Generalized likelihood ratio test multiple-symbol detection for MIMO-UWB: A semidefinite relaxation approach

In this paper, semidefinite relaxation (SDR) technology is exploited for the multiple-symbol detection (MSD) over the multiple-input multiple-output (MIMO) ultra-wideband (UWB) systems. The existing scheme generalized likelihood ratio test (GLRT) MSD jointly detect multiple symbols, however, it entails a complexity of O(2^M), where M is the observation window size. To this end, SDR is employed to reformulate the GLRT detection into a semidefinite programming (SDP) model, and two detectors, randomization-SDR (RSDR) and eigenvector-SDR (ESDR) are proposed on the order of O(M^3.5) and O(M³), respectively. Complexity analysis validates that the SDR-MSD strategy is desirable owing to its reduced complexity, compared with the exponential-complexity sphere decoding (SD) MSD. Furthermore, Monte-Carlo simulations demonstrate that the proposed SDR detectors provide the bit error rate (BER) performance almost the same with that of the SD method, and the RSDR outperforms the ESDR at the price of slightly higher complexity.