Multiple-Antenna Cooperative Wireless Systems: A Diversity–Multiplexing Tradeoff Perspective

We consider a general multiple-antenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity-multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (half-duplex or full-duplex), and the network geometry (clustered or nonclustered). We first study the multiple-antenna relay channel with a full-duplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), and compress-and-forward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link are increased, whereas CF continues to perform optimally. We also study the multiple-antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the half-duplex relay DMT. We next study the multiple-access relay channel (MARC) DMT. Finally, we investigate a system with a single source-destination pair and multiple relays, each node with a single antenna, and show that even under the ideal assumption of full-duplex relays and a clustered network, this virtual multiple-input multiple-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains in effect.     

Decode‐and‐forward two‐way relaying protocol with one retransmission

This paper investigates the decode‐and‐forward two‐way relaying channel without direct link and proposes a protocol based on the physical‐layer network coding (PNC) protocol. The proposed protocol (termed ORT) introduces one retransmission into PNC, aiming at enhancing its outage performance. To manifest the merits of ORT, we compare it with PNC and the time‐division broadcast (TDBC) protocol, in terms of outage performance, expected rate, and diversity‐multiplexing tradeoff (DMT). Firstly, we derive the outage probability of the three protocols and then the expected rate. Secondly, asymptotic analysis is conducted to shed light on the diversity and coding gains. Finally, the DMT is obtained for the three protocols. The numerical results reveal the following: (i) that ORT performs better than PNC in both outage and expected rate performance when the nodes transmit with different powers. However, it has the same DMT performance with PNC; (ii) that ORT possesses improved DMT performance over TDBC whereas its expected rate is only better than the latter at medium to high signal‐to‐noise ratio. Copyright © 2012 John Wiley & Sons, Ltd.     

Spectrally-efficient relay selection with limited feedback

This paper addresses the multiplexing loss that occurs in relay networks due to causality of relays and the half-duplex constraint. We devise relay selection methods to recover the multiplexing loss in decode-and-forward (DF) relay networks, while requiring very little feedback (merely bits/relay). Two network topologies are studied: First the case is considered where a direct link is available between the source and destination, in addition to the relayed links. For this configuration, an incremental transmission scheme is proposed, and comprehensively analyzed, which uses limited feedback to improve both diversity as well as multiplexing gain. Then, the case without a direct link is considered, for which efficient non-orthogonal DF protocols are produced and analyzed. An interesting feature of the latter methods is unequal error protection capability via a family of embedded diversity-multiplexing (DMT) curves, which can be very useful for practical applications. Even considering this method's minimal DMT, a marked improvement over previous DF methods is observed, especially in high spectral efficiencies.     

Cross Layer Design of Downlink Multi-Antenna OFDMA Systems with Imperfect CSIT for Slow Fading Channels

In most existing works, perfect knowledge of channel state information at the transmitter (CSIT) is assumed to realize the potential benefit of cross-layer scheduling and spatial multiplexing gains of MIMO/OFDMA systems. However, perfect knowledge of CSIT is not easy to achieve in practice due to estimation noise or delay in feedback. In this paper, we shall focus on the cross-layer design of downlink multi-antenna OFDMA systems with imperfect CSIT for slow fading channels. We shall show that our proposed cross-layer scheduler can exploit the multiuser diversity and spatial multiplexing gain even in the presence of moderate CSIT error.     

Optimal bandwidth allocation for the data and feedback channels in MISO-FDD systems

In frequency-division duplex (FDD) systems, channel-state information (CSI) is estimated by the receiver and then fed back to the transmitter through a feedback link, which inevitably requires additional bandwidth and power. In this letter, we jointly study optimal bandwidth allocation between the data channel, modeled as a flat-fading multiple-input single-output (MISO) channel, and the feedback channel for maximum average throughput in the data channel using a beamforming scheme. We consider two models of the partial CSI at the transmitter (CSIT): the noisy CSIT, modeled as jointly Gaussian with the actual channel state, and the quantized CSIT. In the first model, we use distortion-rate theory to relate the CSIT accuracy to the feedback-link bandwidth. In the second model, we derive a lower bound on the achievable rate of the data channel based on the ensemble of a set of random quantization codebooks. We show that in the MISO flat-fading channel case, beamforming based on feedback CSI can achieve an average rate larger than the capacity without CSIT under a wide range of mobility conditions.     

On the Fundamental Tradeoff of Spatial Diversity and Spatial Multiplexing of MISO/SIMO Links with Imperfect CSIT

In this paper, we analyze the role of CSIT on the fundamental performance tradeoff for a MISO/SIMO link. Defining CSIT quality order as alpha = - log sigma² _Deltah / log SNR, we showed that using rate adaptation, one can achieve an average diversity order of d ^macr(alpha, r macr) = (1 + alpha - r macr)n where n is the number of transmit or receive antennas, r macr is the average multiplexing gain and alpha is the CSIT quality. We also showed that this diversity order is optimal for r macr isin [0.1 - alpha] and alpha < 1. The relationship suggests that imperfect CSIT can also provide additional diversity order and interpret the CSIT quality order as the maximum achievable spatial multiplexing gain with n diversity order.     

Co-ordinate Interleaved Spatial Multiplexing with Channel State Information

Performance of spatial multiplexing multiple-input multiple-output (MIMO) wireless systems can be improved with channel state information (CSI) at both ends of the link. This paper proposes a new linear diagonal MIMO transceiver, referred to as co-ordinate interleaved spatial multiplexing (CISM). With CSI at transmitter and receiver, CISM diagonalizes the MIMO channel and interleaves the co-ordinates of the input symbols (from rotated QAM constellations) transmitted over different eigenmodes. The analytical and simulation results show that with co-ordinate interleaving across two eigenmodes, the diversity gain of the data stream transmitted over the weaker eigenmode becomes equal to that of the data transmitted on the stronger eigenmode, resulting in a significant improvement in the overall diversity. The diversity-multiplexing tradeoff (DMT) is analyzed for CISM and is shown that it achieves higher diversity gain at all positive multiplexing gains compared to existing diagonal transceivers. Over rank n MIMO channels, with input symbols from rotated n-dimensional constellations, the DMT of CISM is a straight line connecting the endpoints (0,N_tN_r) and (min{N_t,N_r}, 0), where N_t, and N_r} are the number of transmit and receive antennas, respectively.     

On the achievable diversity-multiplexing tradeoff in half-duplex cooperative channels

We propose novel cooperative transmission protocols for delay-limited coherent fading channels consisting of N (half-duplex and single-antenna) partners and one cell site. In our work, we differentiate between the relay, cooperative broadcast (down-link), and cooperative multiple-access (CMA) (up-link) channels. The proposed protocols are evaluated using Zheng-Tse diversity-multiplexing tradeoff. For the relay channel, we investigate two classes of cooperation schemes; namely, amplify and forward (AF) protocols and decode and forward (DF) protocols. For the first class, we establish an upper bound on the achievable diversity-multiplexing tradeoff with a single relay. We then construct a new AF protocol that achieves this upper bound. The proposed algorithm is then extended to the general case with (N-1) relays where it is shown to outperform the space-time coded protocol of Laneman and Wornell without requiring decoding/encoding at the relays. For the class of DF protocols, we develop a dynamic decode and forward (DDF) protocol that achieves the optimal tradeoff for multiplexing gains 0/spl les/r/spl les/1/N. Furthermore, with a single relay, the DDF protocol is shown to dominate the class of AF protocols for all multiplexing gains. The superiority of the DDF protocol is shown to be more significant in the cooperative broadcast channel. The situation is reversed in the CMA channel where we propose a new AF protocol that achieves the optimal tradeoff for all multiplexing gains. A distinguishing feature of the proposed protocols in the three scenarios is that they do not rely on orthogonal subspaces, allowing for a more efficient use of resources. In fact, using our results one can argue that the suboptimality of previously proposed protocols stems from their use of orthogonal subspaces rather than the half-duplex constraint.     

Optimal Diversity‐Multiplexing Tradeoff of MIMO Multi‐way Relay Channel

A MIMO multi‐way relay channel with full data exchange in which K users exchange messages with each other via the help of a single relay is considered. For the case in which each link is quasi‐static Rayleigh fading and the relay is full‐duplex, the fundamental diversity‐multiplexing tradeoff (DMT) is investigated, and we show that a compress‐and‐forward relay protocol can achieve the optimal DMT.     

Statistical channel knowledge-based optimum power allocation for relaying protocols in the high SNR regime

We are concerned with transmit power optimization in a wireless relay network with various cooperation protocols. With statistical channel knowledge (in the form of knowledge of the fading distribution and the path loss information across all the nodes) at the transmitters and perfect channel state information at the receivers, we derive the optimal power allocation that minimizes high signal-to-noise ratio (SNR) approximations of the outage probability of the mutual information (MI) with amplify-and-forward (AF), decode-and-forward (DF) and distributed space-time coded (DSTC) relaying protocols operating over Rayleigh fading channels. We demonstrate that the high SNR approximation-based outage probability expressions are convex functions of the transmit power vector, and the nature of the optimal power allocation depends on whether or not a direct link between the source and the destination exists. Interestingly, for AF and DF protocols, this allocation depends only on the ratio of mean channel power gains (i.e., the ratio of the source-relay gain to the relay-destination gain), whereas with a DSTC protocol this allocation also depends on the transmission rate when a direct link exists. In addition to the immediate benefits of improved outage behavior, our results show that optimal power allocation brings impressive coding gains over equal power allocation. Furthermore, our analysis reveals that the coding gain gap between the AF and DF protocols can also be reduced by the optimal power allocation     

On the diversity gain region of the dynamic decode-and-forward relay-assisted Z-channel

In an interference-limited system, the interference forwarding by a relay enhances the interference level and thereby enables the cancellation of the interference. In this work, interference forwarding by a half-duplex dynamic decode-and-forward (HD DDF) relay in a two-user Z-channel is considered. In the two-user Z-channel, one user is interference-limited while the other user is interference-free. The diversity gain region (DGR), which characterizes the tradeoff between the achievable diversity orders between the two users, is an appropriate performance metric for the Z-channel. Closed-form expression for the achievable DGR with the interference forwarding by the HD DDF relay is presented. The multiplexing gain regions (MGRs) where the HD DDF protocol achieves better DGR over the direct transmission scheme, full-duplex decode-and-forward (FD DF) and FD partial DF relay assisted Z- channel are identified. The HD DDF protocol is shown to achieve better DGR than the FD DF and FD PDF relay for a large range of MGR. The achievable DGRs for the HD DDF, FD DF, and FD PDF relay-assisted Z-channel and direct transmission scheme are presented for various interference levels and multiplexing gain pairs.     

On optimum selection relaying protocols in cooperative wireless networks

In this letter, the outage probabilities of selection relaying protocols are analyzed and compared for cooperative wireless networks. It is assumed that both source and relay use equal allocated time in transmission. Depending on the quality of the source-relay channel, the relay may choose either Decode-and-Forward (DF), Amplify-and-Forward (AF), or Direct-Transmission (DT) to forward signals. It turns out that in terms of outage probability, two selection relaying schemes are better than others: selecting between DF and AF protocols (DF-AF) or selecting between DF and DT protocols (DF-DT). It is shown that with an equal power allocation, both of the DF-AF and DF-DT selection relaying protocols have the same asymptotic outage probability. However, with an optimum power allocation strategy, the DF-AF selection scheme is in general better than the DF-DT selection scheme. Note that the optimum power allocations depend on channel variances, not on instantaneous channel gains. When the quality of the relay-destination link is much better than that of the source-relay link, observed from simulation, the outage probability of the DF-AF selection protocol with its optimum power allocation is 1.5dB better than that of the DF-DT selection with its own optimum power allocation. Extensive simulations are presented to validate the analytical results.     

On the capacity of some channels with channel state information

We study the capacity of some channels whose conditional output probability distribution depends on a state process independent of the channel input and where channel state information (CSI) signals are available both at the transmitter (CSIT) and at the receiver (CSIR). When the channel state and the CSI signals are jointly independent and identically distributed (i.i.d.), the channel reduces to a case studied by Shannon (1958). In this case, we show that when the CSIT is a deterministic function of the CSIR, optimal coding is particularly simple. When the state process has memory, we provide a general capacity formula and we give some more restrictive conditions under which the capacity has still a simple single-letter characterization, allowing simple optimal coding. Finally, we turn to the additive white Gaussian noise (AWGN) channel with fading and we provide a generalization of some results about capacity with CSI for this channel. In particular, we show that variable-rate coding (or multiplexing of several codebooks) is not needed to achieve capacity and, even when the CSIT is not perfect, the capacity achieving power allocation is of the waferfilling type     

Quantifying the Loss of Compress–Forward Relaying Without Wyner–Ziv Coding

The compress-and-forward (CF) strategy achieves the optimal diversity–multiplexing tradeoff (DMT) of a three-node half-duplex relay network in slow fading, under the assumption that the relay has perfect knowledge of all three channel coefficients and that the relay makes use of Wyner–Ziv (WZ) source coding with side information. This paper studies the achievable DMT of the same network when the relay is constrained to make use of standard (non-WZ) source coding. Under a short-term power constraint at the relay, using source coding without side information results in a significant loss in terms of the DMT. For multiplexing gains $r leq {2over 3}$, this loss can be fully compensated for by using power control at the relay. On the contrary, for $r in ({2over 3},1)$, the loss with respect to WZ coding remains significant.      

The effect of channel errors on the performance of a contention-based tdma protocol

A previously proposed contention-based TDMA protocol is modified to remain operational for a channel which is not noise free. The protocol is a mixture of random accessing and time division multiplexing and is suitable for data transmission through a channel which is characterized by non-negligible round-trip signal propagation delay. The effect of channel errors on the performance of the protocol is studied. Through numerical calculation it is observed that for the bit-error-rates encountered in practice the protocol remains stable. When the channel becomes rather noisy, error correcting codes can be imbedded to improve the performance. The validity of analysis has been verified by computer simulation.     

Decode-and-Forward Relaying With Quantized Channel State Feedback: An Outage Exponent Analysis

The problem of resource allocation to maximize the outage exponent over a fading relay channel using the decode-and-forward protocol with quantized channel state feedback (CSF) is studied. Three different scenarios are considered: relay-to-source, destination-to-relay, and destination-to-source-and-relay CSF. In the relay-to-source CSF scenario, it is found that using merely one bit of CSF to control the source transmit power is sufficient to achieve the multiantenna upper bound in a range of multiplexing gains. In the destination-to-relay CSF scenario, the systems slightly outperform dynamic decode-and-forward (DDF) at high multiplexing gains, even with only one bit of feedback. Finally, in the destination-to-source-and-relay CSF scenario, if the source-relay channel gain is unknown to the feedback quantizer at the destination, the diversity gain only grows linearly in the number of feedback levels, in sharp contrast to an exponential growth for multiantenna channels. In this last scenario, a simple scheme is shown to perform close to the corresponding upper bound.      

Exact and asymptotic BEP of cooperative DS-CDMA systems using decode and forward relaying in the presence of multipath propagation

In this paper, we derive the bit error probability (BEP) of cooperative DS-CDMA systems using decode and forward (DF) relaying. We consider a conventional DF protocol where all the relays that have correctly decoded transmit and a selective DF (S-DF) protocol where we activate only the relay that offers the best instantaneous signal to noise ratio (SNR) of the relay to destination link among the relays that have correctly decoded. The derived results are valid for any multipath intensity profile of the channel, any path delays and take into account the correlation of the multipath gains.     

Cross-Layer Design of FDD-OFDM Systems Based on ACK/NAK Feedbacks

It is well known that cross-layer scheduling which adapts power, rate and user allocation can achieve significant gain on system capacity. However, conventional cross-layer designs all require channel state information at the base station (CSIT) which is difficult to obtain in practice. In this paper, we focus on cross-layer resource optimization based on ACK/NAK feedback flows in orthogonal frequency-division multiplexing (OFDM) systems without explicit CSIT. While the problem can be modeled as Markov decision process (MDP), brute-force approach by policy iteration or value iteration cannot lead to any viable solution. Thus, we derive a simple closed-form solution for the MDP cross-layer problem, which is asymptotically optimal for sufficiently small target packet error rate (PER). The proposed solution also has low complexity and is suitable for real-time implementation. It is also shown to achieve significant performance gain compared with systems that do not utilize the ACK/NAK feedbacks for cross-layer designs or cross-layer systems that utilize very unreliable CSIT for adaptation with mismatch in CSIT error statistics. Asymptotic analysis is also provided to obtain useful design insights.     

On the Optimality of the ARQ-DDF Protocol

In this correspondence, the performance of the automatic repeat request-dynamic decode and forward (ARQ-DDF) cooperation protocol is analyzed in two distinct scenarios. The first scenario is the multiple access relay channel where a single relay is dedicated to simultaneously help two multiple access users. For this setup, it is shown that the ARQ-DDF protocol achieves the channel's optimal diversity multiplexing tradeoff (DMT). The second scenario is the cooperative vector multiple access channel where two users cooperate in delivering their messages to a destination equipped with two receiving antennas. For this setup, a new variant of the ARQ-DDF protocol is developed where the two users are purposefully instructed not to cooperate in the first round of transmission. Lower and upper bounds on the achievable DMT are then derived. These bounds are shown to converge to the optimal tradeoff as the number of transmission rounds increases.     

On the Diversity–Multiplexing Tradeoff in Multiple-Relay Network

This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between either one or several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh-fading channel, or disconnected. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity–multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay $(K > 1)$ networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple-access single-relay setup, we show that the RS scheme reduces to the naive amplify-and-forward (AF) relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward (DF) scheme is shown to be optimum for this scenario.