Alternating projections for designing locally orthogonal waveform pairs

We propose an approach to design locally orthogonal waveform pairs (LOWP). The approach is based on alternating projection, in which an algorithm framework called alternating projections to synthesize LOWP (APLOWP) is derived. Two specialized versions of APLOWP, namely, APLOWP dynamic ideal autocorrelation construction (DIAC) and APLOWP inner product constraint (IPC), are developed. APLOWP-DIAC is used to synthesize waveform pairs for instantaneous polarization radar, because its designed waveforms have very low auto- and cross-correlation magnitudes in specified lag intervals. APLOWP-IPC is used for joint transmit-receive optimization. The IPC of APLOWP-IPC guarantees that the signal-to-noise ratio (SNR) loss is below the specified bound even though a mismatched filter leads to SNR loss. The effectiveness of the proposed algorithms is demonstrated by using numerical simulations.