A New BER Upper Bound for Multiuser Downlink Systems

We consider improvement of bit error rate (BER) upper bounds, based on the notion of decomposable error vectors (DEVs) introduced by S. Verdu, for downlink multiuser space-time systems over Rayleigh fading channels. Although omission of DEVs and limiting before averaging (LBA) technique are known to improve the standard union bound (UB) considerably, it is mathematically intractable to obtain a bound in a closed-form. In this paper, assuming maximum-likelihood (ML) detection for downlink multiuser space-time spreading (STS) systems, we introduce a new modification of the decomposability of error vectors and propose a new BER upper bound. We prove that the proposed bound is tighter than the standard union bound and the bound based on the overall decomposability. The numerical results show that the proposed bound is also tighter than the bound based on positive-sum-decomposability (PSD) in the scenario of downlink multiuser transmission.