On the Limitation of Linear MMSE Detection and (Generalized) Welch Bound Equality Signals

This paper addresses signal optimization for CDMA systems under linear minimum mean-squared error (MMSE) detection. In particular, generalized Welch-bound equality (WBE) signals, which have been found to be optimum for various measures/problems, are studied from a new perspective. Specifically, we consider the asymptotic effective energy (AEE) criterion which characterizes bit error rate (BER) faithfully in the high signal-to-noise ratio regime, and conservatively in low/medium regimes. Our analysis and numerical examples show that, with generalized WBE signals, at least one user has a BER that does not decay exponentially. In fact, in the equalenergy case, all users have an AEE that is provably equal to zero. Numerical simulations illustrate that, in general, the joint error rate floors at very high values. We also prove for sufficient overload and conjecture for other overloaded cases that no signal set yields a joint error rate that decays exponentially under linear MMSE detection, thereby highlighting a severe limitation of such detection. The results extend to the case where the received phases are unknown

Signal design for bandwidth efficient multiple access with guaranteed bit error rate

Abstract — The problem of signal design for bandwidth efficient multiple access is addressed under quality of service (QoS) constraints specified by (possibly different) BER. Indeed, BER more accurately measures the performance than the signal-to-interference ratio (SIR) for uncoded communication. Furthermore, we argue that the asymptotic effective energy (AEE) faithfully characterizes BER, and we translate the BER-specified QoS into AEE-specified ones. We then propose a recursive, greedy algorithm for joint signal design to minimize the system bandwidth while ensuring that each user achieves its desired AEE (and hence BER). This algorithm successfully converts excess power into bandwidth savings under reliability constraints, and significantly improves spectral efficiency over full-rank (e.g. orthogonal) signaling and SIR-based approaches. I

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