Tight Error Bounds for Space-Time Orthogonal Block Codes Under Slow Rayleigh Flat Fading

Abstract

Abstract-The performance of space-time orthogonal block (STOB) codes over slow Rayleigh fading channels and maximum-likelihood (ML) decoding is investigated. Two Bonferroni-type bounds (one upper bound and one lower bound) for the symbol error rate (SER) and bit error rate (BER) of the system are obtained. The bounds are expressed in terms of the pairwise error probabilities (PEPs) and the two-dimensional pairwise error probabilities (2-D PEPs) of the transmitted symbols. Furthermore, the bounds can be efficiently evaluated and they hold for arbitrary (nonstandard) signaling schemes and mappings. Numerical results demonstrate that the bounds are very accurate in estimating the performance of STOB codes. In particular, the upper and lower bounds often coincide even at low channel signal-to-noise ratios, large constellation sizes, and large diversity orders.Index Terms-Bit and symbol error rates, diversity, maximumlikelihood decoding, multiple antennas, pairwise error probability, slow Rayleigh fading, space-time coding, wireless communications.

New bounds on the probability of a finite union of events

“…The optimal bound can be obtained numerically by solving a linear programming (LP) problem with 2 variables [4]. Since the number of variables is exponentially increasing with the number of events, , some suboptimal numerical bounds are proposed, such as the bounds in [5], [6] using the dual basic feasible solutions to reduce the complexity of the LP problem, and the algorithmic Bonferroni-type upper and lower bounds in [7] [8].…”

“…It is observed in [2], [3], [11] that the analytical bounds can be further improved algorithmically by optimizing over subsets. Furthermore, these general bounds can be applied to estimating the probability error in different coded or uncoded communication systems (e.g., see [2], [7], [8], [12]- [16]). …”

On Symbol and Bit Error Probabilities of Orthogonal Space-Time Block codes with Antenna Selection over Keyhole Fading Channels

“…The greedy algorithm [18] can then be applied to construct the optimal spanning tree T 0 for (12). The Bonferroni-type bounds have been applied to analyze the performance of OSTBCs in various scenarios [19], [20], but without antenna selection. In the following, the Bonferroni-type bounds are applied to derive the tight upper and lower bounds on the SER and BER of OSTBCs with antenna selection.…”

“…where P ( |s u ) is the conditional error probability given that s u was sent and p,u is the event that s p has a larger metric than s u [19]. In order to obtain the two Bonferronitype bounds for the SER, one needs to compute the pairwise error probability (PEP), P u ( p,u ), and the two dimensional PEP, P u ( p,u ∩ q,u ), for given q, p, and u.…”

“…Following the analysis in [18], [19], one has the conditional two-dimensional PEP expressed in terms of two-dimensional joint Gaussian function as follows:…”