Doppler tolerant and detection capable polyphase code sets

In this paper, sections of P3/P4 polyphase codes are concatenated to construct a new class of polyphase code sets. They are defined by closed-form mathematical expressions, from which code sets can be easily generated with properties dependent on the values of the key design parameters. The phases of the resulting codes need not have any degree of uniformity. However, if desired, then at the cost of slightly degraded correlation and Doppler properties, the phase values of the generated code sets can be quantized to have equally spaced phases on the unit circle. The correlation and Doppler properties of several design examples of polyphase code sets are examined in terms of the autocorrelation, cross-correlation, and ambiguity functions. For comparison with existing quadphase code sets, an example of the proposed code sets is quantized to quadphase. The correlation properties of the resulting quadphase code set are found to be similar but slightly inferior to those of the existing code sets, while they are found to be superior in terms of Doppler tolerance and detection capability. In contradistinction to the proposed sets with both Doppler tolerance and detection capability, the existing code sets are, at best, moderately Doppler tolerant, while they are entirely lacking Doppler detection capability. The receiver is modeled as a matched filter that is decomposed into two parallel parts, the outputs of which allow for the detection of the target's radial direction in addition to its radial speed. For additional improvement in the Doppler properties at the cost of a slight signal-to-noise ratio (SNR) loss and small degradation in the correlation properties, the two parts of the decomposed matched filter can be extended in either direction.