, with each overall carrier pulse phase-modulated by a set of 
subpulses, organized according to one of the complementary codes. The two 
transmitted pulses from transmitters 816 and 820 at their respective 
carrier frequencies are applied to the two inputs of duplexer 814. 
Duplexer 814 combines the signals for application through circulator 813 
to antenna 810. Antenna 810 transmits the two signals simultaneously, as 
represented by arrow 831. A target, represented by 832, reflects a portion 
834 of the energy back toward antenna 810. The velocity of propagation is 
the same for transmitted signals at both frequencies, so both signals 
arrive at the target simultaneously. 
The coded signals at the two frequencies are reflected by the target to 
form echo signals, which return to antenna 810 of FIG. 8, and from antenna 
810 to circulator 813. Circulator 813 separates transmit and receive path 
809 and 807. The signal in receive path 807 is applied to protective 
circuitry, well known in the art, and illustrated as a block 852, to 
protect subsequent circuits from the large signal that "leaks" through 
circulator 813 into the receive path during transmission. The received 
signal is then applied to an RF amplifier 854 to boost the signal to a 
level appropriate for input to mixer 856. The combination of RF amplifier 
854, mixer 856, and the local oscillator (L.O.) signal applied over path 
855 together provides low noise amplification, RF bandpass filtering, and 
downconversion to an intermediate frequency (IF) signal which appears on 
IF path 857. When mixed or heterodyned with local oscillator (LO) signal 
applied over a path 855, the resulting mixed intermediate frequency (IF) 
signal includes components resulting from echoes at both transmitted 
frequencies. The mixed intermediate frequency signal is applied through an 
IF signal path 857 to a first receiver 836, and to a second receiver 838, 
for filtration as known in the art. The IF signal in path 857 is 
sufficiently wide in frequency so that it covers the band of frequencies 
encompassed by receivers 836 and 838. Receivers 836 and 838 have the same 
bandwidths. Receiver 836 is centered at an intermediate frequency F3, and 
receiver 838 is centered at an intermediate frequency F4. Frequencies F3 
and F4 are far enough apart so there is no significant overlap of the pass 
bands of the two receivers. Each receiver 836 and 838 is an analog 
filter-amplifier in the sense that each amplifies and passes a frequency 
band appropriate to the bandwidths of the two transmitted waveforms, with 
enough frequency separation to prevent significant frequency overlap. 
The echo signals at the outputs of receiver 36 and of receiver 38 of FIG. 8 
will be phase coded differently, in accordance with the first and second 
mutually complementary codes. Analog receivers 36 and 38 perform 
approximate matched filtering of the subpulses of the two phase coded 
waveforms, as is well known in the art. The passbands of the two analog 
receivers are shaped to approximate the frequency characteristics of the 
subpulses in each waveform. 
The analog echo signals at the output of receiver 836 of FIG. 8 are applied 
to an analog-to-digital converter (ADC) 840, for conversion from analog 
form to digital form. ADC 840 may also include a buffer, if desired. 
Similarly, the output of receiver 838 is applied to ADC & buffer 842, in 
which the signals are processed for conversion to digital form. The 
conversion from analog to digital form may be accomplished in at least two 
ways, both well known in the art. One way uses direct conversion from an 
offset intermediate frequency to digital form. The other way uses a pair 
of product detectors comprising two mixers and two lowpass filters feeding 
into two baseband analog to digital converters to form the real and 
imaginary parts of the complex baseband signal. The digital signals 
produced by ADCs 840 and 842 are applied to a phase alignment block 863 
over paths 861 and 862, respectively. Phase alignment block 863 brings the 
signals in the two receiver paths into phase alignment. The phase aligned 
digital signals are applied via paths 843 and 845 to digital signal 
processors (DSPs) 844 and 846, respectively, for processing by steps 
including the steps of filtering matched to the codes of first and second 
pulse sets, as described below, so as to form first and second compressed 
pulses in which the main range lobes are of the same sign or polarity, and 
in which the range sidelobes are of the same amplitude and of mutually 
opposite polarity. The compressed pulses produced by DSPs 844 and 846 are 
applied to the input ports of a summing (.SIGMA.) circuit 848, which 
includes a plurality of summing circuits 868a-868m, to thereby vectorially 
sum the compressed A and B pulses from DSP 844 and 845, thereby canceling 
the range sidelobes, and leaving the main range lobe, to produce the 
desired range sidelobe suppressed pulses. 
FIGS. 9a and 9b show alternative embodiments which may be used for 
producing phase alignment in block 863 of FIG. 8. In FIGS. 9a and 9b, two 
input paths 861 and 862 carry signals at carrier frequencies F1 and F2, 
respectively. Therefore, for any given range delay r.tau..sub.o, where 
.tau..sub.o is the range sampling period and r is an integer index, two 
signals will be misaligned in phase by an amount 
EQU 2.pi.r.tau..sub.o (F1-F2) (2) 
A phase correction of this magnitude may be applied entirely to the signal 
in path 861, as in FIG. 9a. Alternatively, the correction may be split 
between paths 861 and 862, as in FIG. 9b. 
FIG. 9a shows a first embodiment in which phase alignment block 863 
contains two inputs 861 and 862, but only input 861 is multiplied, via a 
complex digital multiplier 874, by the correction signal 
EQU exp [2.pi.r.tau..sub.o (F1-F2) (3) 
which brings the two output signals on paths 843 and 845 into phase 
alignment. FIG. 9b shows a second embodiment, in which phase alignment 
block 863 accepts signals over two input paths 861 and 862, with both 
multiplied, respectively, via complex digital multipliers 874 and 876, by 
phase corrections: 
EQU exp [j.pi. (F1-F2) r.tau..sub.o ] (4) 
for signal on path 861, and 
EQU exp [-j.pi. (F1-F2) r.tau..sub.o ] (5) 
for signal on path 862, which introduces equal and opposite phase 
corrections to bring the output signals on paths 843 and 845 into phase 
congruence. 
The radar system of FIG. 8, by comparison with the arrangement of U.S. Pat. 
No. 5,151,702, reduces the time required to produce range information in 
the presence of clutter and may provide reduced sidelobes in those cases 
in which the target exhibits rapid changes in reflective characteristics, 
since both of the echoes used to produce the reduced range sidelobe 
compressed range pulse are reflected by the target simultaneously. 
FIG. 10a is a simplified block diagram of summer 848, and of digital signal 
processors 844 and 846 of FIG. 8. Elements of FIG. 10a corresponding to 
those of FIG. 8 are designated by like reference numerals. In general, 
received signals encoded with code sequences A and B are separately 
applied to Doppler filters 216 and 266, respectively, of FIG. 10a. The 
output of each Doppler filter of FIG. 10a is heterodyned, as described 
below, with the output of a complex digital oscillator, the frequency of 
which corresponds to the Doppler frequency of that filter. The oscillator 
wave is preferably a digital stream at the range sampling frequency. The 
heterodyning removes the Doppler phase shift along the range dimension. 
The result is a signal whose spectrum has been shifted to zero frequency. 
The resulting zero frequency wave then undergoes matched filtering (i.e., 
pulse compression) by a filter matched to the corresponding code sequence 
A or B to produce compressed output signals, and the compressed output 
signals are summed. The resulting sums are pulse compressed, range 
sidelobe suppressed, signals. The range sidelobe suppression occurs 
because, as described above, the range sidelobes are complementary (i.e., 
equal in magnitude but opposite in sign). Each resulting sum is ultimately 
coupled to a corresponding amplitude detector (not illustrated in FIG. 
10a) to generate signals which, when arrayed, can be sorted according to 
the velocity of the target by selecting the appropriate detector output. 
Thus, the presence of a target signal at the output of a Doppler filter 
indicates that the target has a particular radial velocity. Within each 
Doppler frequency bin, the target range is known from the time of arrival 
of the signal. Also, the signals produced by the detectors may be coupled 
to threshold circuits in further digital processing, to allow separation 
of significant returns from noise, and thence for further processing and 
display. The several outputs of the detectors form a "periodogram", which 
is an estimate of Doppler power density spectrum of the echo. Such an 
estimate is useful when the echo is produced by meteorological phenomena, 
and can be used to help in determining the presence of hazardous weather 
conditions. The circuits fed by the sums of the various pairs of Doppler 
filter elements f.sub.0, f'.sub.0, f.sub.1, f'.sub.1, f.sub.2, f'.sub.2, . 
. . ; f.sub.M-1, f'.sub.M-1 of filter banks 216 and 266 may each be 
considered a "Doppler channel." Thus, filter element f.sub.0 and the 
following circuits, namely matched filter 218a constitute a Doppler 
channel relating to targets with a low radial velocity, while filter 
element f.sub.2, multiplies 220b and matched filter 218b together 
constitute another Doppler channel relating to targets with a larger 
radial velocity, corresponding to f.sub.2. 
Referring now to FIG. 10a, a digital signal comprising in-phase (I) and 
quadrature (Q) baseband components encoded with a first code sequence (A) 
is applied from phase alignment block 863 of FIG. 8 over data path 843 to 
digital signal processor 844 of FIG. 10a. Within processor 844 of FIG. 
10a, the signal is applied to a Doppler filter bank 216. Filter bank 216, 
which includes a plurality of narrow-band Doppler filters, each of which 
responds to a particular narrow frequency band f.sub.0, f.sub.1, f.sub.2, 
. . . ,f.sub.M-1, to thereby separate the incoming signal corresponding to 
phase code A into a plurality of frequency bins, the frequencies of which 
depend upon the Doppler frequency attributable to the radial velocity of 
the target. The frequency-separated signal in each frequency bin is also 
encoded with phase sequence A. 
Similarly, a digital signal comprising inphase (I) and quadrature (Q) 
baseband components encoded with a second code sequence (B), which is 
complementary to code A, is applied from phase alignment block 863 of FIG. 
8 over data path 845 to digital signal processor 846 of FIG. 10a. Within 
processor 846, the signal is applied to a Doppler filter bank 266 of FIG. 
10a, which is similar to Doppler filter bank 216. As in filter bank 216, 
Doppler filter bank 266 includes a plurality of narrowband Doppler 
filters. In Doppler filter bank 266, each filter responds to a particular 
frequency band f.sub.0, f'.sub.1, f'.sub.2, . . . f'.sub.M-1, to thereby 
separate the incoming signal corresponding to the complementary B phase 
code, into a plurality of frequency bins, the frequencies of which depend 
upon the Doppler frequency attributable to the radial velocity of the 
target. The frequency separated signal in each frequency bin is encoded 
with phase sequence B. The Doppler frequencies f'.sub.1, f'.sub.2, . . . 
f'.sub.M-1 at the outputs of the frequency bins of Doppler filter 266 of 
FIG. 10a differ from the Doppler frequencies f.sub.1, f.sub.2, . . . 
f.sub.M-1 at the outputs of the frequency bins of Doppler filter 216 of 
FIG. 10a because, for the same radial target velocity, the Doppler 
frequencies are proportional to the two carrier frequencies. The 
relationships between Doppler frequencies f.sub.1, f.sub.2, . . . 
f.sub.M-1 and f'.sub.1, f'.sub.2, . . . f'.sub.M-1 for a set of radial 
velocities v.sub.1, v.sub.2, . . . v.sub.M-1 and for carrier frequencies 
F1 and F2, are 
##EQU1## 
For a stationary target, v.sub.o =0, so that f.sub.o =f'.sub.o =0. 
The filtered output signals from Doppler filter bank 216 of FIG. 10a are 
applied (except for the f.sub.0 signal) to a bank of multipliers, for 
reasons described at length above, whereby all the signals are at 
frequency f.sub.0. The m signals from Doppler filter bank 216 are applied 
by way of paths 262a-262m to A sequence matched filters 218a-218m, 
respectively, for generating a plurality of compressed A sequences, which 
are applied to first inputs of summing circuits 868a-868m, respectively. 
The filtered output signals from Doppler filter bank 266 of FIG. 10a are 
similarly applied (except for the f.sub.0 signal) to a bank of 
multipliers, whereby all the signals are at frequency f.sub.0. The m 
signals from Doppler filter bank 266 are applied by way of paths 263a-263m 
to A sequence matched filters 268a-268m, respectively, for generating a 
plurality of compressed A sequences, which are applied to second inputs of 
summing circuits 868a-868m, respectively. Summing circuits 868a-868m of 
summing block 848 sum the A and B compressed pulses in each of the Doppler 
channels to produce the desired compressed range pulses. 
In FIG. 10a, pulse compression is accomplished by performing matched 
filtering on each individual Doppler channel. The matched filter is 
matched to the pattern of phase changes associated with the dispersed 
pulse code A or B transmitted with carrier frequency F1 or F2, 
respectively. One A-code matched filter 218, which may also be termed a 
pulse compressor, is associated with each Doppler filter element f.sub.0, 
f.sub.1, f.sub.2, . . . f.sub.M-1 of Doppler filter bank 216. One B-code 
matched filter 268 is associated with each Doppler filter element 
f'.sub.0, f'.sub.1, f'.sub.2, . . . f'.sub.M-1 of Doppler filter bank 266. 
It would be possible to make each pulse compressor with different 
filtering parameters to optimize pulse compression for the center 
frequency of the associated Doppler filter element. This would improve the 
overall performance, because the range of frequencies at the output of 
each filter is small, on the order of a few Hertz. This may represent a 
small percentage of the center frequency of the filter. Thus, each pulse 
compressor may be optimized at one frequency, and its performance will not 
be excessively degraded by the small phase shifts attributable to a range 
of frequencies which is a small percentage of the optimized frequency. To 
avoid the need for different filter parameters in each of the pulse 
compressors so that identical compressors may be used with each Doppler 
filter bank for cost reasons, the filtered output signal from each filter 
element of filter banks 216 and 266 (except the lowest-frequency filter 
element f.sub.0, f'.sub.0) is converted to a common frequency range. A 
suitable range is the zero frequency range of filter element f.sub.0, 
which may for example be the range extending from zero Hertz to a few 
Hertz. 
The same heterodyning principles apply to the outputs of both Doppler 
filter banks 216 and 266, the heterodyne processing of the output of 
Doppler filter bank 216 is described in detail. In FIG. 10a, the output 
from filter element f.sub.0 of filter bank 216 is applied directly to a 
pulse compressor 218a, because the output frequency range of filter 
element f.sub.0 is already at zero frequency, and therefore no frequency 
conversion is necessary. The outputs from all the other filter elements 
f.sub.1, f.sub.2, . . . , f.sub.M-1 are individually applied to 
multipliers 220 for converting each filter output to zero frequency. For 
example, filter element f.sub.1 of filter bank 216 has its output 
connected to a first input port of a multiplier 220b. Multiplier 220b has 
a second input port coupled to an oscillation source (not illustrated in 
FIG. 10a) of signal 
EQU exp (-j2.pi.f.sub.1 k.tau..sub.o), k=0, 1, . . . 
where 
f.sub.1 is the center frequency of the corresponding filter element of 
filter bank 216, 
.tau..sub.0 is the range sampling period, and 
k is the integer time index. 
The oscillator frequency is thus the negative (i.e., same absolute 
frequency but 180.degree. out-of-phase) of the center Doppler frequency at 
which the corresponding filter element of filter bank 216 of FIG. 10a is 
centered. For example, the oscillator signal exp (-j2.pi.f.sub.2 
k.tau..sub.0) applied to multiplier 220c has a frequency that is the 
negative of frequency f.sub.2 at which filter element f.sub.2 of filter 
bank 216 is centered. Essentially, the output signals of the individual 
elements f.sub.1, f.sub.2, . . . , f.sub.M-1 of Doppler filter bank 216 
are heterodyned by multipliers 220 to be centered at zero frequency, 
whereupon identical zero frequency pulse compression filters 218 may be 
used in each Doppler channel. For example, pulse compressor 218a is 
coupled to filter element f.sub.0, and provides zero frequency A-code 
matched filtering; pulse compressor 218b is coupled to the output of 
multiplier 220b for receiving therefrom filtered signals originally at 
f.sub.1 but downconverted to zero frequency, and performs A-code matched 
filtering in the zero frequency signal. The process of downconversion is 
illustrated generally in FIG. 3, in which filtered signals at frequencies 
f.sub.1 . . . f.sub.M-1 are converted to zero frequency by the multiplying 
processes represented by arrows 912, 913, 914, . . . 91m. Each of the 
other pulse compressors 218c . . . 218m of FIG. 2 also receives signals 
downconverted to zero frequency. Thus, all A-code matched pulse 
compressors 218 are mutually identical. Similarly, all B-code matched 
pulse compressors 268a, 268b, 268c, . . . 268m associated with the output 
of Doppler filter bank 266 are mutually identical. 
The A-code filtered output signals from pulse compressors 218a . . . 218m 
of FIG. 10a are applied to a multiplicity of adders 222a, 222b, . . . , 
222m. Each adder 222a, 222b, . . . 222m of FIG. 2 has as its other input 
the downconverted, B-coded pulse compressed output of the corresponding 
Doppler channel of Doppler filter bank 266. 
As mentioned above, Doppler filter bank 266 is similar to Doppler filter 
bank 216 in that it is a bank of filters, but the specific Doppler 
frequencies at which these filters are centered differ slightly from those 
of filter bank 216 as described below, because a given target closing 
speed results in different Doppler frequencies resulting from the two 
carrier frequencies F1 and F2. 
In Doppler filter bank 266, the center frequencies to which the filters are 
tuned are: 
EQU f'.sub.0 (same as f.sub.0), f'.sub.1, f'.sub.2, . . . , f'.sub.M-1(9) 
The following relationship exists between f.sub.k and f'.sub.k 
EQU f'.sup.k =(F3/F1)f.sub.k, k=0, 1, 2, . . . , M-1 (10) 
In FIG. 10a, the f.sub.0 output from filter element f'.sub.0 of filter bank 
266 is applied directly to a pulse compressor (i.e., a filter matched to 
biphase code sequence B that is complementary to the biphase code sequence 
A) because the output of filter element f'.sub.0 is already at zero 
frequency and therefore no frequency conversion is necessary. The outputs 
from all the other filter elements f'.sub.1, f'.sub.2, . . . , f'.sub.M-1 
are individually coupled to multipliers 270 for converting each filter 
output to zero frequency. For example, filter element f'.sub.1 of filter 
bank 266 has its output connected to a first input port of a multiplier 
270b. Multiplier 270b has a second input port coupled to an oscillation 
source (not illustrated in FIG. 10a) of signal 
EQU exp (-j2.pi.f.sub.1 k.tau..sub.0), r=0, 1, 2, . . . (11) 
where 
f'.sub.2 ', is the center frequency of the corresponding filter element of 
filter bank 266, 
.tau..sub.0 is the range sampling period 
k is the integer time index all as described above in conjunction with 
filter bank 216, so that identical zero frequency pulse compression 
filters 268 (matched to code sequence B) may be used in each Doppler 
channel. For example, pulse compressor (i.e., B-code matched filter) 268a 
is coupled to filter element f'.sub.0 (which is the same frequency as 
f.sub.0), and provides zero frequency matched filtering; B-code matched 
pulse compressor 268b is coupled to the output of multiplier 270b for 
receiving therefrom filtered signals originally at f'.sub.1 but 
downconverted to zero frequency, and performs matched filtering (i.e., 
pulse compression) in the zero frequency signal, all as described above in 
conjunction with FIG. 11, but in which f.sub.1, f.sub.2, . . . , f.sub.M-1 
are replaced, respectively, by f'.sub.1, f'.sub.2, . . . f'.sub.M-1. Each 
of the other pulse compressors 218c, . . . , 218m also receives signals 
downconverted to zero frequency. The output signals from pulse compressors 
268a, . . . , 268m are applied to the other input ports of adders 222a, . 
. . , 222m for summing with the corresponding A-code pulse compressed 
signals. The set of resulting summed signals goes to detectors and/or 
further processing as mentioned above. 
The two inputs to each of the adders 222a, 222b, 222c, . . . 222m of FIG. 
10a are mutually complementary compressed signals from, respectively, 
Doppler filtered first and second code sets, code set A and code set B. 
The compressed codes A and B have main lobes which are the same, as 
described below which therefore add, but have range sidelobes of equal but 
mutually opposite polarities, which cancel when summed. The signals on 
output paths 49a, . . . , 49m, are therefore almost completely free of 
range sidelobes. 
A pulse compressor follows each of the complex multipliers in FIG. 10a. 
Since each complex multiplication removes the residual Doppler phase shift 
across the uncompressed pulse, no residual Doppler phase shift remains on 
the uncompressed pulse. Each pulse compressor is a zero Doppler design. 
All of the pulse compressors are therefore identical for each of the 
Doppler filter banks in FIG. 10a. FIG. 5 illustrates a tapped delay line 
or transversal filter of the type known as a "finite impulse response" 
(FIR) filter, because a change in the input causes a change in the output 
which extends over a finite time. The FIR filter of FIG. 5 may be used as 
a matched filter (pulse compressor) 218 or 268 component in the 
arrangement of FIG. 10a. For definiteness, the structure of FIG. 5 
represents a zero Doppler matched filter 218 of FIG. 10a. As illustrated, 
matched filter 218b of FIG. 5 includes a delay structure 440 which 
receives signal at its input port 442 and causes the signal to propagate 
to the right, past taps illustrated as nodes 444a, 444b . . . 444n. The 
temporal spacing (delay) between adjacent taps equals range sampling 
period .tau..sub.0. The delay structure, if in digital form, may be a 
shift register. Each node 444 is coupled to a tap weight multiplier 
illustrated by a triangular symbol 446a, 446b . . . 446n. The weighted, 
delayed signals from multipliers 446 are applied to a combinatorial summer 
(.SIGMA.) 450 for producing the desired matched filtered (pulse 
compressed) signals, which are applied to the corresponding summer 222 of 
FIG. 10a. 
FIG. 10b is a simplified block diagram of a digital signal processing 
according to the invention, which may be used with the arrangement of FIG. 
8. The arrangement of FIG. 10b differs from the arrangement of FIG. 10a in 
that a single Doppler filter bank 216 is coupled to the output of the 
digital signal processing, as was described generally in conjunction with 
FIG. 4. The outputs of phase alignment block 863 of FIG. 8 on paths 843 
and 845 are coupled, in common as to each path, to the A sequence matched 
filters 218a-218m and the B sequence matched filters 219a-219m, 
respectively, of FIG. 10b. As illustrated in FIG. 10b, downconversion to 
baseband is performed on unfiltered A and B input signals by two sets of 
multipliers, namely on the A sequence by multipliers 220b-220m in digital 
signal processing block 844, and on the B sequence by multipliers 
221b-221m in digital signal processing block 846. The reasons for the 
multiplication are described above. Thus, the phase aligned complementary 
signals applied to the matched filters are not Doppler filtered before 
application to the multipliers. In digital signal processor block 844 of 
FIG. 10b, the f.sub.0 signal and the downconverted signals from 
multipliers 220 are applied to matched filters 218. Similarly, in digital 
signal processor block 846, the f.sub.0 signal and the downconverted 
signals from multipliers 221 are applied to matched filters 219, without 
previously being Doppler filtered. The compressed pulses at the outputs of 
matched filters 218a-218m of digital signal processor 844 of FIG. 10b are 
applied to first inputs of corresponding summing circuits 868a-868m of 
summing block 848. The compressed pulses at the outputs of matched filters 
219a-219m of digital signal processor 846 of FIG. 10b are applied to 
second inputs of corresponding summing circuits 868a-868m of summing block 
848, in which the compressed A and B sequences are added together to 
reduce range sidelobes. According to the invention, Doppler filter bank 
216 of FIG. 10b is coupled to the outputs of summing circuits 868a-868m. 
It should particularly be noted that instead of a single Doppler filter 
bank 216 coupled to the outputs of summing circuits 868a-868m as in FIG. 
10b, two Doppler filter banks could be used in a corresponding 
arrangement. Such an arrangement would place one of the two Doppler filter 
banks between the outputs of A sequence matched filters 218a-218m and 
first input ports of summing circuits 868a-868m of FIG. 10b, and the other 
of the two Doppler filter banks would be placed between the outputs of B 
matched filters 219a-219m and the second input ports of summing circuits 
868a-868m. 
FIG. 11 illustrates a zero frequency spectrum f.sub.0 and additional 
spectra f.sub.1, f.sub.2, f.sub.3 . . . f.sub.M-1, which together 
represent the output signals from filter bank 216 of FIG. 10a. An echo 
having a given Doppler shift produces a substantial output from the output 
port of only one filter. For best velocity selectivity, the bandwidths of 
filter elements f.sub.0, f.sub.1, f.sub.2 . . . f.sub.M-1 of filter bank 
216 of FIG. 4, 6, 10a or 10b are narrow, in the range of a few Hertz or 
less. The bank of Doppler filters represented as block 216 may be 
implemented by a signal processor performing a discrete Fourier transform 
(DFT) by means of a fast Fourier transform (FFT) algorithm. The output of 
each filter is a range trace which is the sum of a sequence of Doppler 
filtered range traces. A particular filter output, therefore, represents 
target echoes having the particular Doppler frequency shift corresponding 
to its center frequency, and a small range of Doppler shifts about that 
center frequency, which depends upon the bandwidth of the filter. 
In order to perform the invention, transmitters 16 and 20 of FIG. 8 must 
cause each transmitted pulse (each sequence of phase-modulated subpulses 
or chips) to be matched or accompanied by a corresponding simultaneously 
transmitted pulse in which the phase sequence of the subpulses is 
complementary to the first phase sequence. For this purpose, the term 
complementary means that the sum of the time autocorrelation functions of 
the two pulse sets or sequences ideally has no sidelobes outside of the 
main lobe. Waveform 1000 of FIG. 12a represents a pulse formed from four 
subpulses or chips 1001, 1002, 1003 and 1004, having amplitudes of 1, -1, 
1, 1, respectively, which may be viewed as unit vectors with relative 
phases of 0, .pi., 0, 0, respectively. FIGS. 12a-12i (where the hyphen 
represents the word "through") represent steps in forming an 
autocorrelation function, and FIGS. 12j-k 12m-s represent the result of 
the autocorrelation. As is well understood by those skilled in the art, 
autocorrelation "scans" the time function across a corresponding time 
function "moving" in the negative time direction, multiplying together the 
"overlapping" portions and summing the products. For example, an 
autocorrelation is performed on waveform 1000 of FIG. 12a by allowing it 
to stand still (or move to the right), while causing a similar waveform 
1000', including subpulses 1001', 1002', 1003' and 1004' to move to the 
left, as indicated by the direction arrows in FIG. 12a. In FIG. 12a, 
waveforms 1000 and 1000' do not overlap, so their product is zero, and no 
output signal is produced, as illustrated in FIG. 12j. While the 
amplitudes of the positive and negative excursions of both pulses 1000 and 
1000' are unity, pulse 1000' is illustrated as slightly larger than pulse 
1000 to allow them to be visually distinguished. In FIG. 12b, 
corresponding to time interval 0-1 (where one time interval corresponds to 
the duration of a subpulse or chip), subpulses 1004 and 1001' overlap, 
both are positive so their product is positive, and the overlap region is 
increasing in area, so the resulting autocorrelation 1010 is a 
positive-going ramp increasing from zero amplitude, as illustrated between 
times 0 and 1 in FIG. 12k. 
At the end of time interval 0 to 1, the overlap of subpulses 1004 and 1001' 
is complete, and ramp 1010 of FIG. 12k reaches a maximum value of 1. 
Immediately thereafter, negative subpulse 1002' begins to overlap positive 
subpulse 1004, while positive subpulse 1001' moves to the left, to overlap 
portions of subpulse 1003, as illustrated in FIG. 12c. The product of 
subpulse 1001' multiplied by portions of subpulses 1004 and 1003 remains 
constant in the time interval 1-2, while the product of negative subpulse 
1002' multiplied by portions of positive subpulse 1004 increases in 
magnitude, with a negative sign. The sum of these products in the time 
interval 1 to 2 is a negative-going ramp portion of waveform 1010, as 
illustrated in FIG. 12m. At time 2, positive subpulse 1001' overlaps 
positive subpulse 1003 for a product of +1, and negative subpulse 1002' 
overlaps positive subpulse 1004, for a product of -1, the net of which is 
zero, as illustrated by plot 1010 in FIG. 12n at time 2. In the time 
interval 2 to 3, the summed product continues to ramp toward a value of 
-1, as illustrated in FIG. 12n. 
In the time interval 3 to 4, waveforms 1000 and 1000' move toward 
congruence, as illustrated in FIG. 12e. The main autocorrelation lobe 
peaks during congruence of identical waveforms. At time 4, congruence is 
reached, with positive subpulse pairs 1001, 1001'; 1003, 1003', and 1004, 
1004', and negative subpulse 1002, 1002' overlapping for a total magnitude 
of 4, as illustrated in FIG. 12p. 
Following time 4 represented in FIG. 12p, waveforms 1000 and 1000' move 
away from congruence, as illustrated in FIG. 12f. The negative subpulses, 
1002 and 1002' have significant overlaps with positive subpulses, and the 
overlap of positive subpulses 1001' and 1004 with their counterparts is 
progressively reduced in the time interval 4-5, resulting in a sharp drop 
of the autocorrelation toward a value of -1, as illustrated in FIG. 12q 
near time 5. From the above description, the mode of generation of 
autocorrelation waveform 1010 in the time interval 5-8, illustrated in 
FIGS. 12r and 12s, will be apparent, based upon the subpulse overlaps 
illustrated in FIGS. 12h and 12i. 
FIG. 13a illustrates another subpulse 1100, which has positive unit value 
during the first of four clock cycles, and negative value for the three 
following clock cycles. Plot 1110 of FIG. 13b illustrates the 
autocorrelation of subpulse 1100 of FIG. 13a. comparison of the waveform 
of FIG. 13a with the waveform of FIG. 13s reveals that, while their main 
lobes each have positive amplitude at center time 4, the sidelobes are of 
equal magnitude and opposite polarity. 
When waveforms 1010 and 1110 are summed in the adders 222 of summer 48 of 
FIG. 10a, the sidelobes in the intervals 0-3 and 5-8 cancel, leaving only 
the main lobe in the interval 3-5, as illustrated by waveform 1200 of FIG. 
14. Waveform 1200 is the desired range lobe, with sidelobes cancelled by 
use of complementary pulse sequences. 
As described above, the range sidelobes tend to cancel. If the input 
Doppler shift is not exactly equal to the center frequency of a Doppler 
filter element of filter bank 216, the range sidelobes may not cancel 
exactly, but the deterioration in the cancellation will not exceed that 
caused by a frequency shift equal to half the bandwidth of a filter 
element. Normally, this equals half the frequency spacing between adjacent 
filters of the filter bank. 
Other embodiments of the invention will be apparent to those skilled in the 
art. For example, while a radar context is described in which 
electromagnetic radiation is directed toward a target, acoustic waves in a 
fluid medium could as easily be used, as in a sonar system, or other 
anomaly detector. While binary phase sequences have been described, other 
phase variations, such as continuous analog phase variations, may be used, 
so long as appropriate processing is used, and the autocorrelation 
functions have the desired property of low range sidelobes. 
As noted in the Urkowitz '702 patent the AAA . . . AABB . . . BBB pulse 
sequence is not the only possible sequence, as sequences such as ABABAB . 
. . AB or AABBAABB . . . are also paired. So long as the sequences are 
summed so that the range sidelobes cancel, any sequences can be used. 
Other possibilities include ABCDABCDA . . . ABCD where A and B are 
mutually complementary, and C and D are mutually complementary. With 
appropriate storage of all M echoes, the matched filters would be selected 
and switched accordingly, and appropriate delays and summing provided. 
ADDENDUM 
INTERCHANGE OF INTRAPULSE AND INTERPULSE FILTERING 
A.1 Introduction 
The purpose of this appendix is to show the equivalence of interchanging 
intrapulse (i.e., along the pulse in the range dimension) and interpulse 
(i.e., pulse-to-pulse) filtering operations. This will establish the 
functional equivalence of the present invention with that described the 
aforementioned Urkowitz '702 patent. 
A.2 Glossary of Symbols 
Note: 
(1) A tilde .about. above letter denotes complex envelope. 
(2) A double underline denotes the pre-envelope. 
c=speed of light 
f.sub.c =carrier frequency 
f.sub.d =Doppler frequency shift 
f.sub.r =pulse repetition frequency 
f.sub.k =internal reference Doppler frequency 
g(t)=basic transmitted pulse 
g.sub.R (t)=received pulse 
g.sub.1 (=complex envelope of g.sub.R (t) excluding initial phase shift 
h(t)=impulse response of the filter performing pulse compression and 
sidelobe suppression (if any) 
p(t)=output of filter whose impulse response is k(t) 
q(t)=output of pulse-to-pulse Doppler filter 
R=range of a target 
R =range rate 
s(t)=transmitted signal 
t' =time along the duration of a pulse measured from the leading edge of 
the pulse 
y.sub.n =sequence of complex envelope samples from a particular range 
delay, n=1, 2, . . . 
z(t)=result of filtering the sequence y.sub.n 
.tau..sub.i =range delay of a target 
.phi. =initial phase shift of a target echo 
.omega..sub.d =2.pi.f.sub.d 
.omega..sub.r =2.pi.f.sub.r 
.omega..sub.k =2.pi.f.sub.k 
A.3 The Transmitted and Received Waveforms 
Ordinary radar transmission consists of a sequence of pulses that are all 
similar and occur at a uniform rate called "pulse repetition frequency 
(PRF). This is illustrated in FIG. 15 for pulses 1501, 1502, . . . 15N of 
a simple form. Before we go into the mathematics, let's look into the 
situation qualitatively. We want to add echoes from these pulses and we 
want to add them in phase so that the sum will be a "coherent" sum. This 
means that the starting phase of each pulse 1501, 1502 . . . with respect 
to its own origin must be the same as that of every other pulse with 
respect to its origin. The origin for second pulse 1502 is T.sub.r ; for 
the third it is 2T.sub.r, etc. What this means is this: if the carrier 
frequency is f.sub.c, there must effectively be an integer number of 
cycles in the time interval T.sub.r. That is 
EQU f.sub.c T.sub.r =integer (A.1) 
In an actual radar system, this is automatically accomplished (with 
acceptable error) by using an internal oscillator as the reference for the 
echoes from each pulse. Whatever the actual phase of the transmission, it 
is used as the reference phase, and thus labeled zero phase, for each 
transmitted pulse. This will ensure that (A.1) is satisfied. 
Now we can turn to the algebra. Let g(t) denote the pre-envelope of the 
basis transmitted pulse. Then the sequence of N transmitted pulses may be 
described in pre-envelope form as 
##EQU2## 
where g(t) is the complex envelope of g(t) and 
EQU g(t)=g(t)e.sup.j.omega..sbsp.c.sup.t (A. 3) 
In view of (A.1), the exponent in (A.2) can be written 
EQU e.sup.j.omega..sbsp.c.sup.t-j.omega..sbsp.c.sup.nT.sbsp.r 
=e.sup.j.omega..sbsp.c.sup.t (A. 4) 
and (A.2) becomes 
##EQU3## 
Now let's look at the echo. We presume that the time NT.sub.r is not too 
large for a moving target to move more than a resolvable range interval. 
Then each pulse undergoes the same delay .tau..sub.i. Furthermore, let a 
Doppler frequency f.sub.d =.omega..sub.d /2.pi. be imposed upon the echo. 
The relation between doppler frequency f.sub.d and range rate R is 
EQU f.sub.d =-2Rf.sub.c /C (A.6) 
where f.sub.c is the reference or carrier frequency and c is the speed of 
light. The echo pre-envelope g.sub.R (t) may then be found by substituting 
t-.tau..sub.i for t and f.sub.c +f.sub.d for f.sub.c in (A.5): 
##EQU4## 
We seek the complex envelope g(t). This is just the coefficient of exp 
(j.omega..sub.c t). Thus, the complex envelope is 
##EQU5## 
The factor e.sup.-j.omega..sbsp.c.sup..tau..sbsp.j represents an initial 
phase shift that is, in general, unknown. We therefore treat that phase as 
a random variable with a uniform probability density function over the 
interval (0.2.pi.). This is the least favorable distribution. We set 
EQU .phi.=-.omega..sub.c .tau..sub.i (A. 9) 
The factor e.sup.j.omega..sbsp.d.sup.(t-.tau..sbsp.i.sup.) is the doppler 
modulation upon the sequence of echoes. This modulation is illustrated in 
FIGS. 16a and 16b. FIG. 16a illustrates the in-phase modulation component 
I of a Doppler modulated pulse train. FIG. 16b illustrates the quadrature 
modulation component Q of the Doppler modulated pulse train. I and Q are, 
respectively, the real and imaginary parts of the complex envelope. 
T.sub.r is the pulse repetition period and .tau..sub.i is the range delay 
of the target echo. Now we may write (A.8) as 
##EQU6## 
In many cases, the pulse duration is a small fraction of the doppler period 
1/f.sub.d. Thus, over a pulse duration, exp (j.omega..sub.d [t-.tau..sub.i 
]) is nearly a constant whose value at the n-th pulse is obtained by 
setting t to .tau..sub.i +nT.sub.r, so 
EQU exp (j.omega..sub.d [t-.tau..sub.i ]).sub.t =.tau..sub.i +nT.sub.r =exp 
(j.omega..sub.d nT.sub.r) (A.12) 
Thus, we may write (A.11) as 
##EQU7## 
However, in our case, the pulse duration may be a significant fraction of 
the doppler period 1/f.sub.d, and we can no longer consider exp 
(j.omega..sub.d [t-.tau..sub.i ]) to be nearly a constant. Then there will 
be significant doppler phase shift during the pulse duration. To make this 
evident, let us set 
EQU t=t'+.tau..sub.i +nT.sub.r (A. 14) 
t' is the time along the duration of each pulse; i.e., along the range 
dimension, measured from the leading edge of the n-th received pulse. With 
this change (A.13) becomes 
##EQU8## 
(A.15) shows that the echo complex envelope consists of the product of two 
parts: 
1. A part e.sup.j.omega..sbsp.d.sup.t' g(t') characterizing variation along 
a range trace. 
2. A part 
##EQU9## 
characterizing pulse to pulse variation. Any signal processing to be 
performed can therefore be divided into a per pulse operation (i.e., along 
a range trace) and a pulse to pulse operation. It is clear that these may 
be done in either order. 
A.2 The Pulse to Pulse Operation 
(A.15) expresses a sequence of quantities y.sub.n such that 
EQU y.sub.n =e.sup.j.omega..sbsp.d.sup.t' 
g(t')e.sup.jn.omega..sbsp.d.sup.T.sbsp.r, n=0,1, . . . , N-1(A.16) 
The pulse to pulse operation is a doppler filtering as ordinarily 
considered. It is illustrated in FIG. 17. the symbols are explained in the 
Glossary of Symbols at the start of this Appendix. The sequence of complex 
envelopes y.sub.n, given by (A.16), is multiplied by a sequence of complex 
exponentials. The output, labeled z(t'), is given by 
##EQU10## 
Note that the summation in z(t') is simply a constant as far as t' is 
concerned. t' is the time along the range dimension and in the digital 
processing version t'=r.tau..sub.o, where .tau..sub.o is the range 
sampling period. 
The next step is to mix z(t') with an exponential wave having the frequency 
2.pi.f.sub.k =.omega..sub.k and to follow this mixing operation by the 
filtering operation, along the range dimension t', that performs pulse 
compression and range sidelobe suppression. This is illustrated in FIG. 
18. FIG. 18 shows pulse compression and range sidelobe suppression (if 
present) following the doppler filter bank. h(t') is the impulse response 
of the cascaded pulse compression filter and sidelobe suppression filter 
(if present). The centered asterisk denotes convolution. The result of the 
convolution indicated in FIG. 18 is 
##EQU11## 
A.3 Interchange of the Operations 
Now we look at an interchange of the operations illustrated in FIGS. 17 and 
18. This interchange is shown in FIG. 19. The operation of pulse 
compression and range sidelobe suppression precedes the pulse to pulse 
doppler filtering, reversing the cascade operation of FIGS. 17 and 18. 
Using (A.16) for y.sub.n, the output of the first filter can be written as 
##EQU12## 
The second operation is the pulse to pulse mixing and filtering yielding 
##EQU13## 
This is q(t') of (A.18) . 
This establishes the equivalence of FIG. 19 with the cascade of FIG. 17 and 
18 and, therefore, the equivalence of FIGS. 3 and 4 when we set 
t'=r.tau..sub.0, where .tau..sub.0 is the range sampling period and r is 
an integer index.