Zero-forcing based MIMO two-way relay with relay antenna selection: Transmission scheme and diversity analysis

Abstract

Abstract-Combining of physical-layer network coding (PNC) and multiple-input multiple-output (MIMO) can significantly improve the performance of the wireless TWRN. This paper proposes novel Max-Min optimization based relay antenna selection (RAS) schemes for zero-forcing (ZF) based MIMO-PNC transmission. RAS relaxes ZF's constraints on the number of antennas and extends the applications of ZF based MIMO-PNC to more practical scenarios, where the dedicated relay has more antennas than the end-node. Moreover, RAS also brings diversity advantages to TWRN and the achievable diversity gains of the proposed schemes are theoretically analyzed. In particular, an equivalence relation is carefully built for the diversity gains obtained by 1) RAS for ZF based MIMO-PNC and 2) transmit antenna selection (TAS) for MIMO broadcasting (BC) with ZF receivers. This equivalence transforms the original problem to a more tractable form which eventually allows explicit analytical results. It is interesting to see that Max-Min RAS keeps the network diversity gain of ZF based MIMO-PNC to be the same as the diversity gain of the point-to-point link within the TWRN. This insight extends the understanding on the behaviors of ZF transceivers with antenna selection (AS) to relatively complicated MIMO-TWRN/BC scenarios.

Achievable sum‐rate maximization using relay/antenna selection for MIMO two‐way AF relaying with channel uncertainties

“…Here, the instability value means the upper bound of the step size of the least mean square adaptation algorithm [17] in Table I, which is determined by 2/‖π[w]‖ 2 . Figure 5 provides the sum-rate comparisons of various LRAS techniques for an N ; R; K; ρ; σ 2 e  à ¼ 2; 4; 10; 0:6; 0:003 ½ two-way MIMO AF multi-relay system in terms of SNR parameterized by L. Results of 'Best relay' and 'Uniformly-selected relay', which can be achieved by means of the relay determined, respectively, in (7) and in a uniformly selected manner, depict the upper bound and average ASR capacities for the two-way MIMO AF relaying system with the use of N ; R; K; ρ; σ 2 e  à ¼ 2; 4; 10; 0:6; 0:003 ½ . Moreover, the curve of 'Exhaustive-mode GS, L = 3', which is obtained by examining through all possible candidates of C K 1  C R L À Á 2 from K relays, sets up the ASR benchmark for the GS-based RAS on a single activated relay scenario.…”

“…In Figure 8, sum-rate comparisons of a wide variety of RAS strategies are demonstrated for an [N, R, K, L, ρ] = [2, 4, 10, 2, 0.6] two-way MIMO AF relaying system in terms of SNR parameterized by σ 2 e . For the purpose of comparisons, three other RAS algorithms, namely, the two-layered antenna selection (LAS) [18] scheme, the layered distributed orthogonal relay selection (LDORS) [19] technique, and the harmonic-mean [19] method, are employed to explore the L-antenna subset from the selected relay based on the ASR maximization criterion in (7). The DORS RAS selection scheme operates in the layered search criterion by adding an antenna to an empty set incrementally until a total of L Tx/Rx antenna pairs on the single best relay are chosen.…”

“…The authors [6] investigate achievable information rate and relay precoder design of MIMO-AF relay networks under imperfect CSI including channel estimation errors and feedback/feedforward delay errors. The Max-Min optimization-based relay antenna selection (RAS) methods are developed in [7] for the zero-forcing MIMO physical-layer network coding transmission scheme in the three-node two-way relay network. The distributed relay selection (RS) problem is studied based on the post-processing signal-to-noise ratio (SNR) in spectral efficient broadcasting networks employing virtual MIMO in [8].…”

Achieving Full Diversity in Multi-Antenna Two-Way Relay Networks via Symbol-Based Physical-Layer Network Coding

“…In multi-antenna TWR systems, the diversity gain can be achieved by several different methods [8]- [14]. These methods vary in complexity and performance.…”

“…Comparing the results of (21) and (22), we conclude that the randomness of θ degrades the diversity performance. Besides, referring to (14), we note that in single-antenna TWRC the detector of (16) only takes the real component of ρs NC to construct the decision statistics, which introduces θ that deteriorates the achievable diversity. The above analysis inspires us to cope with the randomness of the effective angle to achieve full diversity in the multi-antenna relay scenario.…”