Permutation-Based Noncoherent Space-Time Codes With Analog Energy Detection for IR-UWB Communications With PPM

Abstract

In this paper, we consider the problem of space-time (ST) coding for the noncoherent ultra-wideband (UWB) systems with pulse position modulation (PPM). In particular, we propose the first known family of ST codes that lends itself to optimal decoding with the energy detectors. Energy detection avoids the sampling of the received signal where the sampling rates can be prohibitively high and escapes from the challenging task of estimating the dense multi-path UWB channel. In the absence of design criteria that are adapted to the problem under consideration, we derive two novel design criteria and propose the novel construction accordingly. The proposed code is based solely on permutations, and hence it does not introduce any constellation expansion on the totally-real and unipolar PPM signal set. In other words, the components of the constructed codewords are limited to either zero or one indicating the absence or presence of an UWB pulse in the corresponding PPM slot, respectively. The above characteristics result in a remarked simplicity of the ST encoder/decoder making it an appealing solution to low-cost and low-power UWB systems. For a system equipped with n transmit antennas, we prove that the proposed code is capable of achieving a full transmit diversity order with M-PPM constellations for M>n+1 while transmitting at the rate of (1/n)log2 (nM-1) bits per channel use.