D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), non-orthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the OAF and NAF protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. In the two-relay case, the variable-NSDF protocol is shown to improve on the DMT of the best previously-known static protocol for higher values of multiplexing gain. Our results also establish that the fixed-NSDF protocol has a better DMT than the NAF protocol for any number of relays.

MIMO cooperative communication network design with relay selection and CSI feedback

In this paper, we investigate an amplify-and-forward (AF) multiple-input multiple-output - spatial division multiplexing (MIMO-SDM) cooperative wireless networks, where each network node is equipped with multiple antennas. In order to deal with the problems of signal combining at the destination and cooperative relay selection, we propose an improved minimum mean square error (MMSE) signal combining scheme for signal recovery at the destination. Additionally, we propose two distributed relay selection algorithms based on the minimum mean squared error (MSE) of the signal estimation for the cases where channel state information (CSI) from the source to the destination is available and unavailable at the candidate nodes. Simulation results demonstrate that the proposed combiner together with the proposed relay selection algorithms achieve higher diversity gain than previous approaches in both flat and frequency-selective fading channels.

Outage-optimal relay strategy under outdated channel state information in decode-and-forward cooperative communication systems

In this study, the authors investigate the outage-optimal relay strategy under outdated channel state information (CSI) in a decode-and-forward cooperative communication system. They first confirm mathematically that minimising the outage probability under outdated CSI is equivalent to minimising the conditional outage probability on the outdated CSI of all the decodable relays' links. They then propose a multiple-relay strategy with optimised transmitting power allocation (MRS-OTPA) that minimises the conditional outage probability. It is shown that this MRS is a generalised relay approach to achieve the outage optimality under outdated CSI. To reduce the complexity, they also propose a MRS with equal transmitting power allocation (MRS-ETPA) that achieves near-optimal outage performance. It is proved that full spatial diversity, which has been achieved under ideal CSI, can still be achieved under outdated CSI through MRS-OTPA and MRS-ETPA. Finally, the outage performance and diversity order of MRS-OTPA and MRS-ETPA are evaluated by simulation.

Slotted cooperative communication in half duplex relay networks

In cooperative communication systems, several wireless communication terminals collaborate to form a virtual-multiple antenna array system and exploit the spatial diversity to achieve a better performance. This thesis proposes a practical slotted protocol for cooperative communication systems with half-duplex single antennas. The performance of the proposed slotted cooperative communication protocol is evaluated in terms of the pairwise error probability and the bit error rate. The proposed protocol achieves the multiple-input single-output performance bound with a novel relay ordering and scheduling strategy.

Leveraging coherent distributed space-time codes for noncoherent communication in relay networks via training

For point to point multiple input multiple output systems, Dayal-Brehler-Varanasi have proved that training codes achieve the same diversity order as that of the underlying coherent space time block code (STBC) if a simple minimum mean squared error estimate of the channel formed using the training part is employed for coherent detection of the underlying STBC. In this letter, a similar strategy involving a combination of training, channel estimation and detection in conjunction with existing coherent distributed STBCs is proposed for noncoherent communication in Amplify-and-Forward (AF) relay networks. Simulation results show that the proposed simple strategy outperforms distributed differential space-time coding for AF relay networks. Finally, the proposed strategy is extended to asynchronous relay networks using orthogonal frequency division multiplexing.

Diversity and degrees of freedom of cooperative wireless networks

Two key parameters in the outage characterization of a wireless fading network are the diversity and the degrees of freedom (DOF). These two quantities represent the two endpoints of the diversity multiplexing gain tradeoff, In this paper, we present max-flow min-cut type theorems for computing both the diversity and the DOF of arbitrary single-source single-sink networks with nodes possessing multiple antennas. We also show that an amplify-and-forward protocol is sufficient to achieve the same. The DOF characterization is obtained using a conversion to a deterministic wireless network for which the capacity was recently found. This conversion is operational in the sense that a capacity-achieving scheme for the deterministic network can be converted into a DOF-achieving scheme for the fading network. We also show that the diversity result easily extends to multisource multi-sink networks whereas the DOF result extends to a single-source multi-cast network. Along the way, we prove that the zero error capacity of the deterministic network is the same as its c-error capacity.

DMT of Multi-hop Cooperative Networks-Part II: Layered and Multi-Antenna Networks

We consider single-source, single-sink (ss-ss) multi-hop relay networks, with slow-fading Rayleigh links. This two part paper aims at giving explicit protocols and codes to achieve the optimal diversity-multiplexing tradeoff (DMT) of two classes of multi-hop networks: K-parallel-path (KPP) networks and Layered networks. While single-antenna KPP networks were the focus of the first part, we consider layered and multi-antenna networks in this second part. We prove that a linear DMT between the maximum diversity d(max). and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks under the half-duplex constraint. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4. For the multiple-antenna case, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks. Along the way, we compute the DMT of parallel MIMO channels in terms of the DMT of the component channel. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable using an amplify-and-forward (AF) protocol. Explicit short-block-length codes are provided for all the proposed protocols. Two key implications of the results in the two-part paper are that the half-duplex constraint does not necessarily entail rate loss by a factor of two as previously believed and that simple AN protocols are often sufficient to attain the best possible DMT.

A non-orthogonal distributed space-time coded protocol - Part 1:Signal model and design criteria

In this two-part series of papers, a generalized non-orthogonal amplify and forward (GNAF) protocol which generalizes several known cooperative diversity protocols is proposed. Transmission in the GNAF protocol comprises of two phases - the broadcast phase and the cooperation phase. In the broadcast phase, the source broadcasts its information to the relays as well as the destination. In the cooperation phase, the source and the relays together transmit a space-time code in a distributed fashion. The GNAF protocol relaxes the constraints imposed by the protocol of Jing and Hassibi on the code structure. In Part-I of this paper, a code design criteria is obtained and it is shown that the GNAF protocol is delay efficient and coding gain efficient as well. Moreover GNAF protocol enables the use of sphere decoders at the destination with a non-exponential Maximum likelihood (ML) decoding complexity. In Part-II, several low decoding complexity code constructions are studied and a lower bound on the Diversity-Multiplexing Gain tradeoff of the GNAF protocol is obtained.

Voluntary Energy Harvesting Relays and Selection in Cooperative Wireless Networks

The use of energy harvesting (EH) nodes as cooperative relays is a promising and emerging solution in wireless systems such as wireless sensor networks. It harnesses the spatial diversity of a multi-relay network and addresses the vexing problem of a relay's batteries getting drained in forwarding information to the destination. We consider a cooperative system in which EH nodes volunteer to serve as amplify-and-forward relays whenever they have sufficient energy for transmission. For a general class of stationary and ergodic EH processes, we introduce the notion of energy constrained and energy unconstrained relays and analytically characterize the symbol error rate of the system. Further insight is gained by an asymptotic analysis that considers the cases where the signal-to-noise-ratio or the number of relays is large. Our analysis quantifies how the energy usage at an EH relay and, consequently, its availability for relaying, depends not only on the relay's energy harvesting process, but also on its transmit power setting and the other relays in the system. The optimal static transmit power setting at the EH relays is also determined. Altogether, our results demonstrate how a system that uses EH relays differs in significant ways from one that uses conventional cooperative relays.

Multi-hop Cooperative Wireless Networks: Diversity Multiplexing Tradeoff and Optimal Code Design

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP)networks and layered networks.KPP networks, can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4.For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks.For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable.Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. We also give alternative and often simpler proofs of several existing results and show that codes achieving full diversity on a MIMO Rayleigh fading channel achieve full diversity on arbitrary fading channels. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT

On four-group ML decodable distributed space time codes for cooperative communication

A construction of a new family of distributed space time codes (DSTCs) having full diversity and low Maximum Likelihood (ML) decoding complexity is provided for the two phase based cooperative diversity protocols of Jing-Hassibi and the recently proposed Generalized Non-orthogonal Amplify and Forward (GNAF) protocol of Rajan et al. The salient feature of the proposed DSTCs is that they satisfy the extra constraints imposed by the protocols and are also four-group ML decodable which leads to significant reduction in ML decoding complexity compared to all existing DSTC constructions. Moreover these codes have uniform distribution of power among the relays as well as in time. Also, simulations results indicate that these codes perform better in comparison with the only known DSTC with the same rate and decoding complexity, namely the Coordinate Interleaved Orthogonal Design (CIOD). Furthermore, they perform very close to DSTCs from field extensions which have same rate but higher decoding complexity.

Collocated and Distributed STBCs with Partial Interference Cancellation Decoding, Part II: Code Construction

In this second part of a two part series of papers, we construct a new class of Space-Time Block Codes (STBCs) for point-to-point MIMO channel and Distributed STBCs (DSTBCs) for the amplify-and-forward relay channel that give full-diversity with Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC) decoders. The proposed class of STBCs include most of the known full-diversity low complexity PIC/PIC-SIC decodable STBCs as special cases. We also show that a number of known full-diversity PIC/PIC-SIC decodable STBCs that were constructed for the point-topoint MIMO channel can be used as full-diversity PIC/PIC-SIC decodable DSTBCs in relay networks. For the same decoding complexity, the proposed STBCs and DSTBCs achieve higher rates than the known low decoding complexity codes. Simulation results show that the new codes have a better bit error rate performance than the low ML decoding complexity codes available in the literature.

DMT of Multihop Networks: End Points and Computational Tools

In this paper, the diversity-multiplexing gain tradeoff (DMT) of single-source, single-sink (ss-ss), multihop relay networks having slow-fading links is studied. In particular, the two end-points of the DMT of ss-ss full-duplex networks are determined, by showing that the maximum achievable diversity gain is equal to the min-cut and that the maximum multiplexing gain is equal to the min-cut rank, the latter by using an operational connection to a deterministic network. Also included in the paper, are several results that aid in the computation of the DMT of networks operating under amplify-and-forward (AF) protocols. In particular, it is shown that the colored noise encountered in amplify-and-forward protocols can be treated as white for the purpose of DMT computation, lower bounds on the DMT of lower-triangular channel matrices are derived and the DMT of parallel MIMO channels is computed. All protocols appearing in the paper are explicit and rely only upon AF relaying. Half-duplex networks and explicit coding schemes are studied in a companion paper.

Decode-and-forward relay beamforming for secrecy with finite-alphabet input

In this letter, we compute the secrecy rate of decode-and-forward (DF) relay beamforming with finite input alphabet of size M. Source and relays operate under a total power constraint. First, we observe that the secrecy rate with finite-alphabet input can go to zero as the total power increases, when we use the source power and the relay weights obtained assuming Gaussian input. This is because the capacity of an eavesdropper can approach the finite-alphabet capacity of 1/2 log(2) M with increasing total power, due to the inability to completely null in the direction of the eavesdropper. We then propose a transmit power control scheme where the optimum source power and relay weights are obtained by carrying out transmit power (source power plus relay power) control on DF with Gaussian input using semi-definite programming, and then obtaining the corresponding source power and relay weights which maximize the secrecy rate for DF with finite-alphabet input. The proposed power control scheme is shown to achieve increasing secrecy rates with increasing total power with a saturation behavior at high total powers.