Diversity-multiplexing Tradeoff Analysis Research Articles

Outage Probability and Finite-SNR DMT Analysis for IRS-Aided MIMO Systems: How Large IRSs Need to be?

Intelligent reflecting surfaces (IRSs) are promising enablers for high-capacity wireless communication systems by constructing favorable channels between the transmitter and receiver. However, general, accurate, and tractable outage probability analysis for IRS-aided multiple-input-multiple-output (MIMO) systems is not available in the literature. In this paper, we first characterize the distribution of the mutual information (MI) for IRS-aided MIMO systems by capitalizing on large random matrix theory (RMT). Based on this result, a closed-form approximation for the outage probability is derived and a gradient-based algorithm is proposed to minimize the outage probability with statistical channel state information (CSI). We also investigate the diversity-multiplexing tradeoff (DMT) with finite signal-to-noise ratio (SNR). Based on these theoretical results, we further study the impact of the IRS size on system performance. In the high SNR regime, we provide closed-form expressions for the ergodic mutual information (EMI) and outage probability as a function of the IRS size, which analytically reveal that the benefit of increasing the IRS size saturates quickly. Simulation results validate the accuracy of the theoretical analysis and confirm the increasing cost to improve system performance by deploying larger IRSs. For example, for an IRS-aided MIMO system with 20 antennas at both the transmitter and receiver, we need to double the size of the IRS to increase the throughput from 90% to 95% of its maximum value.

DMT analysis and optimal scheduling for FSO relaying communications

In this paper, two-hop parallel N-relay networks are considered and the diversity-multiplexing tradeoff (DMT) is derived over Gamma-Gamma free-space optical (FSO) channels with identical average received signal to noise rations in all links. In the derivations, both local and global channel state information (CSI) are investigated. In the local CSI case, the node only knows its incoming link conditions, while in the global CSI case, the nodes are aware of all the CSIs in the network. The listening and transmitting times at the relays as variables in the DMT derivation are further considered which are later used to optimize the performance of the network. It is demonstrated that the optimal DMT is obtained with the static quantize map and forward (SQMF) and dynamic quantize map and forward (DQMF) strategies for different ranges of the multiplexing gain. In addition, the optimal schedule of relays in the DQMF strategy is determined as a function of the local channel conditions in the relays.

DMT analysis and optimal scheduling for two-hop parallel relay networks

Two-hop parallel networks with half-duplex relays over quasi-static Rayleigh fading channels are considered. Assuming relays have only local channel state information, optimal communication schemes for these networks in terms of the diversity multiplexing trade-off (DMT) are obtained. It is shown that the dynamic quantize-map-and-forward (DQMF) and the static quantize-map-and-forward (SQMF) communication strategies achieve the optimal DMT at different ranges of the multiplexing gain. In the DQMF scheme, a relay sets its transmitting/listening times according to the instantaneous source-relay channel condition. However, in the SQMF scheme, a relay sets its transmitting/listening times to be a constant independent of the instantaneous source-relay channel gain. Essentially, we calculate the DMT of the network under the general setting for arbitrary average signal-to-noise ratios over links and it is shown that the DMT of the proposed schemes matches the upper bounds. Moreover, the optimal transmitting/listening times of the half-duplex relays as functions of the instantaneous channel realizations are derived for different communication strategies in the general setting. Finally, various simulation scenarios are considered and the DMT of the proposed schemes and the dynamic decode and forward communication strategy are compared.

Combining Non-orthogonal Transmission with Network-Coded Cooperation: Performance Analysis Over Nakagami-m Fading Channels

This paper investigates efficient transmission design in a class of multi-user cooperation networks, in which multiple information sources intend to distribute their messages to a sufficient proportion of ambient destinations with the assistance of multiple relays. We apply a relaying scheme that combines non-orthogonal transmission with network coding techniques to balance channel consumption and inter-user interference. The sources and relays are divided into clusters, terminals within each of which are allowed to non-orthogonally access the same channel. A class of finite-field network codes are adopted in the relays. We provide the methods to derive the system transmission error probability and diversity-multiplexing tradeoff (DMT), over Nakagami- $m$ fading channels. Through error probability and finite-SNR DMT analysis for certain clustering strategies, and infinite-SNR DMT analysis for general situations, we show that the considered relaying scheme can notably improve system performance over the conventional approach that demands only orthogonal transmission in network-coded cooperation networks.

Successive Decode-and-Forward Relaying With Privacy-Aware Interference Suppression

Successive relaying holds the promise of achieving spatial diversity gain for single-antenna users while recovering the multiplexing loss due to the half-duplex relaying in B5G/6G. However, how to mitigate inter-relay interference (IRI) with privacy protection in low complexity remains open. In this paper, we present a successive decode-and-forward (DF) relaying protocol based on an analog network interference cancellation (NICE) method, which may suppress IRI, using linear processing without decoding the signals from the source. More specifically, a relay actively keeps receiving signals from the source, which are then used as prior knowledge to enable an amplify-and-cancel (AC) IRI mitigation strategy. The AC based IRI suppression is capable of improving high information privacy, because a relay does not need to know codebooks used by other relays and will not decode any signals intended for other relays. We obtain the closed-form expression of the minimum residual interference power, based on which the average throughput and the optimal diversity-multiplexing tradeoff (DMT) are presented. The DMT analysis along with simulations shows that the proposed method outperforms conventional two-timeslot half-duplex relaying in terms of the spectral efficiency. It also achieves lower complexity than CAO-SIR based on decode-and-cancel (DC) in [1] and lower IRI than the successive amplify-and-forward (AF) relaying in [2] .

Outage and Diversity Analysis of Underlay Cognitive Mixed RF-FSO Cooperative Systems

We investigate the performance of asymmetric radio frequency (RF) and free-space optical (FSO) dual-hop cognitive amplify-and-forward relay networks where RF links are subject to independent and nonidentically distributed Nakagami-m fading. We consider that the RF link transmitter and receiver are secondary users of an underlay cognitive network. Specifically, the transmit power conditions of the proposed spectrum-sharing network are governed by either the combined power constraint of the interference on the primary network and the maximum transmission power at the secondary network, or the single power constraint of the interference on the primary network. Also, we consider a double generalized gamma fading channel with pointing error and both heterodyne and intensity modulation/direct detection methods in the FSO link. The closed-form and asymptotic expressions of outage probability for this system are calculated for fixed gain and channel-state-informationassisted relaying techniques. It is demonstrated that the diversity order is a function of the fading severity of the RF link, turbulence parameters of the FSO link, and pointing error, regardless of the interference channel parameter of the primary user. However, the coding gain is impressed by the interference link parameter and RF-FSO links parameters. The diversity-multiplexing trade-off analysis is done for this network, where we show that this trade-off is independent of the primary network.

Diversity-Multiplexing Tradeoff in an Interweave Multiuser Cognitive Radio System

In an interweave cognitive radio system, the spectrum sensing performance affects the rate and reliability of data transmission. In wireless communications, the tradeoff between the reliability and data rate can be evaluated by diversity-multiplexing tradeoff (DMT) analysis. In this paper, through the analysis of the error probability at the secondary receiver, we derive the DMT for the multiple-access channel and user-selection schemes in an interweave multiuser cognitive radio system considering the spectrum sensing effect on the rate and reliability. We show that the DMT of the system can be improved by cooperative spectrum sensing. Simulations also approve our analytical results.

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.

Multi-Source Cooperative Communication With Opportunistic Interference Cancelling Relays

In this paper we present a multi-user cooperative protocol for wireless networks. Two sources transmit simultaneously their information blocks and relays employ opportunistically successive interference cancellation (SIC) in an effort to decode them. An adaptive decode/amplify-and-forward scheme is applied at the relays to the decoded blocks or their sufficient statistic if decoding fails. The main feature of the protocol is that SIC is exploited in a network since more opportunities arise for each block to be decoded as the number of used relays NRU is increased. This feature leads to benefits in terms of diversity and multiplexing gains that are proven with the help of an analytical outage model and a diversity-multiplexing tradeoff (DMT) analysis. The performance improvements are achieved without any network synchronization and coordination. In the final part of this work the closed-form outage probability model is used by a novel approach for offline pre-selection of the NRU relays, that have the best SIC performance, from a larger number of NR nodes. The analytical results are corroborated with extensive simulations, while the protocol is compared with orthogonal and multi-user protocols reported in the literature.

Space-Time Encoded MISO Broadcast Channel With Outdated CSIT: An Error Rate and Diversity Performance Analysis

Studies of the MISO Broadcast Channel (BC) with delayed Channel State Information at the Transmitter (CSIT) have so far focused on the sum-rate and Degrees-of-Freedom (DoF) region analysis. In this paper, we investigate for the first time, the error rate performance at finite SNR and the diversity-multiplexing tradeoff (DMT) at infinite SNR of a space-time encoded transmission over a two-user MISO BC with delayed CSIT. We consider the so-called MAT protocol obtained by Maddah-Ali and Tse, which was shown to provide 33% DoF enhancement over TDMA. While the asymptotic DMT analysis shows that MAT is always preferable to TDMA, the Pairwise Error Probability analysis at finite SNR shows that MAT is in fact not always a better alternative to TDMA. Benefits can be obtained over TDMA only at a very high rate or once concatenated with a full-rate full-diversity space-time code. The analysis is also extended to spatially correlated channels, and the influence of transmit correlation matrices and user pairing strategies on the performance are discussed. Relying on statistical CSIT, signal constellations are further optimized to improve the error rate performance of MAT and make it insensitive to user orthogonality. Finally, other transmission strategies relying on delayed CSIT are discussed.

Performance of optimal three‐phase two‐way system with relay interference

In this work, the authors consider an amplify-and-forward (AF)-based three-phase two-way system with interference at the relay. An optimum scheme to minimise the outage probability is formulated, and a closed form expression for the ‘channel-dependent’ combining coefficient ‘α’ at the relay is derived. A novel approach is presented to derive an expression for the overall outage probability of the proposed three-phase outage-optimal two-way relaying (3P-OTWR) system. The authors also perform finite signal-to-noise (SNR) diversity-multiplexing tradeoff and throughput analysis of the system. Furthermore, the problem of outage-optimum power allocation is investigated. Using the asymptotic expression for the outage probability, it is shown that there is loss of diversity owing to interference at the relay. The authors perform Monte Carlo simulations to demonstrate that the 3P-OTWR system outperforms a conventional three-phase two-way scheme. With outage-optimum power allocation, the proposed scheme achieves a gain of approximately 3 dB in the medium-to-high SNR regime over a conventional scheme with α = 0.5 and equal power at terminals. The proposed three-phase scheme in presence of co-channel interference can provide a better throughput for higher transmission rates as compared with a two-phase scheme when operated in the high SNR regime. Numerical results demonstrate accuracy of the derived expressions.

Diversity‐multiplexing tradeoff of opportunistic relay system with multiple‐antenna destination

In this study, the authors investigate the diversity-multiplexing tradeoff (DMT) of a wireless system in which user equipments (UEs) are equipped with only one antenna while the destination has multiple antennas. Each UE is assisted by M half-duplex cooperative users serving as relay nodes. They combine the opportunistic relaying scheme and the cooperative spatial multiplexing (C-SM) scheme to produce an opportunistic C-SM (OC-SM) scheme. The fraction of time allocated to the source–relay link and the relay–destination link is treated as a design parameter to minimise the outage probability of the system. At high signal-to-noise ratio regime, the optimal time allocated factor is obtained in a closed-form expression through DMT analysis. Based on the DMT result of the proposed OC-SM scheme, an adaptive OC-SM (AOC-SM) approach in which the system can switch between different C-SM models adaptively based on the rate transmitted is proposed. To reduce the complexity of the relay nodes, an AOC-SM scheme with relay selection (SAOC-SM) in which a constant number of relay nodes is selected from the set of relay nodes that have successfully decoded the source message is investigated. The DMT results of the SAOC-SM scheme and the AOC-SM scheme are obtained and compared.

A Lightweight Selection Cooperation Protocol with Multiple Available Best Relays

Selection cooperation has shown to be a practical cooperative strategy for wireless networks. In order to obtain full diversity gain, conventional selection cooperation schemes must select the node with the maximum relay-destination channel as the best relay, which restricts the choice of relay selection for the system. To overcome this limitation, we propose a lightweight selection cooperation protocol without requiring the radio of nodes to perform combining reception. Through outage probability and diversity-multiplexing tradeoff (DMT) analysis, we reveal an interesting fact that choosing any node that successfully receives the message from the source and the feedback frame from the destination as the best relay, the protocol always achieves the full diversity order and the optimal DMT. This result establishes a framework for obtaining multiple optimization objectives in selection cooperation networks. As an illustrative example, we then develop two best relay selection methods for relay balance without sacrificing the full diversity order. Simulation results demonstrate the remarkable performance and balance effect of the proposed protocol and selection methods.

Performance analysis of outage probability and diversity-multiplexing tradeoff for two-path relaying cooperative communications

In order to improve the spectral efficiency and outage performance of the cooperative communication system,a Two-Path Relaying(TPR) cooperative communications model based on the Decode-and-Forward(DF) protocol was proposed.Meanwhile,two data transmission modes were presented for the proposed system.The closed-form expressions for outage probability and the relations between diversity gain and multiplexing gain were derived.The simulation results show that,compared with the conventional two-relay DF protocol,the outage probability performance of the two proposed transmission models is greatly improved.

Round-Robin Relaying With Diversity in Amplify-and-Forward Multisource Cooperative Communications

In this paper, a round-robin-based relay protocol dubbed round-robin relaying with source selection protocol (R3SSP) is proposed to achieve full cooperative diversity in multisource cooperative communication networks. In R3SSP, all the sources transmit their individual information in turn. The relays then forward the messages of some specific sources in a fixed order according to the limited feedback information. Compared with traditional relay selection-based protocols, R3SSP is based on round-robin relaying, thus avoiding relay selection and requiring no specific channel state information feedback. R3SSP can therefore be implemented with lower complexity. Furthermore, the exact and asymptotic expressions of the outage probability are derived. The diversity-multiplexing tradeoff (DMT) performance is also analyzed. Theoretical analysis shows that R3SSP achieves full cooperative diversity and provides better DMT performance than relay selection-based protocols in a system where the number of sources is higher than that of the relays. Based on the DMT analysis, we further propose an adaptive relay activation scheme that is capable of achieving higher DMT by dynamically selecting the number of relays to be activated in the entire network. Simulation results also verify the validity and superiority of R3SSP.

Diversity-Multiplexing Tradeoff Analysis of Wireless Multiple-Antenna Cooperative Systems in General Fading Channels

Diversity-Multiplexing Tradeoff Analysis of Wireless Multiple-Antenna Cooperative Systems in General Fading Channels

MMSE-Based MIMO Cooperative Relaying Systems: Closed-Form Designs and Outage Behavior

In this paper, we investigate minimum mean squared error (MMSE) based amplify-and-forward cooperative multiple antenna relaying systems where a non-negligible direct link exists between the source and the destination. First, we provide a new design strategy for optimizing the relay amplifying matrix. Instead of conventional optimal design approaches resorting to an iterative gradient method, we propose a near optimal closed-form solution which provides an insight. As relay systems with a direct link incur a non-convex problem in general, we exploit the decomposable property of the error covariance matrix and a relaxation technique imposing a structural constraint on the problem. Next, we study the error performance limit of the proposed scheme using diversity-multiplexing tradeoff analysis, which leads to several interesting observations on MMSE-based cooperative relaying systems. Finally, through numerical simulations, we confirm that the proposed solution shows the performance very close to the optimum with much reduced complexity and the analysis closely matches with simulation results.

Diversity-Multiplexing Tradeoff in Selective Cooperation for Cognitive Radio

In this paper, we first explore a selective cooperation framework for secondary user transmissions in a cognitive radio network with single relay. In the selective cooperation framework, two transmission modes (i.e., relay diversity transmission and non-relay direct transmission) are considered. We study two specific selective cooperation schemes with and without an acknowledgement (ACK) from a cognitive destination as to if it succeeds in decoding or not, called ACK and non-ACK based selective cooperation, respectively. We derive closed-form outage probability expressions for the two schemes with imperfect spectrum sensing, showing that an outage probability floor occurs in high signal-to-noise ratio (SNR) regions due to mutual interference between primary and secondary users. We consider the use of the outage probability floor to generalize the traditional diversity-multiplexing tradeoff (DMT) definition, based on which a DMT analysis is conducted for the non-ACK and ACK based selective cooperation schemes. We then extend the selective cooperation framework to a multiple-relay cognitive radio network considering the best cognitive relay only to participate in assisting secondary transmissions, referred to as the selective best-relay cooperation. We also consider the non-ACK and ACK based selective best-relay cooperation schemes and develop their DMTs by using the generalized DMT definition.

Diversity-multiplexing tradeoff analysis and optimization for OFDM-based multihop relaying systems

In this article, we consider a single-antenna orthogonal frequency division multiplexing-based multihop relaying system over frequency selective fading channels employing subcarrier grouping and linear constellation precoding at the source, and linear detection at the destination. We derive closed-form expressions of the diversity-multiplexing tradeoff relation, and propose the optimal precoder design and symbol loading strategy to achieve the optimal diversity performance. Simulation results are presented to verify our theoretical analysis.

Diversity-Multiplexing Tradeoff of MIMO Multiple-Access Systems with Successive Cancellation Receivers Having Imperfect Cancellation

The diversity-multiplexing tradeoff (DMT) of a multiple-input multiple-output (MIMO) multiple-access system is analyzed, where a successive cancellation (SC) receiver is employed. In order to analyze the asymptotic performance of each user in a practical MIMO multiple-access system, we derive the per-user DMT considering error propagation due to imperfect cancellation of the SC process. The diversity gain of each user is shown to be expressed as a simple function of the multiplexing gains of the previously detected users as well as its own multiplexing gain. Also, we show that the diversity gain of each user who suffers from error propagation is strictly smaller than that under the assumption of perfect cancellation in a range of multiplexing gains of the users. Numerical results show that our DMT analysis matches well with the performance of practical multiple-access systems.