Compressive Sampling Based Energy Detection of Ultra-Wideband Pulse Position Modulation

Compressive sampling (CS) based energy detectors are developed for ultra-wideband (UWB) pulse position modulation (PPM), in multipath fading environments so as to reduce the sampling complexity at the receiver side. Due to sub-Nyquist rate sampling, the CS process outputs a compressed version of the received signal such that the original signal can be recovered from this low dimensional representation. Using the principles of generalized maximum likelihood (GML), we propose two types of energy detectors for such signals. The first type of detectors involves the reconstruction of the received signal followed by a detection stage. Statistical properties of the reconstruction error have been used for the realization of such kind of detectors. The second type of detectors does not rely on reconstruction and carries out the detection operation directly on the compressed signal, thereby offering a further reduction in the implementation complexity. The performance of the proposed detectors is independent of the spreading factor. We analyze the bit error performance of the proposed energy detectors for two scenarios of the propagation channel: when the channel is deterministic, and when it is Gaussian distributed. We provide exact bit error probability (BEP) expressions of the CS based energy detectors for each scenario of the channel. The BEP expressions obtained for the detectors working on the compressed signal directly can naturally be extended to BEP expressions for the related energy detectors working on the Nyquist-rate sampled signal. Simulation results validate the accuracy of these BEP expressions.