Optimal and suboptimal receivers for code-multiplexed transmitted-reference ultra-wideband systems

In this study, optimal and suboptimal receivers are investigated for code-multiplexed transmitted-reference (CM-TR) ultra-wideband systems. First, a single-user scenario is considered, and a CM-TR system is modeled as a generalized noncoherent pulse-position modulated system. Based on that model, the optimal receiver that minimizes the bit error probability is derived. Then, it is shown that the conventional CM-TR receiver converges to the optimal receiver under certain conditions and achieves close-to-optimal performance in practical cases. Next, multi-user systems are considered, and the conventional receiver, blinking receiver, and chip discriminator are investigated. Also, the linear minimum mean-squared error (MMSE) receiver is derived for the downlink of a multi-user CM-TR system. In addition, the maximum likelihood receiver is obtained as a performance benchmark. The practicality and the computational complexity of the receivers are discussed, and their performance is evaluated via simulations. The linear MMSE receiver is observed to provide the best trade-off between performance and complexity/practicality.