In this letter, we present a closed-form bound of the average bit error rate (BER) performance for the multi-hop amplify-and-forward (AF) relaying systems with fixed gain in Rayleigh fading channel. The proposed bound is derived from the probability density function (PDF) of the overall multi-hop relay channel under the assumption of asymptotic high signal-to-noise ratio (SNR) at every intermediate relays. When intermediate relays actually operate at finite SNR, the proposed BER bound becomes looser as the SNR of the last hop increases. In order to reflect the effect of all the noise variances of relay links to the BER evaluation, a hop-indexed recursive BER approximation is proposed, in which the proposed bound of BER under asymptotic high SNR is used. The simulation results manifest that the proposed hop-indexed recursive BER approximation can not only guarantee accuracy regardless of the SNR of the last hop but also provide higher accuracy than the previous works.

In this letter, a pre-processed lattice reduction (PLR) scheme is developed for the lattice reduction aided (LRA) detection of multiple input multiple-output (MIMO) systems in spatially correlated channel. The PLR computes the LLL-reduced matrix of the equivalent matrix, which is the product of the present channel matrix and unimodular transformation matrix for LR of spatial correlation matrix, rather than the present channel matrix itself. In conjunction with PLR followed by recursive lattice reduction (RLR) scheme [7], pre-processed RLR (PRLR) is shown to efficiently carry out the LR of the channel matrix, especially for the burst packet message in spatially and temporally correlated channel while matching the performance of conventional LRA detection.

We study a joint optimal design of the receive equalizer and relaying architecture in terms of the weighted sum of mean square errors for the multi-user multiple-input multiple-output (MIMO) relaying system. We show that the optimal relaying architecture depends on the weight factors and that conventional diagonal relaying is a special case of the proposed relaying architecture. Interestingly, for unequal weights, it turns out that the optimal relaying is different from the existing diagonal relaying schemes. By simulation, we show that the proposed joint design improves the weighted sum of mean square error (MSE) over the existing MIMO relaying schemes.

Achievable rates of two different transmission schemes of the two-cell cooperative single user (CSU) multi-input multi-output (MIMO) system with hybrid feedback is studied, in which one cell has the channel state information (CSI) from a mobile station (MS) and the other has channel covariance information (CCI) from it. Disjoint encoding over two base stations (BSs) is shown to achieve the capacity of the CSU-MIMO with hybrid feedback. Rather than finding an optimal transmission scheme, a suboptimal one is proposed such that the transmit directions of the BSs with CSI and CCI are eigen directions of the instantaneous channel correlation matrix and transmit covariance matrix respectively. The optimum power allocation for these transmit directions is derived as an iterative power allocation (IPA) similar to that of the MIMO multiple access channel (MAC) with CCI only. We also propose a simple disjoint power allocation (DPA). The simulation results show that the proposed transmit directions and IPA for the CSU-MIMO with hybrid feedback outperforms the MIMO-MAC with CCI only, while the DPA achieves almost the same performance as the IPA, only when the SNR is low.