Multiple-input multiple-output (MIMO) system has been the defining mobile communications technology in recent generations. With the ever-increasing demands looming towards the sixth generation (6G), we are in need of additional degrees of freedom that deliver further gains beyond MIMO. To this goal, fluid antenna system (FAS) has emerged as a new way to obtain spatial diversity using reconfigurable position-switchable antennas. Considering the case with more than one ports activated on a 2D fluid antenna surface at both ends, we take the information-theoretic approach to study the achievable performance limits of the MIMO-FAS. First of all, we propose a suboptimal scheme, referred to as QR MIMO-FAS, to maximize the rate at high signal-to-noise ratio (SNR) via joint port selection, transmit and receive beamforming and power allocation. We then derive the optimal diversity and multiplexing tradeoff (DMT) of MIMO-FAS. From the DMT, we highlight that MIMO-FAS outperforms traditional MIMO antenna systems. Further, we introduce a new metric, namely q-outage capacity, which can jointly consider rate and outage probability. Through this metric, our results indicate that MIMO-FAS surpasses traditional MIMO greatly.
This paper studies the performance of transmission schemes that have rate that increases with average SNR while maintaining a fixed outage probability. This is in contrast to the classical Zheng-Tse diversity-multiplexing tradeoff (DMT) that focuses on increasing rate and decreasing outage probability. Three different systems are explored: antenna diversity systems, time/frequency diversity systems, and automatic repeat request (ARQ) systems. In order to accurately study performance in the fixed outage setting, it is necesary to go beyond the coarse, asymptotic multiplexing gain metric. In the…
This paper considers the distribution of the mutual information of frequency-selective spatially-uncorrelated Rayleigh fading MIMO channels. Results are presented for OFDM-based spatial multiplexing. New exact closed-form expressions are derived for the variance of the mutual information. In contrast to previous results, our new expressions apply for systems with both arbitrary numbers of antennas and arbitrary-length channels. Simplified expressions are also presented for high and low SNR regimes. The analytical variance results are used to provide accurate analytical approximations for the d…
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…
A hybrid-duplex aeronautical communication system (HBD-ACS) consisting of a full-duplex (FD) enabled ground station (GS), and two half-duplex (HD) air-stations (ASs) is proposed as a direct solution to the spectrum crunch faced by the aviation industry. Closed-form outage probability and finite signal-to-noise ratio (SNR) diversity gain expressions in aeronautical communications over Rician fading channels are derived for a successive interference cancellation (SIC) detector. Similar expressions are also presented for an interference ignorant (II) detector and HD-equivalent modes at GS and ASs…
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 …
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…
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.…
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 work investigates spatial-mode multiplexing (SMM) for practical free-space optical communication (FSO) systems using direct detection. Unlike several works in the literature where mutually incoherent channels are assumed, we consider mutually coherent channels that accurately describe SMM FSO systems employing a single laser source at the transmitter with a narrow linewidth. We develop an analytical model for such mutually coherent channels and derive expressions for aggregate achievable rate (AAR). Through numerical simulations, it was shown that there exist optimal transmit mode sets wh…
Massive MIMO is seen as a main enabler for low latency communications, thanks to its high spatial degrees of freedom. The channel hardening and favorable propagation properties of Massive MIMO are particularly important for multiplexing several URLLC devices. However, the actual utility of channel hardening and spatial multiplexing is dependent critically on the accuracy of channel knowledge. When several low latency devices are multiplexed, the cost for acquiring accurate knowledge becomes critical, and it is not evident how many devices can be served with a latency-reliability requirement an…
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…
Previous work on cooperative communications has concentrated primarily on the diversity benefits of such techniques. This paper, instead, considers the multiplexing benefits of cooperative communications. First, a new interpretation on the fundamental tradeoff between the transmission rate and outage probability in multi-antenna relay networks is given. It follows that multiplexing gains can be obtained at any finite SNR, in full-duplex multi-antenna relay networks. Thus relaying can offer not only stronger link reliability, but also higher spectral efficiency. Specifically, the decode-and-for…
In this paper, the outage performance of relay-assisted millimeter wave (mmWave) cellular systems employing joint spatial division and multiplexing (JSDM) is investigated. It is assumed that the macro base station (BS) equipped with a large number of antennas serves the single antenna pico BS (as a relay) and users simultaneously, and that the pico BS is located at the edge of the macro cell. Theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) outage probability of each user is first obtained. The cell SINR outage probability is then derived. Under the noise-limited assu…
We investigate the effect of imperfect feedback on the ε-outage capacity of incremental relaying in the low signal-to-noise ratio (SNR) regime. We show that imperfect feedback leads to a rescaling of the pre-log factor (comparable to the multiplexing gain for networks operating in the high SNR regime) and thus reduces the ε-outage capacity considerably. Moreover, we investigate the effect of different degrees of feedback reliability on the system performance. We further derive a simple binary tree-based construction rule to analyze networks with an arbitrary number of relay nodes with respect …
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…
Multiple-Input-Multiple-Output (MIMO) communication systems have seen wide application due to its performance benefits such as multiplexing gain. For MIMO systems with non-ergodic Gaussian channel, a conjecture regarding its outage probability has been proposed by Telatar in [1]. This conjecture has been proved for the special single-output case, and is in general assumed to be true. In this work, we analyze the special Two-Input-Multiple-Output (TIMO) case theoretically, and provide a counter-example to the conjecture. The counter-example is verified both theoretically and by numerical experi…
The Rayleigh product channel model is useful in capturing the performance degradation due to rank deficiency of MIMO channels. In this paper, such a performance degradation is investigated via the channel outage probability assuming slowly varying channel with delay-constrained decoding. Using techniques of free probability theory, the asymptotic variance of channel capacity is derived when the dimensions of the channel matrices approach infinity. In this asymptotic regime, the channel capacity is rigorously proven to be Gaussian distributed. Using the obtained results, a fundamental tradeoff …
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…
This paper considers the asymptotic behavior of two-source block-fading single-antenna Gaussian interference channels in the high-SNR regime by means of the diversity-multiplexing tradeoff. We consider a general setting where the users and the average channel gains are not restricted to be symmetric. Our results are not just extensions of previous results for symmetric networks, as our setting covers scenarios that are not possible under the symmetric assumption, such as the case of "mixed" interference, i.e., when difference sources have different distances from their intended receivers. We d…
Due to the relatively high cost of deploying optical fibers, free space optical (FSO) links have been developed as a cost-effective alternative technology for next generation cellular networks. However, in order to have a practical role in the physical layer of future communication systems, data rate of FSO links must be improved. To this aim, in this paper we employ a multiple-input multiple-output (MIMO) multiplexing scheme with two transceivers to increase the data rate of the considered FSO system. Unlike MIMO diversity case, the performance of MIMO multiplexing is significantly affected b…
Fluid antenna is a novel technology that can make an antenna appear instantly at one of N preset locations in a predefined space. An important application is to adopt fluid antenna in a small space of mobile device for obtaining the tremendous diversity hidden in the small space. Previous results have revealed that a single-antenna fluid antenna system, even with a very small space, can outperform a multiple antenna maximum ratio combining (MRC) system if $N$ is large enough. This paper explores the potential of using fluid antenna for multiple access through performance analysis. Fluid antenn…
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…
This paper investigates the performance of open-loop multi-antenna point-to-point links in ad hoc networks with slotted ALOHA medium access control (MAC). We consider spatial multiplexing transmission with linear maximum ratio combining and zero forcing receivers, as well as orthogonal space time block coded transmission. New closed-form expressions are derived for the outage probability, throughput and transmission capacity. Our results demonstrate that both the best performing scheme and the optimum number of transmit antennas depend on different network parameters, such as the node intensit…
We study the tradeoff between reliability, data rate, and delay for half-duplex MIMO multihop networks that utilize the automatic-retransmission-request (ARQ) protocol both in the asymptotic high signal-to-noise ratio (SNR) regime and in the finite SNR regime. We propose novel ARQ protocol designs that optimize these tradeoffs. We first derive the diversity-multiplexing-delay tradeoff (DMDT) in the high SNR regime, where the delay is caused only by retransmissions. This asymptotic DMDT shows that the performance of an N node network is limited by the weakest three-node sub-network, and the per…
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…
Performance of cooperative diversity schemes at Low Signal to Noise Ratios (LSNR) was recently studied by Avestimehr et. al. [1] who emphasized the importance of diversity gain over multiplexing gain at low SNRs. It has also been pointed out that continuous energy transfer to the channel is necessary for achieving the max-flow min-cut bound at LSNR. Motivated by this we propose the use of Selection Decode and Forward (SDF) at LSNR and analyze its performance in terms of the outage probability. We also propose an energy optimization scheme which further brings down the outage probability.
Efficient symbol detection algorithms carry critical importance for achieving the spatial multiplexing gains promised by multi-input multi-output (MIMO) systems. In this paper, we consider a maximum a posteriori probability (MAP) based symbol detection algorithm, called M-BLAST, over uncoded quasi-static MIMO channels. Relying on the successive interference cancellation (SIC) receiver, M-BLAST algorithm offers a superior error performance over its predecessor V-BLAST with a signal-to-noise ratio (SNR) gain of as large as 2 dB under various settings of recent interest. Performance analysis of t…
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 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…
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 analysis for IRS-aided multiple-input-multiple-output (MIMO) systems is not available in the literature. In this paper, we first characterize the mutual information (MI) of 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…
In this paper, we propose an impartial simultaneous wireless information and power transfer (SWIPT)-assisted cooperation mechanism for a non-orthogonal multiple access (NOMA) downlink scenario. Specifically, both a cell-center user and a cell-edge user apply the power-splitting technique and utilize the harvested energy to forward the other user's information on the premise of successful decoding of their own information. Both analytical and numerical results show that the proposed impartial user cooperation mechanism (IUCM) outperforms the traditional partial cooperation mechanism in terms of…
In this paper, a cooperative protocol is investigated for a multi-hop network consisting of relays with buffers of finite size, which may operate in different communication modes. The protocol is based on the myopic decode-and-forward strategy, where each node of the network cooperates with a limited number of neighboring nodes for the transmission of the signals. Each relay stores in its buffer the messages that were successfully decoded, in order to forward them through the appropriate channel links, based on its supported communication modes. A complete theoretical framework is investigated…
Faster-than-Nyquist (FTN) signal achieves higher spectral efficiency and capacity compared to Nyquist signal due to its smaller pulse interval or narrower subcarrier spacing. Shannon limit typically defines the upper-limit capacity of Nyquist signal. To the best of our knowledge, the mathematical expression for the capacity limit of FTN non-orthogonal frequency-division multiplexing (NOFDM) signal is first demonstrated in this paper. The mathematical expression shows that FTN NOFDM signal has the potential to achieve a higher capacity limit compared to Nyquist signal. In this paper, we demonst…
In wireless networks, communication links may be subject to random fatal impacts: for example, sensor networks under sudden power losses or cognitive radio networks with unpredictable primary user spectrum occupancy. Under such circumstances, it is critical to quantify how fast and reliably the information can be collected over attacked links. For a single point-to-point channel subject to a random attack, named as a \emph{dying channel}, we model it as a block-fading (BF) channel with a finite and random delay constraint. First, we define the outage capacity as the performance measure, follow…
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 presents a new fading model for MIMO channels, the Jacobi fading model. It asserts that $H$, the transfer matrix which couples the $m_t$ inputs into $m_r$ outputs, is a sub-matrix of an $m\times m$ random (Haar-distributed) unitary matrix. The (squared) singular values of $H$ follow the law of the classical Jacobi ensemble of random matrices; hence the name of the channel. One motivation to define such a channel comes from multimode/multicore optical fiber communication. It turns out that this model can be qualitatively different than the Rayleigh model, leading to interesting pract…
A FAS Channel Fitting Strategy Using Extreme Value Distributions for Accurate Outage Performance Evaluation
Shaanxi Key Laboratory of Information Communication Network and Security, Xi’an University of Posts and Telecommunications（西安邮电大学）；School of Engineering, University of Warwick（华威大学工程学院）
This paper considers the problem of selecting either routes that consist of long hops or routes that consist of short hops in a network of multiple-antenna nodes, where each transmitting node employs spatial multiplexing. This distance-dependent route selection problem is approached from the viewpoint of energy efficiency, where a route is selected with the objective of minimizing the transmission energy consumed while satisfying a target outage criterion at the final destination. Deterministic line networks and two-dimensional random networks are considered. It is shown that when 1) the numbe…
We consider a multi-input multi-output (MIMO) block-fading channel with a general model for channel state information at the transmitter (CSIT). The model covers systems with causal CSIT, where only CSIT of past fading blocks is available, and predictive CSIT, where CSIT of some future fading blocks is available. The optimal diversity-multiplexing tradeoff (DMT) and rate-diversity tradeoff (RDT) of the channel are studied under long-term power constraints. The impact of imperfect (mismatched) CSIT on the optimal DMT and RDT is also investigated. Our results show the outage diversity gain obtai…
Multiple antenna (MIMO) devices are widely used to increase reliability and information bit rate. Optimal error rate performance (full diversity and large coding gain), for unknown channel state information at the transmitter and for maximal rate, can be achieved by approximately universal space-time codes, but comes at a price of large detection complexity, infeasible for most practical systems. We propose a new coded modulation paradigm: error-correction outer code with space-only but time-varying precoder (as inner code). We refer to the latter as Ergodic Mutual Information (EMI) code. The …
MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. In this paper we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant cross talk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in t…
In this paper, we analyze the asymptotic performance of multiple antenna channels where the transmitter has either perfect or finite bit channel state information. Using the diversity-multiplexing tradeoff to characterize the system performance, we demonstrate that channel feedback can fundamentally change the system behavior. Even one-bit of information can increase the diversity order of the system compared to the system with no transmitter information. In addition, as the amount of channel information at the transmitter increases, the diversity order for each multiplexing gain increases and…
In this paper, the outage behavior and diversity order of the mixture transceiver architecture for multiple-input single-output broadcast channels are analyzed. The mixture scheme groups users with closely-aligned channels and applies superposition coding and successive interference cancellation decoding to each group composed of users with closely-aligned channels, while applying zero-forcing beamforming across semi-orthogonal user groups. In order to enable such analysis, closed-form lower bounds on the achievable rates of a general multiple-input single-output broadcast channel with superpo…
The exact average complexity analysis of the basic sphere decoder for general space-time codes applied to multiple-input multiple-output (MIMO) wireless channel is known to be difficult. In this work, we shed the light on the computational complexity of sphere decoding for the quasi-static, LAttice Space-Time (LAST) coded MIMO channel. Specifically, we drive an upper bound of the tail distribution of the decoder's computational complexity. We show that, when the computational complexity exceeds a certain limit, this upper bound becomes dominated by the outage probability achieved by LAST codin…
This work analyzes the high-SNR asymptotic error performance of outage-limited communications with fading, where the number of bits that arrive at the transmitter during any time slot is random but the delivery of bits at the receiver must adhere to a strict delay limitation. Specifically, bit errors are caused by erroneous decoding at the receiver or violation of the strict delay constraint. Under certain scaling of the statistics of the bit-arrival process with SNR, this paper shows that the optimal decay behavior of the asymptotic total probability of bit error depends on how fast the burst…
This paper proposes a novel and simple orthogonal faster than Nyquist (OFTN) data transmission and detection approach for a single input multiple output (SIMO) system. It is assumed that the signal having a bandwidth $B$ is transmitted through a wireless channel with $L$ multipath components. Under this assumption, the current paper provides a novel and simple OFTN transmission and symbol-by-symbol detection approach that exploits the multiplexing gain obtained by the multipath characteristic of wideband wireless channels. It is shown that the proposed design can achieve a higher transmission …
This paper presents a unified analysis of the mixed radio-frequency (RF)/free-space optics (FSO) relaying system, with multiple variable-gain amplify-and-forward relays. The partial relay selection (PRS) is employed to select the active relay for further re-transmission. Due to fast fading statistics of the first RF hop, it is assumed that the channel state information of the RF link is outdated, which is used for both the relay gain adjustment and the PRS procedure. The RF hops are subject to the Rayleigh fading, while the FSO hop is affected by the atmospheric turbulence and the pointing err…
There are currently a plurality of capacity theories of fading channels, including the ergodic capacity for fast fading channels and outage capacity for slow fading channels. However, analyses show that the outage capacity is a misconception. In this paper we use the 1st order Gaussian-Markov process with coherence coefficient $α$ as the unified model for slow and fast fading channels, the capacity of which without channel side information is studied. We demonstrate that the information rate of a fading channel has a structure that the rate of user message is always accompanied by a rate of ch…
