Doppler-improved polyphase pulse expander-compressor
BACKGROUND OF THE INVENTION 
     This invention relates to pulse-type, peak-power limited radar systems, and particularly to methods and apparatus for frequency-derived pulse compression techniques used in peak-power limited radar systems. 
     Two methods of reducing cyclic loss of frequency-derived polyphase coded signals due to doppler shift are known in the art. One method requires two channels instead of one, the first of them a standard direct channel, and the second comprising a phase-compensated channel which has approximately a π phase shift across the uncompressed pulse. The channel having the largest signal is then selected. This method is undesirable from the standpoint of cost and complexity associated with the additional phase shifters, channel and signal-selecting circuitry required. 
     The other known method of reducing cyclic loss due to doppler shift is amplitude weighting of the polyphase-coded signal. The undesirable aspects of this method are the limited degree of reduction in cyclic losses attributable solely to weighting and the reduction in signal-to-noise ratio which results from the general practice of weighting the received polyphase-coded signal. 
     OBJECTS OF THE INVENTION 
     Accordingly, one object of the present invention is to reduce cyclic loss due to doppler shift in frequency-derived polyphase compression codes. 
     Another object of the present invention is to reduce cyclic losses due to doppler shift in such codes with a minimum of hardware and complexity. 
     Yet another object of the invention is to reduce cyclic losses due to doppler shift in such codes without suffering substantial reduction in the signal-to-noise ratio of the received signal. 
     SUMMARY OF THE INVENTION 
     The present invention achieves a reduction in cyclic losses due to doppler shift in frequency-derived polyphase compression codes, such as the Frank, P1, P2, P3 and P4 codes, by altering the code. The modified code phases are derived by sampling the phase characteristics of an underlying chirp or step-chirp waveform at a rate which is higher than the Nyquist rate, thereby increasing the number of code elements within the uncompressed pulse length. These codes are no longer the same codes as before, but they are referred to as oversampled versions of the well known prior codes (e.g. oversampled Frank code). The cyclic losses decrease as the sampling rate increases. The oversampled codes may be expanded and compressed using a variation of the usual DFT (discrete fourier transform) or FET (fast fourier transform) phase filter procedures. Although amplitude weighting may be required to reduce the higher resulting sidelobe peaks, there is a significant increase in the resultant signal-to-noise ratio of the doppler shifted signal even with amplitude weighting. 
     The foregoing, as well as other objects, features and advantages of the invention will be apparent from the following descriptions of the preferred embodiment of the invention, and the novel features will be particularly pointed out hereinafter in connection with the appended claims. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a graph which illustrates the cyclic loss in signal strength of a compressed 100 element Frank code having a pulse compression ratio of 100 as a function of normalized doppler shift. 
     FIG. 2 is a graph which illustrates the zero doppler shift matched-filter output of a compressed 100 element Frank code having a pulse compression ratio of 100 as a function of time referenced in terms of sample number. 
     FIG. 3 is a graph which illustrates the zero doppler shift matched-filter output of a compressed 200 element oversampled Frank code whose phases are derived from the underlying step-chirp phase characteristic associated with the Frank code, which is sampled at twice the Nyquist rate, instead of being sampled at the Nyquist rate to determine the phases of the Frank code, and having a pulse compression ratio of 100 as a function of time referenced in terms of sample number. 
     FIG. 4 is a graph which illustrates the cyclic loss in signal strength of the compressed 200 element oversampled Frank code having a pulse compression rate of 100 as a function of normalized doppler shift. 
     FIG. 5 is an illustration of an implementation of the present invention using an FFT to generate a 32 element compressed polyphase code sampled at twice the Nyquist rate and having a pulse compression ratio of 16. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the preferred embodiment, the phase characteristics of a chirp or step-chirp waveform having a bandwidth B are sampled at a rate corresponding to k times with the Nyquist rate to derive the phases of the polyphase codes. The Nyquist rate at baseband has a frequency of B and k is a factor greater than 1. The sampled signal is then expanded and compressed by modifying the procedure for expanding and compressing polyphase codes sampled at the Nyquist rate. If the total number of phase samples in the sampling period is kN 2 , where N is an integer, the implementation is the same as using a kN point DFT (discrete fourier transform) or FFT (fast fourier transform) phase filter, where only N of the filters are used in transmission and reception. The number of phase samples per filter becomes kN and the total number of phases, or elements of the code is kN 2 . Examples of DFT and FFT filter implementation may be found in &#34;Digital Signal Processing,&#34; by A Oppenheim and R. Schafter, Prentice Hall, 1975, herein incorporated by reference. 
     For example, using the Frank code, the code phases for the nth element of the mth frequency or phase group is given by 
     
         φn,m=2π(m-1)(n-1)/kN 
    
     where the index n ranges from 1 to kN (an integer) for each value of m which ranges over the same values. 
     Referring to the drawings, wherein like reference characters designate like or corresponding parts throughout the views, FIG. 5 shows a schematic for an expander/compressor using the Frank code according to the present invention for k=2 and N=4. 
     For expansion, a well known clocking circuit 10 generates a clock signal fed through line 12 into a well known pulse generator 14. A pulse from pulse generator 14 passes through line 16 into a well known FFT filter 18 the signal passing directly into input port 20, and with time delays into input ports 22-34 through a time delay network system 36-48, each network having a time delay corresponding to τ/2, where τ=1/B. FFT filter 18 generates 32 phase coded elements each having phases corresponding to consecutive samples of a chirp or step chirp waveform sampled at twice its information bandwidth B. The expanded polyphase coded signal is taken from line 50, which combines the signals from output port 52 of the FFT 18 with delayed output signals from output ports 54-58 through a time delay network system 60-64, each network having a time delay of 4τ, where τ=1/B. 
     For compression, an echo signal corresponding to the expanded polyphase coded signal passes through line 66 into a well known conjugator 68. The conjugated signal output is fed directly into the input port 34 of the FFT 18, and with time delays into the input ports 20-32 through the time delay network system 36-48. The compressed polyphase coded signal is taken from line 70, which combines the signal from the output port 58 of the FFT with the delayed output signals from the output ports 52-58 through the time delay network system 60-64. 
     Other frequency-derived polyphase codes, such as P1, P2, P3 and P4, may be implemented using well known circuit modifications added to the above described preferred embodiment. Other embodiments, such as those using the well known &#34;brute-force&#34; or fast convolution techniques, also may be used with the present invention. 
     The improvement in resistance to doppler shift may be seen by comparing the output of an ordinary 100 element Frank code pulse compression system having a compression ratio of 100, as shown in FIG. 1, with a 200 element oversampled Frank code having a compression ratio of 100, as shown in FIG. 4, using sampling of the step-chirp phase characteristic at twice the sampling rate according to the present invention. Using the present invention, the peak-to-trough ratio of the output is significantly reduced, from 4 db to 0.8 db, compared with the standard pulse-compression technique. 
     The change in sidelobe response using the present invention may be seen by comparing the ordinary 100 element Frank code, as shown in FIG. 2, with the 200 element oversampled Frank code according to the present invention, as shown in FIG. 3. Peak sidelobes with the oversampled code are approximately 13.5 db down from the main lobe amplitude, thus approximating the response of a compressed step-chirp wave-form. These sidelobes may be reduced by decreasing the amount of oversampling or by using amplitude weighting techniques. 
     Since the oversampled 200 element Frank code according to the present invention has a maximum loss due to doppler shift of approximately 0.8 db and the reduction in signal to noise ratio of amplitude weighting necessary to satisfactorily reduce the peak sidelobe response is on the order of 1 db, the net improvement over the standard 100 element Frank code, which has a maximum doppler shift loss of about 4 db, is approximately 2.2 db. 
     It will be understood that various changes in the details, materials and arrangements of parts which have been herein described and illustrates in order to explain the nature of the invention may be made by those skilled in the art within the principle and scope of the invention as is expressed in the appended claims.