Page 316 - Fundamentals of Radar Signal Processing

FIGURE 4.56 Autocorrelation of an N = 51 polyphase Barker code.

The PSL is –34.2 dB, significantly better than the –24.6 dB for the 51-point
MPS code in Table 4.2.

4.10.3 Mismatched Phase Code Filters

The sidelobe structure of phase-coded waveforms can be improved with the use
o f mismatched filters, just as is done with stepped frequency and FM
waveforms to improve their sidelobe structures. For phase-coded waveforms,
this implies correlating the code sequence with another discrete-time sequence,
not necessarily restricted in the amplitudes or phases of its coefficients, such
that some metric of the sidelobe structure is optimized. Mismatched filters can

be designed to minimize the output PSL, minimize the output integrated sidelobe
level (ISL) (sum of the squares of all the sidelobe values of the discrete
correlation of the code and filter, divided by the square of the peak), or to shape
the output sidelobe response, for instance to enforce particularly low near-in
sidelobes at the expense of higher distant sidelobes. The filter order L is usually
larger than the code length. In many cases the design of the mismatched filter
coefficients can be formulated as the solution of a weighted least squares

problem, for which many numerical algorithms are available. Other
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optimization techniques, such as L minimization using convex optimization
algorithms, can also be employed.
Figure 4.57 illustrates two examples of mismatched filter design. In both
cases, the waveform phase code was the same N = 64 MPS biphase code. The

peak sidelobe of the matched filter output for this length is 4, giving a PSL in dB
of 20 log (4/64) = –24.1 dB. The ISL for the matched filter is –6.7 dB. The
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solid line in the figure is the result of a mismatched filter of length L = 130
designed to minimize the PSL. The filter impulse response is normalized to have
the same energy as the code and its matched filter impulse response, namely 64.
This filter achieves a PSL of –31.4 dB, an 8.3 dB improvement compared to the
matched filter. The ISL is –9.8 dB, an improvement of about 3.1 dB. However,

there is now an LPG of 1.11 dB relative to the matched filter.