This paper investigates simultaneous wireless information and power transfer (SWIPT) in energy harvesting (EH) relay systems. Unlike the existing SWIPT schemes requiring the instantaneous channel state information (CSI) for coherent information delivery, we propose a noncoherent SWIPT framework for decode-and-forward (DF) relay systems bypassing the need for the instantaneous CSI and consequently saving energy in the network. The proposed SWIPT framework embraces both the power-splitting noncoherent DF (PS-NcDF) and timeswitching noncoherent DF (TS-NcDF) in a unified form, and supports arbitrary M-ary noncoherent frequency-shift keying (FSK) and differential phase-shift keying (DPSK). The exact (noncoherent) maximum-likelihood detectors (MLDs) for PS-NcDF and TS-NcDF are derived in a unified form, which involves integral evaluations yet serves as the optimum performance benchmark for noncoherent SWIPT. To reduce the computational cost of the exact MLDs, we also propose closed-form approximate MLDs achieving near-optimum performance, thus serving as a practical solution for noncoherent SWIPT. Numerical results demonstrate a performance tradeoff between the first and second hops through the adjustment of time switching or power splitting parameters, whose optimal values minimizing the symbol-error rate (SER) are strictly between 0 and 1. We demonstrate that M-FSK results in a significant energy saving over M-DPSK for M ≥ 8; thus M-FSK may be more suitable for EH relay systems.

In energy harvesting (EH) relay networks, the coherent communication requires accurate estimation/tracking of the instantaneous channel state information (CSI) which consumes extra power. As a remedy, we propose two noncoherent EH relaying protocols based on the amplify-and-forward (AF) relaying, namely, power splitting noncoherent AF (PS-NcAF) and time switching noncoherent AF (TS-NcAF), which do not require any instantaneous CSI. We develop a noncoherent framework of simultaneous wireless information and power transfer (SWIPT), embracing PS-NcAF and TS-NcAF in a unified form. For arbitraryM-ary noncoherent frequency-shift keying (FSK) and differential phase-shift keying (DPSK), we derive maximum-likelihood detectors (MLDs) for PS-NcAF and TS-NcAF in a unified form, which involves integral evaluations yet serves as the optimum performance benchmark. To avoid expensive integral computations, we propose a closed-form detector using the Gauss-Legendre approximation, which achieves almost identical performance as the MLD but at substantially lower complexity. These EH-based noncoherent detectors achieve full diversity in Rayleigh fading. Numerical results demonstrate that our proposed PS-NcAF and TS-NcAF may outperform the conventional grid-powered relay system under the same total power constraint. Various insights which are useful for the design of practical SWIPT relaying systems are obtained. Interestingly, PS-NcAF outperforms TS-NcAF in the single-relay case, whereas TS-NcAF outperforms PS-NcAF in the multi-relay case.

Unlike the existing detectors, which are developed for decode-and-forward (DF) networks in the ideal interference-free case, we consider a more practical scenario where arbitrary interference exists. We consider a DF cooperative network consisting of a source, multiple relays, a destination, and multiple interferers affecting both the relays and the destination. Each relay is equipped with multiple antennas and knows its local instantaneous channel state information (CSI). Assuming that the destination knows the instantaneous CSI of the source-relay, relay-destination, and source-destination channels, we develop, for the first time in the literature, the end-to-end optimum maximum-likelihood (ML) detectors in closed-form for DF systems employing either simultaneous or orthogonal transmissions in the presence of interference. Furthermore, theoretical analysis shows that the proposed detectors achieve full diversity gains in the presence of interference with finite interference-to-noise ratios. Numerical results demonstrate that the proposed optimum detectors substantially outperform the conventional schemes which simply ignore interference.

We develop closed-form generalized likelihood ratio test (GLRT) sequence detectors for multi-relay amplify-and-forward (AF) cooperative networks employing M-ary differential phase-shift keying (M-DPSK) and noncoherent M-ary frequency-shift keying (M-FSK). The proposed detectors achieve robust performance in a wide range of fading environments where prior knowledge of channels, signal powers, noise variances, and relay functionalities is unavailable to the destination. A comprehensive error probability performance analysis is carried out in Rayleigh fading. Specifically, we derive unified pairwise error probability (PEP) expressions for both detectors in a dual-hop network, which are valid for arbitrary modulation order M and arbitrary sequence length Ns. We also derive unified bit-error probability (BEP) expressions for both detectors employing binary signalings in various networks for Ns= 1. It is further shown that both detectors achieve near full diversity orders. Finally, the superiorities of the proposed detectors over the state-of-the-art noncoherent detectors are justified through extensive comparisons in practical scenarios. For example, in a multi-relay network where the relays are uniformly distributed between the source and destination, the proposed detector for noncoherent FSK with Ns= 1 outperforms the well-known maximum energy selector by almost 15 dB in high signal-to-noise ratios.

We propose a reactive opportunistic relaying (OR) scheme for time-division broadcast (R-TDBC) in a bidirectional cooperative network. In the proposed R-TDBC, a subset of relays that reliably decode both signals from the sources is determined reactively after two source-transmissions; then a single relay among the determined set is selected by maximizing the achievable rate of the broadcast phase. A somewhat surprising result is that the proposed R-TDBC achieves identical outage performance as its proactive counterpart in bidirectional cooperative networks with the direct link. We then derive the exact outage probability, tight closed-form bounds, and the diversity-multiplexing tradeoff (DMT) for the R-TDBC.

We study relay selection (RS) for time-division broadcast (TDBC) in a bidirectional network consisting of two different end-sources and multiple relays. By modifying the well-known proactive RS scheme valid only for unidirectional cooperative networks, we propose a proactive RS with TDBC (P-TDBC) for bidirectional cooperative networks. In the P-TDBC scheme, a single best relay is selected proactively before two consecutive source-transmissions by maximizing the bottleneck of the end-to-end maximal achievable rates in both directions. We then derive the exact outage probability of P-TDBC in closed-form for Es≤ Er, and in a single-integral form for Es>; Er, where Esand Erdenote the transmission powers at each end-source and the selected relay, respectively. Moreover, we derive very tight closed-form upper and lower bounds on the outage probability for Es>; Er. Finally, we study the diversity-multiplexing tradeoff (DMT) and show that the P-TDBC scheme achieves full diversity.

We investigate the exact error performance of hard minimum mean-squared error (MMSE) detection possibly with successive interference cancellation (SIC) in multiple-input multiple-output (MIMO) systems. To facilitate the analysis, we start with an exact bit-error rate (BER) analysis for a general system with decision statistic, z=ax+u, where a>;0, x is the transmitted signal, and u is an arbitrarily distributed noise component which is possibly dependent on the signal component x. For this general system, we derive the exact and closed-form BER expressions for M-ary pulse amplitude modulation (PAM) and arbitrary rectangular quadrature amplitude modulation (QAM), which include the well-known BER result of as a special case. Furthermore, by formulating the MIMO MMSE decision statistics in the same form as z in the general system, we derive the exact and closed-form instantaneous BER and symbol-error rate (SER) expressions for MIMO hard MMSE detection with/without SIC employing PAM and QAM. Finally, the validity of our derived error probability expressions is verified through extensive Monte Carlo simulations and the results reported in the literature.

We investigate the exact error performance of hard minimum mean-squared error (MMSE) detection in multipleinput multiple-output (MIMO) systems. To facilitate the analysis, we first conduct error analysis for a general system with decision statistic, z = ax + u, where a >; 0, x is the transmitted signal, and u is the arbitrarily distributed noise component which is independent of x. For this general system, we derive the exact and closed-form bit-error rate (BER) expressions for M-ary pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) signalings, which include the well-known BER result in [12] as a special case. For the first time in the literature (to the best of our knowledge), we then derive the exact and closed-form instantaneous BER and symbol-error rate (SER) expressions for hard MMSE detection. Finally, the validity of the derived error probability expressions is verified through our own Monte Carlo simulations and the simulation results reported in the literature.

We study and compare the performance of three very typical bidirectional communication protocols based on the decode-and-forward relaying: time-division broadcast (TDBC), physical-layer network coding (PNC), and opportunistic source selection (OSS). We first derive the exact closed-form outage probabilities for the PNC and OSS protocols and an exact but one-integral form outage probability for the TDBC protocol. To gain more insight, we also derive closed-form asymptotic outage probability expressions for all protocols, with which we obtain further analytical results on the asymptotic optimal power allocation, the asymptotic optimal relay location, and the performance gain of the OSS protocol over the TDBC protocol in the high signal-to-noise ratio (SNR) regime. Finally, we study the diversity-multiplexing tradeoff (DMT) for each protocol both in the finite and infinite SNR regimes.

We study the optimum maximum-likelihood (ML) detection and sub-optimum detection for a multi-branch dual-hop cooperative diversity network with limited channel state information (CSI). Compared to the full CSI strategy, the signalling overhead at each relay involved with the limited CSI is reduced by 50%. We derive optimum ML detection with the limited CSI, which involves numerical integral evaluations. We also propose two closed-form sub-optimum detection rules of low complexity. It is shown that the first sub-optimum detection has almost identical performance to the optimum ML detection when Gaussianity in the added noise dominates, and the second sub-optimum detection has almost identical performance to the optimum ML detection when non-Gaussianity dominates. Finally, we propose a hybrid sub-optimum detection and demonstrate that its performance is almost identical to that of the optimum ML detection for general cases.

We study the optimum maximum-likelihood (ML) detection and sub-optimum detection with limited channel state information (CSI) for a multi-branch dual-hop cooperative diversity network which consists of a source, multiple relays, and a destination without a direct source-destination path. With the limited CSI, the signalling overhead at each relay is reduced by 50%. We first derive the optimum ML detection with the limited CSI, which involves numerical integral evaluations. To reduce the computational complexity, we then propose a closed-form suboptimum detection rule. It is demonstrated that the proposed sub-optimum detection rule performs almost identically to the optimum ML detection when the non-Gaussianity in the added noise component dominates.

In this letter, the average bit-error rate (BER) performance is analyzed for uncoded decode-and-forward (DF) cooperative diversity networks. We consider two typical networks: a single-relay cooperative network with the direct source destination link and a two-relay cooperative network with the direct source-destination link, under dissimilar network settings, i.e., the fading channels of different relay branches may have different variances. We first derive a closed-form approximate average BER expression of binary signallings including noncoherent binary frequency shift keying (BFSK), coherent BFSK, and coherent binary phase shift keying (BPSK), for the single relay network. We then generalize our analysis to the two-relay network, and a closed-form approximate average BER expression for binary signallings is derived. We also show that our BER expressions can be considered as generalizations of previously reported results in the literature. Throughout our analysis, only one approximation, so-called the piecewise-linear approximation, is made. Simulation results are in excellent agreement with the theoretical analysis, which validates our proposed BER expressions.