Maximum likelihood detectors for generalized code-multiplexing ultra-wideband systems

Generalized code-multiplexing (GCM) systems have been recently proposed for non-coherent ultra-wideband communications for their simple receiver structure. By simply correlating the outputs of energy integrators with decoding codes, the GCM receiver detects information symbols without the need of delay components for transmitted reference or analog carriers for frequency-shifted reference. In addition, the GCM systems subsume existing code-multiplexing designs such as code-multiplexed transmitted reference (CM-TR) and code-shifted reference (CSR) and could even provide better error performance and/or higher data rate. However, the existing GCM receiver is generally not a maximum likelihood detector (MLD). In this paper, we propose MLDs for GCM systems based on the statistics of the signals of GCM receivers. With the aid of the statistics, the MLDs for GCM systems inherit the simple non-coherent structure of GCM receivers and further improve the error performance. Extensive simulations are conducted to show the considerable performance gain of the proposed MLDs compared to the GCM receivers for both CSR codes and optimal GCM codes.