We establish the optimal diversity-multiplexing (DM) tradeoff of coherent time, frequency and time-frequency selective-fading MIMO channels and provide a code design criterion for DM-tradeoff optimality. Our results are based on the analysis of the "Jensen channel" associated to a given selective-fading MIMO channel. While the original problem seems analytically intractable due to the mutual information being a sum of correlated random variables, the Jensen channel is equivalent to the original channel in the sense of the DM-tradeoff and lends itself nicely to analytical treatment. Finally, as a consequence of our results, we find that the classical rank criterion for space-time code design (in selective-fading MIMO channels) ensures optimality in the sense of the DM-tradeoff.
We show that the diversity-multiplexing tradeoff of a half-duplex single-relay channel with identically distributed Rayleigh fading channel gains meets the 2 by 1 MISO bound. We generalize the result to the case when there are N non-interfering relays and show that the diversity-multiplexing tradeoff is equal to the N + 1 by 1 MISO bound.
In this paper, we extend the diversity and multiplexing tradeoff (DMT) analysis from point-to-point channels to cellular systems to evaluate the impact of inter-cell interference on the system reliability and efficiency. Fundamental tradeoff among diversity order, multiplexing gain and inter-cell interference intensity is characterized to reveal the capability of multiple antennas in cellular systems. And the detrimental effects of the inter-cell interference on the system performance of diversity and multiplexing is presented and analyzed.
The assumption of nodes in a cooperative communication relay network operating in synchronous fashion is often unrealistic. In the present paper, we consider two different models of asynchronous operation in cooperative-diversity networks experiencing slow fading and examine the corresponding diversity-multiplexing tradeoffs (DMT). For both models, we propose protocols and distributed space-time codes that asymptotically achieve the transmit diversity bound for all multiplexing gains and for any number of relays.
This paper demonstrates the significant gains that multi-access users can achieve from sharing a single amplify-forward relay in slow fading environments. The proposed protocol, namely the multi-access relay amplify-forward, allows for a low-complexity relay and achieves the optimal diversity-multiplexing trade-off at high multiplexing gains. Analysis of the protocol reveals that it uniformly dominates the compress-forward strategy and further outperforms the dynamic decode-forward protocol at high multiplexing gains. An interesting feature of the proposed protocol is that, at high multiplexin…
The diversity-multiplexing tradeoff (DMT) for interference networks, such as the interference channel, the X channel, the Z interference channel and the Z channel, is analyzed. In particular, we investigate the impact of rate-splitting and channel knowledge at the transmitters. We also use the DMT of the Z channel and the Z interference channel to distill insights into the "loud neighbor" problem for femto-cell networks.
The diversity-multiplexing tradeoff (DMT) provides a fundamental performance metric for different multiple-input multiple-output (MIMO) schemes in wireless communications. In this paper, we explore the block fading optical wireless communication (OWC) channels and characterize the DMT in the presence of both optical peak- and average-power constraints. Three different fading distributions are considered, which reflect different channel conditions. In each channel condition, we obtain the optimal DMT when the block length is sufficiently large, and we also derive the lower and upper bounds of t…
In this paper, a multiple-relay network in considered, in which $K$ single-antenna relays assist a single-antenna transmitter to communicate with a single-antenna receiver in a half-duplex mode. A new Amplify and Forward (AF) scheme is proposed for this network and is shown to achieve the optimum diversity-multiplexing trade-off curve.
We establish the optimal diversity-multiplexing (DM) tradeoff for coherent selective-fading multiple-access MIMO channels and provide corresponding code design criteria. As a byproduct, on the conceptual level, we find an interesting relation between the DM tradeoff framework and the notion of dominant error event regions, first introduced in the AWGN case by Gallager, IEEE Trans. IT, 1985. This relation allows us to accurately characterize the error mechanisms in MIMO fading multiple-access channels. In particular, we find that, for a given rate tuple, the maximum achievable diversity order i…
An extension of the popular diversity-multiplexing tradeoff framework to the low-SNR (or wideband) regime is proposed. The concept of diversity gain is shown to be redundant in this regime since the outage probability is SNR-independent and depends on the multiplexing gain and the channel power gain statistics only. The outage probability under the DMT framework is obtained in an explicit, closed form for a broad class of channels. The low and high-SNR regime boundaries are explicitly determined for the scalar Rayleigh-fading channel, indicating a significant limitation of the SNR-asymptotic D…
We establish the optimal diversity-multiplexing (DM) tradeoff of coherent time, frequency, and time-frequency selective-fading multiple-input multiple-output (MIMO) channels and provide a code design criterion for DM tradeoff optimality. Our results are based on the new concept of the "Jensen channel" associated to a given selective-fading MIMO channel. While the original problem seems analytically intractable due to the mutual information between channel input and output being a sum of correlated random variables, the Jensen channel is equivalent to the original channel in the sense of the DM…
We establish the optimal diversity-multiplexing (DM) tradeoff of coherent selective-fading multiple-access multiple-input multiple-output (MIMO) channels and provide corresponding code design criteria. As a byproduct, on the conceptual level, we find an interesting relation between the DM tradeoff framework and the notion of dominant error event regions which was first introduced in the AWGN case by Gallager, IEEE Trans. IT, 1985. This relation allows to accurately characterize the error mechanisms in MIMO fading multiple-access channels. In particular, we find that, for a given rate tuple, th…
Network coding and cooperative communication have received considerable attention from the research community recently in order to mitigate the adverse effects of fading in wireless transmissions and at the same time to achieve high throughput and better spectral efficiency. In this work, we analyze a network coding scheme for a cooperative communication setup with multiple sources and destinations. The proposed protocol achieves the full diversity order at the expense of a slightly reduced multiplexing rate compared to existing schemes in the literature. We show that our scheme outperforms co…
Diversity-Multiplexing tradeoff (DMT) is a coarse high SNR approximation of the fundamental tradeoff between data rate and reliability in a slow fading channel. In this paper, we characterize the fundamental DMT of the two user single antenna Gaussian interference channel. We show that the class of multilevel superposition coding schemes universally achieves (for all fading statistics) the DMT for the two-user interference channel. For the special case of symmetric DMT, when the two users have identical rate and diversity gain requirements, we characterize the DMT achieved by the Han-Kobayashi…
Performance of reliable communication over a coherent slow fading channel at high SNR is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. We study the problem of designing codes that optimally tradeoff the diversity and multiplexing gains. Our main contribution is a precise characterization of codes that are universally tradeoff-optimal, i.e., they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel. We denote this characterization as one of approximate universality where the approximation i…
It is well known that the presence of double scattering degrades the performance of a MIMO channel, in terms of both the multiplexing gain and the diversity gain. In this paper, a closed-form expression of the diversity-multiplexing tradeoff (DMT) of double scattering MIMO channels is obtained. It is shown that, for a channel with nT transmit antennas, nR receive antennas and nS scatterers, the DMT only depends on the ordered version of the triple (nT,nS,nR), for arbitrary nT, nS and nR. The condition under which the double scattering channel has the same DMT as the single scattering channel i…
Tradeoff in diversity, multiplexing, and delay in multihop MIMO relay networks with ARQ is studied, where the random delay is caused by queueing and ARQ retransmission. This leads to an optimal ARQ allocation problem with per-hop delay or end-to-end delay constraint. The optimal ARQ allocation has to trade off between the ARQ error that the receiver fails to decode in the allocated maximum ARQ rounds and the packet loss due to queueing delay. These two probability of errors are characterized using the diversity-multiplexing-delay tradeoff (DMDT) (without queueing) and the tail probability of r…
A multi-hop relay channel with multiple antenna terminals in a quasi-static slow fading environment is considered. For both full-duplex and half-duplex relays the fundamental diversity-multiplexing tradeoff (DMT) is analyzed. It is shown that, while decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, the dynamic decode-and-forward (DDF) protocol is needed to achieve the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static protocols are considered as well, and the corresponding achievable DMT performance is charac…
This paper investigates the Diversity Multiplexing Tradeoff (DMT) of the generalized quantize-and-forward (GQF) relaying scheme over the slow fading half-duplex multiple-access relay channel (HD-MARC). The compress-and-forward (CF) scheme has been shown to achieve the optimal DMT when the channel state information (CSI) of the relay-destination link is available at the relay. However, having the CSI of relay-destination link at relay is not always possible due to the practical considerations of the wireless system. In contrast, in this work, the DMT of the GQF scheme is derived without relay-d…
We analyze two-user single-antenna fading interference channels with perfect receive channel state information (CSI) and no transmit CSI. We compute the diversity-multiplexing tradeoff (DMT) region of a fixed-power-split Han and Kobayashi (HK)-type superposition coding scheme and provide design criteria for the corresponding superposition codes. We demonstrate that this scheme is DMT-optimal under moderate, strong, and very strong interference by showing that it achieves a DMT outer bound that we derive. Further, under very strong interference, we show that a joint decoder is DMT-optimal and "…
The performance of a multiuser communication system with single-antenna transmitting terminals and a multi-antenna base-station receiver is analytically investigated. The system operates under independent and non-identically distributed rank-$1$ Rician fading channels with imperfect channel estimation and residual hardware impairments (compensation algorithms are assumed, which mitigate the main impairments) at the transceiver. The spatial multiplexing mode of operation is considered where all the users are simultaneously transmitting their streams to the receiver. Zero-forcing is applied alon…
We analyze two-user single-antenna fading interference channels with perfect receive channel state information (CSI) and no transmit CSI. For the case of very strong interference, we prove that decoding interference while treating the intended signal as noise, subtracting the result out, and then decoding the desired signal, a process known as "stripping", achieves the diversity-multiplexing tradeoff (DMT) outer bound derived in Akuiyibo and Leveque, Int. Zurich Seminar on Commun., 2008. The proof is constructive in the sense that it provides corresponding code design criteria for DMT optimali…
In this paper, we analyze the fundamental tradeoff of diversity and multiplexing in multi-input multi-output (MIMO) channels with imperfect channel state information at the transmitter (CSIT). We show that with imperfect CSIT, a higher diversity gain as well as a more efficient diversity-multiplexing tradeoff (DMT) can be achieved. In the case of multi-input single-output (MISO)/single-input multi-output (SIMO) channels with K transmit/receive antennas, one can achieve a diversity gain of d(r)=K(1-r+Kα) at spatial multiplexing gain r, where αis the CSIT quality defined in this paper. For gener…
The impact of spatial correlation on the performance limits of multielement antenna (MEA) channels is analyzed in terms of the diversity-multiplexing tradeoff (DMT) at finite signal-to-noise ratio (SNR) values. A lower bound on the outage probability is first derived. Using this bound accurate finite-SNR estimate of the DMT is then derived. This estimate allows to gain insight on the impact of spatial correlation on the DMT at finite SNR. As expected, the DMT is severely degraded as the spatial correlation increases. Moreover, using asymptotic analysis, we show that our framework encompasses w…
The fundamental diversity-multiplexing tradeoff of the three-node, multi-input, multi-output (MIMO), quasi-static, Rayleigh faded, half-duplex relay channel is characterized for an arbitrary number of antennas at each node and in which opportunistic scheduling (or dynamic operation) of the relay is allowed, i.e., the relay can switch between receive and transmit modes at a channel dependent time. In this most general case, the diversity-multiplexing tradeoff is characterized as a solution to a simple, two-variable optimization problem. This problem is then solved in closed form for special cla…
In the Cloud Radio Access Network (C-RAN) architecture, the baseband signals from multiple remote radio heads are processed in a centralized baseband unit (BBU) pool. This architecture allows network operators to adapt the BBU's computational resources to the aggregate access load experienced at the BBU, which can change in every air-interface access frame. The degree of savings that can be achieved by adapting the resources is a tradeoff between savings, adaptation frequency, and increased queuing time. If the time scale for adaptation of the resource multiplexing is greater than the access f…
Network coding and cooperative communication have received considerable attention from the research community recently in order to mitigate the adverse effects of fading in wireless transmissions and at the same time to achieve high throughput and better spectral efficiency. In this work, we design and analyze deterministic and random network coding schemes for a cooperative communication setup with multiple sources and destinations. We show that our schemes outperform conventional cooperation in terms of the diversity-multiplexing tradeoff (DMT). Specifically, it achieves the full-diversity o…
In this work, we analyze the fundamental performance tradeoff of the single-antenna Automatic Retransmission reQuest (ARQ) Z-interference channel (ZIC). Specifically, we characterize the achievable three-dimensional tradeoff between diversity (reliability), multiplexing (throughput), and delay (maximum number of retransmissions) of two ARQ protocols: A non-cooperative protocol and a cooperative one. Considering no cooperation exists, we study the achievable tradeoff of the fixed-power split Han-Kobayashi (HK) approach. Interestingly, we demonstrate that if the second user transmits the common …
This paper develops a diversity-multiplexing tradeoff (DMT) over a bidirectional random relay set in a wireless network where the distribution of all nodes is a stationary Poisson point process. This is a nontrivial extension of the DMT because it requires consideration of the cooperation (or lack thereof) of relay nodes, the traffic pattern and the time allocation between the forward and reverse traffic directions. We then use this tradeoff to compare the DMTs of traditional time-division multihop (TDMH) and network coding (NC). Our main results are the derivations of the DMT for both TDMH an…
Since the invention of space-time coding numerous algebraic methods have been applied in code design. In particular algebraic number theory and central simple algebras have been on the forefront of the research. In this paper we are turning the table and asking whether information theory can be used as a tool in algebra. We will first derive some corollaries from diversity-multiplexing gain (DMT) bounds by Zheng and Tse and later show how these results can be used to analyze the unit group of orders of certain division algebras. The authors do not claim that the algebraic results are new, but …
A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) block code. This tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>= n_t+n_r-1 where T is the number of time slots over which coding takes place and n_t,n_r are the number of transmit and receive antennas respectively. For T < n_t+n_r-1, only upper and lower bounds on the D-MG tradeo…
In this paper the fading multiple antenna (MIMO) wire-tap channel is investigated under short term power constraints. The secret diversity gain and the secret multiplexing gain are defined. Using these definitions, the secret diversitymultiplexing tradeoff (DMT) is calculated analytically for no transmitter side channel state information (CSI) and for full CSI. When there is no CSI at the transmitter, under the assumption of Gaussian codebooks, it is shown that the eavesdropper steals both transmitter and receiver antennas, and the secret DMT depends on the remaining degrees of freedom. When C…
Diversity-multiplexing tradeoff (DMT) presents a compact framework to compare various MIMO systems and channels in terms of the two main advantages they provide (i.e. high data rate and/or low error rate). This tradeoff was characterized asymptotically (SNR-> infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse [1]. The asymptotic DMT overestimates the finite-SNR one [2]. In this paper, using the recent results on the asymptotic (in the number of antennas) outage capacity distribution, we derive and analyze the finite-SNR DMT for a broad class of channels (not necessarily Rayleigh fad…
To improve diversity gain in an interference channel and hence to maximize diversity multiplexing tradeoff (DMT), we propose on-off switched interference alignment (IA) where IA is intermittently utilized by switching IA on/off. For on-off switching, either IA with symbol extension or IA with Alamouti coding is adopted in this paper. Deriving and analyzing DMT of the proposed schemes, we reveal that the intermittent utilization of IA with simultaneous non-unique decoding can improve DMT in the 2-user X-channel with two antennas. Both the proposed schemes are shown to achieve diversity gain of …
In this paper, 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 (up-link) channels. 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. W…
This paper focuses on analog network coding (ANC) and time division broadcasting (TDBC) which are two major protocols used in bidirectional cooperative networks. Lower bounds of the outage probabilities of those two protocols are derived first. Those lower bounds are extremely tight in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Based on those lower bounds, finite-SNR diversity-multiplexing tradeoffs of the ANC and TDBC protocols are obtained. Secondly, we investigate how to efficiently use channel state information (CSI) in those two protocols.…
The secrecy performance of realistic wireless multicast scenarios can be significantly deteriorated by the simultaneous occurrence of multipath and shadowing. To resolve this security threat, in this work an opportunistic relaying-based dual-hop wireless multicast framework is proposed in which the source dispatches confidential information to a bunch of receivers via intermediate relays under the wiretapping attempts of multiple eavesdroppers. Two scenarios, i.e. non-line of sight (NLOS) and line of sight (LOS) communications along with the multiplicative and LOS shadowing are considered wher…
This paper considers a multiple input multiple output (MIMO) two-way relay channel, where two nodes want to exchange data with each other using multiple relays. An iterative algorithm is proposed to achieve the optimal achievable rate region, when each relay employs an amplify and forward (AF) strategy. The iterative algorithm solves a power minimization problem at every step, subject to minimum signal-to-interference-and-noise ratio constraints, which is non-convex, however, for which the Karush Kuhn Tuker conditions are sufficient for optimality. The optimal AF strategy assumes global channe…
This paper addresses the fundamental characteristics of information exchange via multihop network coding over two-way relaying in a wireless ad hoc network. The end-to-end rate regions achieved by time-division multihop (TDMH), MAC-layer network coding (MLNC) and PHY-layer network coding (PLNC) are first characterized. It is shown that MLNC does not always achieve better rates than TDMH, time sharing between TDMH and MLNC is able to achieve a larger rate region, and PLNC dominates the rate regions achieved by TDMH and MLNC. An opportunistic scheduling algorithm for MLNC and PLNC is then propos…
We develop a framework to optimize the tradeoff between diversity, multiplexing, and delay in MIMO systems to minimize end-to-end distortion. We first focus on the diversity-multiplexing tradeoff in MIMO systems, and develop analytical results to minimize distortion of a vector quantizer concatenated with a space-time MIMO channel code. In the high SNR regime we obtain a closed-form expression for the end-to-end distortion as a function of the optimal point on the diversity-multiplexing tradeoff curve. For large but finite SNR we find this optimal point via convex optimization. We then conside…
In the paper "Finite-SNR Diversity-Multiplexing Tradeoff for Network Coded Cooperative OFDMA Systems', the authors adopt a recently proposed subcarrier allocation algorithm aiming at providing optimal frequency diversity to an OFDMA-based network with network-coded cooperation (NCC), where $P$ source nodes transmit independent information to a common destination with the help of $M$ relay nodes, in a frequency-selective channel with $L$ coherence blocks. However, the analysis of the so-called NCC-OFDMA scheme proposed in the aforementioned paper assumes that the subcarrier allocation algorithm…
In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. The DMT expression is given as the solution of a minimization problem in general, and an explicit expression is found when the relay channel is symmetric in terms of number of antennas, i.e. the source and the destination have n antennas each, and the relay has m antennas. It is observed that the static half…
A multi-hop two-way relay channel is considered in which all the terminals are equipped with multiple antennas. Assuming independent quasi-static Rayleigh fading channels and channel state information available at the receivers, we characterize the optimal diversity-multiplexing gain tradeoff (DMT) curve for a full-duplex relay terminal. It is shown that the optimal DMT can be achieved by a compress-and-forward type relaying strategy in which the relay quantizes its received signal and transmits the corresponding channel codeword. It is noteworthy that, with this transmission protocol, the two…
We study the diversity-multiplexing tradeoff (DMT) for the slow fading interference channel with a relay (ICR). We derive four inner bounds on the DMT region: the first is based on the compress-and-forward (CF) relaying scheme, the second is based on the decode-and-forward (DF) relaying scheme, and the last two bounds are based on the half-duplex (HD) and full-duplex (FD) amplify-and-forward (AF) schemes. For the CF and DF schemes, we find conditions on the channel parameters and the multiplexing gains, under which the corresponding inner bound achieves the optimal DMT region. We also identify…
Synchronization of relay nodes is an important and critical issue in exploiting cooperative diversity in wireless networks. In this paper, two asynchronous cooperative diversity schemes are proposed, namely, distributed delay diversity and asynchronous space-time coded cooperative diversity schemes. In terms of the overall diversity-multiplexing (DM) tradeoff function, we show that the proposed independent coding based distributed delay diversity and asynchronous space-time coded cooperative diversity schemes achieve the same performance as the synchronous space-time coded approach which requi…
In this paper, we consider an automatic-repeat-request (ARQ) retransmission protocol signaling over a block-fading multiple-input, multiple-output (MIMO) channel. Unlike previous work, we allow for multiple fading blocks within each transmission (ARQ round), and we constrain the transmitter to fixed rate codes constructed over complex signal constellations. In particular, we examine the general case of average input-power-constrained constellations as well as the practically important case of finite discrete constellations. This scenario is a suitable model for practical wireless communication…
In this work the optimal diversity-multiplexing tradeoff (DMT) is investigated for the multiple-input multiple-output fading multiple-access channels with no power constraints (infinite constellations). For K users (K>1), M transmit antennas for each user, and N receive antennas, infinite constellations in general and lattices in particular are shown to attain the optimal DMT of finite constellations for the case N equals or greater than (K+1)M-1, i.e., user limited regime. On the other hand for N<(K+1)M-1 it is shown that infinite constellations can not attain the optimal DMT. This is in cont…
The diversity-multiplexing tradeoff of the dynamic decode-and-forward protocol is characterized for the half-duplex three-terminal (m,k,n)-relay channel where the source, relay and the destination terminals have m, k and n antennas, respectively. It is obtained as a solution to a simple, two-variable, convex optimization problem and this problem is solved in closed form for special classes of relay channels, namely, the (1,k,1) relay channel, the (n,1,n) relay channel and the (2,k,2) relay channel. Moreover, the tradeoff curves for a certain class of relay channels, such as the (m,k,n>k) chann…
The optimal transmission strategy to minimize the weighted combination of age of information (AoI) and total energy consumption is studied in this paper. It is assumed that the status update information is obtained and transmitted at fixed rate over a Rayleigh fading channel in a packet-based wireless communication system. A maximum transmission round on each packet is enforced to guarantee certain reliability of the update packets. Given fixed average transmission power, the age-energy tradeoff can be formulated as a constrained Markov decision process (CMDP) problem considering the sensing p…
We investigate asymptotic capacity limits of the Gaussian MIMO broadcast channel (BC) with spatially correlated fading to understand when and how much transmit correlation helps the capacity. By imposing a structure on channel covariances (equivalently, transmit correlations at the transmitter side) of users, also referred to as \emph{transmit correlation diversity}, the impact of transmit correlation on the power gain of MIMO BCs is characterized in several regimes of system parameters, with a particular interest in the large-scale array (or massive MIMO) regime. Taking the cost for downlink …
A finite blocklenth analysis of the diversity-multiplexing tradeoff is presented, based on nonasymptotic bounds on the maximum channel coding rate of multiple-antenna block-memoryless Rayleigh-fading channels.The bounds in this paper allow one to numerically assess for which packet size, number of antennas, and degree of channel selectivity, diversity-exploiting schemes are close to optimal, and when instead the available spatial degrees of freedom should be used to provide spatial multiplexing. This finite blocklength view on the diversity-multiplexing tradeoff provides insights on the design…
Zheng and Tse have shown that over a quasi-static channel, there exists a fundamental tradeoff, known as the diversity-multiplexing gain (D-MG) tradeoff. In a realistic system, to avoid inefficiently operating the power amplifier, one should consider the situation where constraints are imposed on the peak to average power ratio (PAPR) of the transmitted signal. In this paper, the D-MG tradeoff of multi-antenna systems with PAPR constraints is analyzed. For Rayleigh fading channels, we show that the D-MG tradeoff remains unchanged with any PAPR constraints larger than one. This result implies t…
In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secrecy diversity gain estimates of ZF are derived. Through asymptotic ana…
Diversity-multiplexing tradeoff (DMT) was characterized asymptotically (SNR-> infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse [1]. The SNR-asymptotic DMT overestimates the finite-SNR one [2]. This paper outlines a number of additional limitations and difficulties of the DMT framework and discusses their implications. Using the recent results on the size-asymptotic (in the number of antennas) outage capacity distribution, the finite-SNR, size-asymptotic DMT is derived for a broad class of fading distributions. The SNR range over which the finite-SNR DMT is accurately approximated …
This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between a/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 \textit{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 divers…
The fundamental diversity-multiplexing tradeoff (DMT) of the quasi-static fading, symmetric $2$-user MIMO interference channel (IC) with channel state information at the transmitters (CSIT) and a short term average power constraint is obtained. The general case is considered where the interference-to-noise ratio (INR) at each receiver scales differently from the signal-to-noise ratio (SNR) at the receivers. The achievability of the DMT is proved by showing that a simple Han-Kobayashi coding scheme can achieve a rate region which is within a constant (independent of SNR) number of bits from a s…
In this paper, an outage limited MIMO channel is considered. We build on Zheng and Tse's elegant formulation of the diversity-multiplexing tradeoff to develop a better understanding of the asymptotic relationship between the probability of error, transmission rate, and signal-to-noise ratio. In particular, we identify the limitation imposed by the multiplexing gain notion and develop a new formulation for the throughput-reliability tradeoff that avoids this limitation. The new characterization is then used to elucidate the asymptotic trends exhibited by the outage probability curves of MIMO ch…
Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels …
This paper investigates the benefits of Amplify-and-Forward (AF) relaying in the setup of multi-antenna wireless networks. The concept of Random Sequential (RS) relaying is previously introduced in the literature and showed that it achieves the maximum diversity gain in a general multi-antenna network. Here, we show that random unitary matrix multiplication at the relay nodes empowers the RS scheme to achieve a better Diversity-Multiplexing Tradeoff (DMT) as compared to the traditional AF relaying. First, we study the case of a multi-antenna full-duplex single-relay two-hop network, for which …
Rate and diversity impose a fundamental tradeoff in communications. This tradeoff was investigated for Intersymbol Interference (ISI) channels in [4]. A different point of view was explored in [1] where high-rate codes were designed so that they have a high-diversity code embedded within them. Such diversity embedded codes were investigated for flat fading channels and in this paper we explore its application to ISI channels. In particular, we investigate the rate tuples achievable for diversity embedded codes for scalar ISI channels through particular coding strategies. The main result of thi…
