Diversity-multiplexing Tradeoff Research Articles

Secrecy Outage Analysis of Buffer-Aided Cooperative MIMO Relaying Systems

This paper investigates the secrecy outage performance of buffer-aided multirelay multiple-input multiple-output cooperative systems in the presence of a passive eavesdropper. Due to the unavailability of the channel state information of eavesdropper's channel, a buffer-aided joint transmit antenna and relay selection scheme based on the main channel is proposed to enhance the secrecy performance. Specifically, we model the evolution of the relay buffers as a Markov chain and derive new exact and asymptotic closed-form expressions for the secrecy outage probability, which provides an efficient way to assess the effect of system parameters on the secrecy outage probability. Moreover, simple asymptotic results are further exploited under two special scenarios, i.e., $L \rightarrow \infty$ and $L \not\rightarrow \infty$ (where $L$ denotes the size of the relay buffers), for characterizing the achievable secrecy diversity gain, the secrecy coding gain, and the secrecy diversity-multiplexing tradeoff. Our results reveal that: 1) a secrecy diversity gain of $N_RM{\rm min}(N_S,N_D)$ is achieved when $L \not\rightarrow \infty$ , however, when $L \rightarrow \infty$ , the secrecy diversity gain increases to $N_RM(N_S+N_D)$ , where $N_S$ , $N_R$ , and $N_D$ represent the number of antennas at the source, each of $M$ relays and the destination, respectively. 2) The eavesdropper's channel does not affect the secrecy diversity gain but only the secrecy coding gain in both the two scenarios.

Joint Relay Selection and Power Allocation in Large-Scale MIMO Systems with Untrusted Relays and Passive Eavesdroppers

In this paper, a joint relay selection and power allocation (JRP) scheme is proposed to enhance the physical layer security of a cooperative network, where a multiple antennas source communicates with a single-antenna destination in the presence of untrusted relays and passive eavesdroppers (Eves). The objective is to protect the data confidentially while concurrently relying on the untrusted relays as potential Eves to improve both the security and reliability of the network. To realize this objective, we consider cooperative jamming performed by the destination while the JRP scheme is implemented. With the aim of maximizing the instantaneous secrecy rate, we derive a new closed-form solution for the optimal power allocation and propose a simple relay selection criterion under two scenarios of non-colluding Eves (NCE) and colluding Eves (CE). For the proposed scheme, a new closed-form expression is derived for the ergodic secrecy rate (ESR) and the secrecy outage probability as security metrics, and a new closed-form expression is presented for the average symbol error rate as a reliability measure over Rayleigh fading channels. We further explicitly characterize the high signal-to-noise ratio slope and power offset of the ESR to highlight the impacts of system parameters on the ESR. In addition, we examine the diversity order of the proposed scheme to reveal the achievable secrecy performance advantage. Finally, the secrecy and reliability diversity-multiplexing tradeoff of the optimized network are provided. Numerical results highlight that the ESR performance of the proposed JRP scheme for NCE and CE cases is increased with respect to the number of untrustworthy relays.

A Unified Stochastic Geometry Model for MIMO Cellular Networks With Retransmissions

This paper presents a unified mathematical paradigm, based on stochastic geometry, for downlink cellular networks with multiple-input-multiple-output (MIMO) base stations. The developed paradigm accounts for signal retransmission upon decoding errors, in which the temporal correlation among the signal-to-interference-plus-noise ratio (SINR) of the original and retransmitted signals is captured. In addition to modeling the effect of retransmission on the network performance, the developed mathematical model presents twofold analysis unification for the MIMO cellular networks literature. First, it integrates the tangible decoding error probability and the abstracted (i.e., modulation scheme and receiver type agnostic) outage probability analysis, which are largely disjoint in the literature. Second, it unifies the analysis for different MIMO configurations. The unified MIMO analysis is achieved by abstracting unnecessary information conveyed within the interfering signals by Gaussian signaling approximation along with an equivalent SISO representation for the per-data stream SINR in the MIMO cellular networks. We show that the proposed unification simplifies the analysis without sacrificing the model accuracy. To this end, we discuss the diversity-multiplexing tradeoff imposed by different MIMO schemes and shed light on the diversity loss due to the temporal correlation among the SINRs of the original and retransmitted signals. Finally, several design insights are highlighted.

Underlay Cognitive Multihop MIMO Networks With and Without Receive Interference Cancellation

This paper investigates the impact of primary network interference on the performance of cognitive multihop secondary network under various multiple-input multiple-output (MIMO) approaches per hop. Specifically, the cognitive system involves a secondary network with MIMO relays that use the amplify-and-forward protocol, and each of which shares the same spectrum resources of multiple primary users (PUs) transmit and receive stations. Two different receive array conditions, and hence processing approaches, per hop in the secondary network are treated separately, which are maximal ratio combining for sufficiently spaced receive antennas to provide receive diversity gain and interference cancellation (IC) for insufficiently spaced antennas to reduce the effect of PUs interference. The latter approach involves two different algorithms that vary in terms of complexity and achieved performance, which are dominant receive IC and adaptive receive IC. Moreover, for both approaches, the transmit array gain is achieved per hop through the low-complexity transmit antenna selection. In doing so, new analytical results for multihop secondary network’s end-to-end outage probability are developed. Moreover, simple asymptotic results for this outage performance in high SNR regime are provided, from which the achieved diversity and coding gains and the diversity-multiplexing tradeoff can be extracted. In addition, to further enhance the secondary network, optimal power allocation among hops is obtained based on the asymptotic outage performance under the constraints of transmit power of a secondary transmit station and interference limit on the primary network. The developed analytical results in this paper are validated through numerical and simulation results.

Finite-SNR Diversity–Multiplexing Tradeoff With Accurate Performance Analysis for Fully Correlated Rayleigh MIMO Channels

Zheng and Tse were the first to discover the fundamental diversity–multiplexing tradeoff (DMT) that occurs in multiple-input multiple-output (MIMO) systems. Their research was limited to infinite signal-to-noise ratio (SNR) situations. Later, research was also conducted on finite-SNR situations; however, this research had significant problems with coarse approximation. In this paper, we propose more accurate approximations of the finite-SNR DMT and the outage probability for Rayleigh fading MIMO channels to solve these problems. The proposed formulas provide more general solutions that are applicable not only to uncorrelated and semicorrelated channels but also to fully correlated channels, which have not been considered in the literature. Utilizing the proposed finite-SNR DMT, we further investigate the influence of the deviation of the finite-SNR DMT on system performance. We also derived an accurate SNR offset quantity, which provides a link for transformation of finite-SNR DMT to actual outage probability. Finally, we present computer simulation results for illustration and comparison to confirm the validity of our research work.

Exploiting Opportunistic Network Coding for Improving Wireless Reliability Against Co-Channel Interference

This paper investigates network coding with full diversity and a high rate for improving the reliability of wireless communications against the co-channel interference. We consider a cellular network composed of two user terminals that are intended to communicate with a common base station (BS), where a two-way relay node is used to assist the bidirectional communications between the users and BS. We propose an opportunistic network coding (ONC) scheme with the two-way relay, called two-way ONC, which operates depending on whether or not the relay node successfully decodes data packets of the user terminals and BS. Closed-form outage probability expressions of the uplink transmission (from users to BS) and downlink transmission (from BS to users) are derived for the proposed two-way ONC scheme in the presence of co-channel interference over Rayleigh fading channels. We also develop the diversity-multiplexing tradeoff (DMT) of the two-way ONC scheme and show that it obtains the full diversity and an increased multiplexing gain , as compared with conventional one-way relay methods. Additionally, numerical outage probability results demonstrate that the proposed two-way ONC scheme outperforms the conventional one-way relay approaches in terms of improving the communication’s reliability against co-channel interference.

A Diversity-Multiplexing Tradeoff Optimal Low Complexity Zero Forcing Method Based on ZP-OFDM

Due to the computational complexity of maximum-likelihood signal decoding, the equalizers with less complexity are considered in the literature. Employing the zero forcing (ZF) equalizer, zero-padded orthogonal frequency-division multiplexing (ZP-OFDM) is capable of benefiting the maximum available multipath diversity with the computational complexity of inverting a matrix of the size of data block length, which incurs an extra implementation cost relative to the fast Fourier transform-based OFDM decoder. In this paper, based on the ZP-OFDM encoding scheme, we propose a two-stage decoder that attains the maximum multipath diversity with lower computational complexity, as compared with the ZF ZP-OFDM and prove analytically that our proposed decoder is diversity-multiplexing tradeoff optimal. It has also been shown that by setting the decoder parameters, it can attain any arbitrary diversity gain smaller than the maximum multipath diversity. Moreover, the more the diversity gain is decreased the more the computational complexity is reduced.

Lower Bound for Finite-SNR DMT With Position Estimation Errors in MIMO Channels

The finite signal-to-noise ratio (SNR) situation for the diversity-multiplexing tradeoff (DMT) of multiple-input-multiple-output (MIMO) systems has become a fundamental research topic in wireless communications. In this letter, the impact of position estimation errors of the receiver on the finite-SNR DMT of the MIMO system is investigated. Formulas of the biased Cramer–Rao bound and the mean-square error lower bound of the biased finite-SNR DMT are proposed when the DMT value is influenced by the position estimation error of the receiver induced by a biased position estimator. Furthermore, based on the developed formulas, the case of the DMT over the Rayleigh fading channel and the position estimation errors raised by a radar is analyzed.

Diversity-Multiplexing Tradeoff for Log-Normal Fading Channels

Although there has been a growing interest on the study of diversity-multiplexing tradeoff (DMT), the existing works are mostly restricted to the outcomes reported for Rayleigh, Rician, and Nakagami fading channels. In this paper, we investigate the optimal tradeoff in the presence of log-normal fading, which provides an accurate model for indoor wireless, optical wireless, and ultra-wideband channels. We consider a multiple-input multiple-output (MIMO) log-normal channel, derive the outage probability expression, and then present the asymptotical DMT expression. It is shown that the asymptotical maximum diversity gain tends to infinity with logarithm of signal-to-noise ratio (SNR). To have further insight, we normalize the DMT with that of single-input single-output case and express the relative asymptotical DMT of the MIMO log-normal channel as a function of the number of transmit and receive antennas. We further study DMT for finite SNRs and demonstrate convergence to the asymptotical case. Extensive numerical results are provided to corroborate the analytical derivation.

On Throughput-Reliability Tradeoff of Two-Layer D-BLAST Transmission Scheme

A contemporary tradeoff analysis concept, recognized as throughput-reliability tradeoff (TRT) analysis, has pioneered for general block fading MIMO systems. The tribute of this analysis is its ability to reveal the reciprocity between outage probability (OP), signal-to-noise ratio (SNR) and transmission rate (R) unlike diversity-multiplexing tradeoff. The present work considers two-layer D-BLAST transmission scheme for two varieties of receiver. First, TRT analysis of D-BLAST with group detection receiver is investigated where each contented diagonal of D-BLAST is detected at once. Later, TRT analysis of D-BLAST with successive interference cancellation receiver detecting a symbol at once is investigated. Based on the derived expressions, the interplay between SNR, R and OP are explored. We verify theoretically derived expressions through simulation using MATLAB programs.

Finite SNR diversity-multiplexing tradeoff with spatial correlation and mutual coupling effects for Rayleigh MIMO channels

In the literature, the finite signal-to-noise ratio (SNR) situation for the fundamental diversity-multiplexing tradeoff (DMT) of multiple-input–multiple-output systems (MIMO systems) has been attached great importance. However, only lower bounds or coarse approximations of the outage probability have been proposed to develop coarse bounds of the finite-SNR DMT in the literature, and their approximation errors are still non-negligible. In order to solve the aforementioned weaknesses, we first propose an accurate finite-SNR outage probability for Rayleigh MIMO fading channels and then use it to derive the corresponding finite-SNR DMT. The proposed finite-SNR DMT can be used as an accurate guideline at finite SNR for rate-adaptive MIMO applications. In addition, the impact of antenna mutual coupling (along with antenna spatial correlation) on the finite-SNR outage probability and consequently its impact on the finite-SNR DMT are analyzed. Our results reveal that the spatial correlation of antenna arrays cannot provide gains to the outage performance and the finite-SNR DMT. In contrast, when the antenna spacing of antenna arrays is appropriately specified, the mutual coupling of antenna arrays is in favor of the outage performance and the finite-SNR DMT. Finally, we present computer simulation results for illustration and comparison to confirm the validity of our research work.

Efficiently sphere-decodable physical layer transmission schemes for wireless storage networks

Three transmission schemes over a new type of multiple-access channel (MAC) model with inter-source communication links are proposed and investigated in this paper. This new channel model is well motivated by, e.g., wireless distributed storage networks, where communication to repair a lost node takes place from helper nodes to a repairing node over a wireless channel. Since in many wireless networks nodes can come and go in an arbitrary manner, there must be an inherent capability of inter-node communication between every pair of nodes. Assuming that communication is possible between every pair of helper nodes, the newly proposed schemes are based on various smart time-sharing and relaying strategies. In other words, certain helper nodes will be regarded as relays, thereby converting the conventional uncooperative multiple-access channel to a multiple-access relay channel (MARC). The diversity-multiplexing gain tradeoff (DMT) of the system together with efficient sphere-decodability and low structural complexity in terms of the number of antennas required at each end is used as the main design objectives. While the optimal DMT for the new channel model is fully open, it is shown that the proposed schemes outperform the DMT of the simple time-sharing protocol and, in some cases, even the optimal uncooperative MAC DMT. While using a wireless distributed storage network as a motivating example throughout the paper, the MAC transmission techniques proposed here are completely general and as such applicable to any MAC communication with inter-source communication links.

Performance-Complexity Analysis for MAC ML-Based Decoding With User Selection

The rate-reliability-complexity limits of a quasi-static $K$ -user multiple access channel (MAC), with or without feedback, are explored in this paper. Using high-SNR asymptotics, bounds on the computational resources required to achieve near-optimal (ML-based) decoding performance are first derived. They, in turn, yield bounds on the (reduced) complexity needed to achieve any (including suboptimal) diversity-multiplexing tradeoff (DMT) performance. Similar complexity-bounds in the presence of feedback-aided user selection are also given. This latter effort reveals the ability of a few bits of feedback not only to improve performance, but also to reduce complexity. In this context, our analysis reveals the interesting finding that a proper calibration of user selection can allow for near-optimal ML-based decoding, with complexity that need not scale exponentially in the total number of codeword bits. The derived bounds constitute the best known performance-versus-complexity behavior to date for ML-based MAC decoding, as well as a first exploration of the complexity-feedback-performance interdependencies in multiuser settings.

Distributed WRBG Matching Approach for Multiflow Two-Way D2D Networks

Device-to-device (D2D) communication has great potential to improve spectrum efficiency and offload traffic for cellular networks. In this paper, we focus on a multiflow two-way D2D network with decode-and-forward (DF) relays, coexisting with OFDMA cellular network. The spectrum sharing and relay selection are considered to minimize the outage probability of the device in D2D networks. The induced problem is a complicated probabilistic integral programming. A novel weighted random bipartite graph (WRBG)-based minimum weight maximum matching (MWMM) approach will be proposed in this paper. To offload not only the traffic but also the signaling and computation overhead, the improved min-sum algorithm will be applied to find the MWMM in the distributed manner with only polynomial complexity. The proposed approach enjoys an advantage that the close-form approximation formulas for optimal outage probability and diversity-multiplexing tradeoff can be derived by analyzing the properties of MWMM on WRBG. Both the theoretical derivations and simulation results will illustrate that the proposed approach for multiflow two-way D2D networks achieves the same performance as single-flow two-way D2D systems. Therefore, the distributed WRBG matching approach yields not only a practical distributed algorithm, but also a simple and elegant theoretical framework for multiflow two-way D2D networks.

Research on the Nth-best Relay Selection with Outdated Feedback in Selection Cooperation Systems

In this paper, the process of the Nth-best relay selection strategy with outdated feedback is given in the selection cooperative system. The performance of the proposed Nth-best relay selection with outdated channel state information is investigated in Rayleigh fading scenarios. The exact closed-form expression for the outage performance is derived. In the high signal-to-noise ratio regime, the asymptotic outage behavior is also analyzed. In addition, based on the asymptotic analysis, the diversity-multiplexing tradeoff of the considered system is obtained. At last, simulation results show that even a small deviation of the channel estimates from the actual values will lead to a severe degradation of the outage performance of the considered system.

Fast-Decodable Space–Time Codes for the -Relay and Multiple-Access MIMO Channel

In this article, the first general constructions of fast-decodable, more specifically (conditionally) $g$-group decodable, space-time block codes for the Nonorthogonal Amplify and Forward (NAF) Multiple-Input Multiple-Output (MIMO) relay channel under the half-duplex constraint are proposed. In this scenario, the source and the intermediate relays used for data amplification are allowed to employ multiple antennas for data transmission and reception. The worst-case decoding complexity of the obtained codes is reduced by up to $75%$. In addition to being fast-decodable, the proposed codes achieve full-diversity and have nonvanishing determinants, which has been shown to be useful for achieving the optimal Diversity-Multiplexing Tradeoff (DMT) of the NAF channel. Further, it is shown that the same techniques as in the cooperative scenario can be utilized to achieve fast-decodability for $K$-user MIMO Multiple-Access Channel (MAC) space-time block codes. The resulting codes in addition exhibit the conditional nonvanishing determinant property which, for its part, has been shown to be useful for achieving the optimal MAC-DMT.

Optimization of Multimedia Progressive Transmission Over MIMO Channels

This paper studies the optimal transmission of multimedia progressive sources, which require unequal target error rates in their bitstream, over multiple-input–multiple-output (MIMO) channels. First, we derive the information outage probability expression of a space–time code for an arbitrarily given piecewise-linear diversity–multiplexing tradeoff (DMT) function and the conditions for the existence of a crossover point of the information outage probability curves of the space–time codes. We prove that as long as the crossover point of the outage probabilities exists, as spectral efficiency increases, the crossover point in the signal-to-noise ratio (SNR) monotonically increases, whereas that of the outage probability monotonically decreases. This analysis can be applied to any space–time code, receiver, and propagation channel with a given DMT function. As a specific example, we analyze the two-layer diagonal Bell Labs space–time architecture (D-BLAST) with a group zero-forcing receiver, the vertical BLAST (V-BLAST) with a minimum mean-square error receiver, and orthogonal space–time block codes (OSTBCs), and prove the monotonic behavior of the crossover point for those codes. Based on that, with respect to D-BLAST, V-BLAST, and OSTBC, we derive a method for the optimal space–time coding of a sequence that contains numerous progressive packets. We show that by employing the optimization method rather than exhaustive search, the computational complexity involved with optimal space–time coding can be exponentially reduced without losing any peak SNR performance.

Joint optimal power allocation and relay selection to establish secure transmission in uplink transmission of untrusted relays network

In this paper, the authors deal with secure transmission in two-hop amplify-and-forward network with untrusted relays. To prevent the untrusted relays from intercepting the source message and to achieve positive secrecy rate, the destination-based cooperative jamming technique is used. The authors propose joint secure best relay selection (BRS) and optimal power allocation (OPA) for uplink transmission of a cellular network when the base station is equipped with very large-scale antenna arrays. Then, the common performance metrics such as ergodic secrecy rate (ESR) and secrecy outage probability are evaluated for the optimised network. Moreover, the diversity order and diversity-multiplexing tradeoff of the system are examined. The authors obtain that the diversity order of joint BRS and OPA scenario is equal to number of relays. Finally, some numerical and simulation results are presented to validate the theoretical analysis and to show the advantages offered by the presented systems. They reveal interesting results that, by increasing number of untrusted relay nodes, the system performance improves. For example, for target ESR 2 bits/s/Hz and ten untrusted relay nodes, the optimised network saves about 5 dB for uplink transmission, in comparison with the system applying the BRS and equal power allocation.

The Diversity-Multiplexing Tradeoff of Secret-Key Agreement Over Multiple Antenna Channels

We study the problem of secret-key agreement between two legitimate parties, Alice and Bob, in the presence of an eavesdropper Eve. There is a public channel with unlimited capacity that is available to the legitimate parties and is also observed by Eve. Our focus is on Rayleigh fading quasistatic channels. The legitimate receiver and the eavesdropper are assumed to have perfect channel knowledge of their channels. We study the system in the high-power regime. First, we define the secret-key diversity gain and the secret-key multiplexing gain. Second, we establish the secret-key diversity multiplexing tradeoff (DMT) under no channel state information (CSI) at the transmitter (CSI-T). The eavesdropper is shown to “steal” only transmit antennas. We show that, like the DMT without secrecy constraint, the secret-key DMT is the same either with or without full channel state information at the transmitter. This insensitivity of secret-key DMT toward CSI-T features a fundamental difference between secret-key agreement and the wiretap channel, in which secret DMT depends heavily on CSI-T. Finally, we present several secret-key DMT-achieving schemes in case of full CSI-T. We argue that secret DMT-achieving schemes are also key DMT-achieving. Moreover, we show formally that artificial noise (AN), likewise zero-forcing (ZF), is DMT-achieving. We also show that the public feedback channel improves the outage performance without having any effect on the DMT.

On the Diversity of Linear Transceivers in MIMO AF Relaying Systems

In this paper, we provide a comprehensive survey on designs and analyses of various relay-destination transceiving schemes, such as zero-forcing (ZF), minimum mean squared error (MMSE), and maximum information rate (MIR) criteria, in multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems. In the first part of the paper, we suggest a new framework for the transceiver designs utilizing a decomposable property of the error covariance matrix to give a general insight on the system and make the analysis more tractable. Then, in the second part of the paper, we provide an in-depth analysis on their diversity performance. Our analysis embraces two different scenarios, namely, the diversity-multiplexing tradeoff (DMT) and the diversity-rate tradeoff (DRT). First, we derive compact closed-form expressions for the DMT through tight upper and lower bounds. Then, we observe that while our DMT analysis accurately predicts performance of the ZF and MIR schemes, the MMSE-based designs exhibit a complicated rate-dependent behavior and, thus, are very unpredictable via DMT for finite rate cases. Thus, second, we highlight this interesting observation and characterize the diversity of the MMSE schemes at all finite rates. This leads to closed-form expressions for the DRT which reveals relationship between diversity, spectral efficiency, and the number of antennas at each node. The DRT analysis compliments our work on DMT, and thus, the paper provides a complete understanding on the diversity of MIMO AF relaying systems.