Optimal signaling for detection in doubly dispersive multipath

In this paper, we revisit the problem of signal detection in multipath scattering. Specifically, we explore the effect of bandwidth and signaling duration on non-coherent signal detection in doubly dispersive non-uniform multipath scattering environments. In such environments, we conjecture that detection performance is optimized if two conditions are met: C1) the number of independent degrees of freedom induced by the transmit signal on the channel is approximately SNR/2, and C2) the variance of the channel coefficients (each corresponding to a degree of freedom) is equal. In uniform multipath, the second condition is inherent. In non-uniform scattering, the variance of the channel coefficients depends on the transmit signal which critically impacts detection performance. As such, non-uniform doubly selective channels afford us an additional design parameter; we can design packets for detection of a specific aspect ratio, the ratio of bandwidth to signaling duration. If our packets meet the two criteria above, numerical and analytical results indicate detection performance is maximized. When the above conditions cannot be met, we present an algorithm for finding the signaling duration and bandwidth that maximize detection performance.