Combinatorial optimisation for pulse position modulation-ultra wideband signal detection based on compressed sensing and analogue-to-information converter

Pulse position modulation-ultra wideband (PPM–UWB) communication signal is hard to detect and sample directly, owing to its ultra-low power spectral density and wide bandwidth. There are already some researches on using analogue-to-information converter (AIC) technology and compressed sensing (CS) theory to under-sample and detect PPM-UWB communication signal, utilising its sparseness in time domain. However, greedy algorithm lacks of restriction on sparseness of reconstructed vector, while common restrictions on sparseness (e.g. convex optimisation) has high computational complexity. To solve these problems, a combinatorial optimisation method is proposed in this study to detect PPM–UWB communication signal based on CS and AIC. Reconstruction error and sparseness of reconstructed vector are restricted by l 2- and l p-norms, respectively. l p-norm (0 < p < 1), which is a non-convex function, has stricter restriction on sparseness than l 1-norm. Meanwhile, the steepest descent method is adopted for l p-norm optimisation, which can rapidly converge to objective values. Proposed method has more comprehensive restriction than greedy algorithm and convex optimisation, while maintain low complexity in computation as greedy algorithm. Numerical experiments demonstrate the validity of proposed method.