Diversity-multiplexing Tradeoff Analysis Research Articles

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

In this paper, diversity-multiplexing tradeoff (DMT) of three-user wireless multiple-antenna cooperative systems is investigated in general fading channels when half-duplex and decode-and-forward relay is employed. Three protocols, i.e., adaptive protocol, receive diversity protocol, and dual-hop relaying protocol, are considered. The general fading channels may include transmit and/or receive correlation and nonzero channel means, and are extensions of independent and identically distributed Rayleigh or Rician fading channels. Firstly, simple DMT expressions are derived for general fading channels with zero channel means and no correlation when users employ arbitrary number of antennas. Explicit DMT expressions are also obtained when all users employ the same number of antennas and the channels between any two users are of the same fading statistics. Finally, the impact of nonzero channel means and/or correlation on DMT is evaluated. It is revealed theoretically that the DMTs depend on the number of antennas at each user, channel means (except for Rayleigh and Rician fading statistics), transmit and/or receive correlation, and the polynomial behavior near zero of the channel gain probability density function. Examples are also provided to illustrate the analysis and results.

Diversity-Multiplexing Tradeoff Analysis for a Dynamic Decode and Forward Relay Protocol with MIMO Channels

In this letter, the diversity-multiplexing tradeoff (DMT) function for a special half-duplex dynamic decode and forward (DDF) relay protocol using two source-antennas, two destination-antennas, and more than two relay-antennas is derived. It is shown that the performance of the DDF relay protocol can be substantially improved by increasing the relay-antenna number, but only for low multiplexing gains.

Analysis of Diversity-Multiplexing Tradeoff in a Cooperative Network Coding System

This paper addresses the analysis of diversity-multiplexing tradeoff (DMT) for a decode-and-forward (DF)-based cooperative network coding (CNC) system. The exact outage probability is also provided. Our results show that network coding can assist the relay node to improve multiplexing and diversity gain.

Multi-Hop Coherent Free-Space Optical Communications over Atmospheric Turbulence Channels

In this paper, we investigate multi-hop relaying as an efficient fading mitigation tool for coherent free-space optical (FSO) systems over atmospheric turbulence channels. We consider an FSO relaying system with decode-and-forward relay nodes and multiple heterodyne receivers with modal compensation. Based on a recently introduced statistical characterization for the combined effects of log-normal turbulence fading and modal compensation, we derive the outage probability and quantify the potential performance improvements through the derivation of diversity-multiplexing tradeoff (DMT) and diversity gain. Our outage analysis yields impressive power savings for multi-hop relaying even with a single-relay. In addition, the DMT analysis in practical signal-to-noise ratio (SNR) ranges demonstrates that multi-hop transmission scheme improves finite-SNR diversity gain throughout the range of the multiplexing gain.

Distributed Amplify and Forward Cooperation While Maintaining Transmission Freedom

Problem statement: This study proposes a novel Distributed Amplify and-Forward (DAF) cooperative scheme, achieving higher diversity order and yet maintaining the same transmission freedom as the conventional Amplify-and-Forward (AF) scheme. In the DAF scheme, a user’s transmitted symbols are partitioned into several sequences in order to be relayed by different users. Approach: In the cooperative network, each user still uses half of their transmission for relaying others’ signals. But instead of relaying one user’s entire transmitted sequence, it helps different users for the relaying. Theoretical analysis of the DAF scheme is carried out in order to justify its advantages over the existing schemes. The outage behavior and Diversity-Multiplexing Tradeoff (DMT) analyses of the DAF scheme are presented. Results: Through outage behavior analysis, it is shown the DAF scheme achieves substantial diversity gains over the AF scheme. Furthermore, the DMT analysis justices both the scheme’s achievable diversity gains and its ability to maintain the same multiplexing gain as the AF scheme. The theoretical analyses are then extended to a general cooperative network consisting of N (N≥2) relays, showing the diversity order can be increased with respect to the number of relays but not at the expense of each user’s multiplexing gain. Conclusion: Finally, a practical coded cooperative system that integrates the DAF scheme with the concatenated Reed-Solomon Convolution Codes (RSCC) is proposed, validating the achievable performance gain offered by the DAF scheme.

Diversity-Multiplexing Tradeoff Analysis of Coded Multi-User Relay Networks

We study the impact of multiple access strategies on the diversity-multiplexing tradeoff (DMT) performance in wireless multi-user relay networks. The networks contain multiple independent sources, multiple half-duplex decode-and-forward (DF) relays, and one common destination. Instead of separately retransmitting each source message, the relays employ a class of spectrally efficient finite field network codes to assist the sources. It is shown that fully orthogonal or fully non-orthogonal transmission among sources/relays does not necessarily provide optimized DMT performance. We propose a novel transmission protocol that divides the sources and relays into individual clusters. The nodes within one cluster transmit non-orthogonally while the transmissions of different clusters span orthogonal channels. We provide the method to calculate the achievable DMT for each clustering strategy. The network DMT performance can thus be optimized by properly clustering the multiple sources and relays.

Diversity-Multiplexing Tradeoff Analysis for OFDM Systems With Subcarrier Grouping, Linear Precoding, and Linear Detection

We consider the use of linear constellation precoding and linear detection in a multicarrier OFDM system with multiple receive antennas to obtain improved performance over multipath fading channels at a low complexity. We split the full set of subcarriers into smaller groups and spread the data symbols assigned to each group via precoding matrices. We adopt the diversity-multiplexing tradeoff (DMT) framework and derive the DMT-optimal split of the subcarriers (DMT-optimal grouping) and the DMT-optimal number of symbols assigned to each group (DMT-optimal symbol loading). We determine necessary and sufficient precoder design conditions to achieve DMT optimality and give specific constructions of such precoders. Next, we consider a multiuser OFDMA system and derive an algorithm which divides the available subcarriers among the active users in order to maximize the diversity order of the system (or joint) error probability. We also extend our analysis to OFDM systems equipped with multiple transmit antennas. Finally, we obtain important insights on the role of outer codes in an OFDM system employing linear precoding and linear equalization.

Multi-hop MIMO relay networks: diversity-multiplexing trade-off analysis

A multi-hop relay network with multiple antenna terminals in a quasi-static slow fading environment is considered. The fundamental diversity-multiplexing gain tradeoff (DMT) is analyzed in the case of half-duplex relay terminals. While decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, it is shown that the dynamic decode-and-forward (DDF) protocol achieves the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static DF protocols are considered as well, and the corresponding DMT performance is shown to fall short of the optimal performance, which indicates that dynamic channel allocation is required for optimal DMT performance. The optimal DMT is expressed as the solution of a convex optimization problem and explicit DMT expressions are presented for some special cases. In the case of multiple relays, it is shown that the optimal diversity gain, which is achieved by exploiting the available "hop-diversity", is dominated by the neighboring two-hops with the minimum diversity gain.

On the diversity-multiplexing tradeoff of cooperative multicast system with wireless network coding

Diversity-multiplexing tradeoff (DMT) is an efficient tool to measure the performance of multiple-input and multiple-output (MIMO) systems and cooperative systems. Recently, cooperative multicast system with wireless network coding stretched tremendous interesting due to that it can drastically enhance the throughput of the wireless networks. It is desirable to apply DMT to the performance analysis on the multicast system with wireless network coding. In this paper, DMT is performed at the three proposed wireless network coding protocols, i.e., non-regenerative network coding (NRNC), regenerative complex field network coding (RCNC) and regenerative Galois field network coding (RGNC). The DMT analysis shows that under the same system performance, i.e., the same diversity gain, all the three network coding protocols outperform the traditional transmission scheme without network coding in terms of multiplexing gain. Our DMT analysis also exhibits the trends of the three network coding protocols' performance when multiplexing gain is changing from the lower region to the higher region. Monte-Carlo simulations verify the prediction of DMT.

Construction Methods for Asymmetric and Multiblock Space–Time Codes

In this paper, the need for the construction of asymmetric and multiblock space-time codes is discussed. Above the trivial puncturing method, i.e., switching off the extra layers in the symmetric multiple-input multiple-output (MIMO) setting, two more sophisticated asymmetric construction methods are proposed. The first method, called the block diagonal method (BDM), can be converted to produce multiblock space-time codes that achieve the diversity-multiplexing tradeoff (DMT). It is also shown that maximizing the density of the newly proposed block diagonal asymmetric space-time (AST) codes is equivalent to minimizing the discriminant of a certain order, a result that also holds as such for the multiblock codes. An implicit lower bound for the density is provided and made explicit for an important special case that contains e.g., the systems equipped with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4Tx</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+2Rx</i> antennas. Further, an explicit scheme achieving the bound is given. Another method proposed here is the smart puncturing method (SPM) that generalizes the subfield construction method proposed in earlier work by Hollanti and Ranto and applies to any number of transmitting and lesser receiving antennas. The use of the general methods is demonstrated by building explicit, sphere decodable codes using different cyclic division algebras (CDAs). Computer simulations verify that the newly proposed methods can compete with the trivial puncturing method, and in some cases clearly outperform it. The conquering construction exploiting maximal orders improves upon the punctured perfect code and the DjABBA code as well as the Icosian code. Also extensive DMT analysis is provided.

Spatial Multiplexing Architectures with Jointly Designed Rate-Tailoring and Ordered BLAST Decoding - Part I: Diversity-Multiplexing Tradeoff Analysis

The V-BLAST (vertical Bell Labs layered Space- Time) architecture involves independent coding/decoding per antenna (layer) with equal rate and power per antenna and a fixed order of nulling/canceling decoding but is known to suffer from poor performance; for example, in a multi-input multioutput (MIMO) Rayleigh fading channel with Mt transmit and Mr receive antennas (M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ⩾ M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> ), the diversity-multiplexing gain (D-M) tradeoff is just (M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> - M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> +1)(1 - r/Mt) for r ε [0,Mt]. There are two remedies available, namely, (i) channel-dependent ordered decoding at the receiver and (ii) allocation of rates and powers across the transmit antennas. However, the former doesn't improve the D-M tradeoff curve and while the latter does (with maximum diversity gain Mr and maximum multiplexing gain Mt), its tradeoff curve is still significantly inferior compared to the D-M tradeoff curve of the optimum (unconstrained) MIMO architecture. In this two-part paper, it is shown that a dramatically better D-M tradeoff and error (e.g. outage) probability can be obtained if the two remedies, i.e., ordered BLAST decoding and rate/power allocation, are judiciously combined. Indeed, a framework is developed for jointly designing channel-dependent ordered decoding at the receiver and decoding order-dependent rate/power allocation at the transmitter. The framework encompasses a large class of new spatial multiplexing architectures (SMAs). In this part, an upper bound to the D-M tradeoff for this class is obtained and found to be quite close to the optimal D-M tradeoff of the MIMO channel. Two special SMAs are proposed corresponding to two different decoding orderings. One is called the Norm ordering Rate Tailored SMA (NRT-SMA), and the other is called the Greedy ordering Rate Tailored SMA (GRT-SMA).

Recovering Multiplexing Loss through Successive Relaying Using Repetition Coding

In this paper, a transmission protocol is studied for a two relay wireless network in which simple repetition coding is applied at the relays. Information-theoretic achievable rates for this transmission scheme are given, and a space-time V-BLAST signalling and detection method that can approach them is developed. It is shown through the diversity multiplexing tradeoff analysis that this transmission scheme can recover the multiplexing loss of the half-duplex relay network, while retaining some diversity gain. This scheme is also compared with conventional transmission protocols that exploit only the diversity of the network at the cost of a multiplexing loss. It is shown that the new transmission protocol offers significant performance advantages over conventional protocols, especially when the interference between the two relays is sufficiently strong.

Recovering Multiplexing Loss through Concurrent Decode-and-Forward (DF) Relaying

In this paper, we develop a novel digital cooperative diversity transmission protocol for a two-source scenario by combining the two sources' two classic decode-and-forward (DF) relaying steps and using 2L + 1 time slots to transmit L codewords from each source. Assuming the relays can perfectly decode their associated source messages, we give an information-theoretic average achievable capacity region for this transmission scheme. Through diversity-multiplexing tradeoff analysis, we show that our so called concurrent DF relaying protocol can effectively recover the multiplexing loss induced by the half-duplex operation in the relays, while still obtaining some diversity gain. Numerical results reveal our scheme offers significant performance advantages over the classic DF relaying protocols, especially for high signal-to-noise ratio (SNR) and large frame length L regime.