With Deep Learning dominating modern applications, area-efficient and simultaneously high through-put acceleration of inference has become a crucial application. Constant Matrix Vector Multiplication (CMVM) dominates the computational complexity of these workloads, and its efficient acceleration is essential. Our proposed architecture introduces a groundbreaking extension to Computation Coding for dataflow architectures, achieving a$2.3 \times$performance boost for small matrices and paving the way for more efficient Deep Learning inference at a performance of up to$93.52 \frac{\text{GOP}}{\mathrm{s}}$using a single core.

This work studies a low-complexity design for re-configurable intelligent surface (RIS)-aided multiuser multiple-input multiple-output systems. The base station (BS) applies receive antenna selection to connect a subset of its antennas to the available radio frequency chains. For this setting, the BS switching network, uplink precoders, and RIS phase-shifts are jointly designed, such that the uplink sum-rate is maximized. The principle design problem reduces to an NP-hard mixed-integer optimization. We hence invoke the weighted minimum mean squared error technique and the penalty dual decomposition method to develop a tractable iterative algorithm that approxi-mates the optimal design effectively. Our numerical investigations verify the efficiency of the proposed algorithm and its superior performance as compared with the benchmark.

Linear computation coding (LCC) has been developed in [1] as a new framework for the computation of linear functions. LCC significantly reduces the complexity of matrix-vector multiplication [1]. In basic LCC, storage is not restricted i.e. the wiring exponents are arbitrary integer exponents of 2.

Utilizing compressive sensing (CS), one can significantly reduce the number of required antenna elements in MIMO radar systems, while preserving a high spatial resolution. Most CS-based studies focus on individual processing of a single set of measurements collected from an stationary scene. In this paper, we propose a new scheme called multiple target measurements (MTM). This scheme uses the target movement to collect multiple sets of measurements from jointly sparse stationary scenes. Invoking approximate message passing, we develop a Bayesian-like iterative algorithm to recover the sparse scenes jointly. Our analytical and numerical investigations demonstrate that MTM can further reduce the array size required to achieve a desired spatial resolution.

It is widely believed that large IRS-aided MIMO settings maintain the fundamental features of massive MIMO systems. This work gives a rigorous proof that confirms this belief. We show that using a large passive IRS, the end-to-end MIMO channel between the transmitter and the receiver always hardens, even if the IRS elements are strongly correlated. For fading direct and reflection links between the transmitter and the receiver, our derivations demonstrate that for a large number of reflecting elements on the IRS, the capacity of the end-to-end channel is accurately approximated by a real-valued Gaussian random variable whose variance goes to zero as the number of IRS elements grows unboundedly large. The order of this drop depends on how the physical dimensions of the IRS grow. We derive this order explicitly. Numerical experiments show that the closed-form approximation very closely matches the histogram of the capacity term, even in practical scenarios. As a sample application of the results, we characterize the dimensional trade-off between the transmitter and the IRS. The result is intuitive: For a target performance, the larger the IRS is, the fewer transmit antennas are required.

Unlike the classical linear model, nonlinear generative models have been addressed sparsely in the literature of statistical learning. This work aims to shed light on these models and their secrecy potential. To this end, we invoke the replica method to derive the asymptotic normalized cross entropy in an inverse probability problem whose generative model is described by a Gaussian random field with a generic covariance function. Our derivations further demonstrate the asymptotic statistical decoupling of the Bayesian estimator and specify the decoupled setting for a given nonlinear model. The replica solution depicts that strictly nonlinear models establish an all-or-nothing phase transition: there exists a critical load at which the optimal Bayesian inference changes from perfect to an uncorrelated learning. Based on this finding, we design a new secure coding scheme which achieves the secrecy capacity of the wiretap channel. This interesting result implies that strictly nonlinear generative models are perfectly secured without any secure coding. We justify this latter statement through the analysis of an illustrative model for perfectly secure and reliable inference.

Inverse probability problems whose generative models are given by strictly nonlinear Gaussian random fields show the all-or-nothing behavior: There exists a critical rate at which Bayesian inference exhibits a phase transition. Below this rate, the optimal Bayesian estimator recovers the data perfectly, and above it the recovered data becomes uncorrelated. This study uses the replica method from the theory of spin glasses to show that this critical rate is the channel capacity. This interesting finding has a particular application to the problem of secure transmission: A strictly nonlinear Gaussian random field along with random binning can be used to securely encode a confidential message in a wiretap channel. Our large-system characterization demonstrates that this secure coding scheme asymptotically achieves the secrecy capacity of the Gaussian wiretap channel.

A new method for linear computation coding is presented. Similar to the Lempel-Ziv algorithm, it dynamically updates its codebook based on the input. In contrast to earlier work, this method shows excellent performance also for very small matrices. It can even be used to compute inner and outer products of vectors.

In intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) systems, the IRS can be utilized to suppress the information leakage towards malicious terminals. This can lead to significant secrecy gains. This work exploits these gains via a tractablejointdesign of downlink beamformers and IRS phase-shifts. In this respect, we consider a generic IRS-aided MIMO wiretap setting and invoke fractional programming and alternating optimization to iteratively find the beamformers and phase-shifts that maximize the achievable weighted secrecy sum-rate. Our design is comprised of two low-complexity algorithms. Performance of the proposed algorithms are numerically evaluated and compared to the benchmark. The results reveal that integrating IRSs into MIMO systems not only boosts the secrecy performance, but also improves the robustness against passive eavesdropping.

This paper characterizes the performance of massive multiuser spatial modulation MIMO systems, when a regularized form of the least-squares method is used for detection. For a generic distortion function and right unitarily invariant channel matrices, the per-antenna transmit rate and the asymptotic distortion achieved by this class of detectors are derived. Invoking an asymptotic characterization, we address two particular applications. Namely, we derive the error rate achieved by the computationally-intractable optimal Bayesian detector, and we propose an efficient approach to tune LASSO-type detectors. We further validate our derivations through various numerical experiments.

Using intelligent reflecting surfaces (IRSs), wireless propagation channels can be manipulated such that information leakage to eavesdropping terminals in a multiple-input multiple-output (MIMO) setting is significantly suppressed. This observation illustrates the potential secrecy gains of IRS-aided MIMO systems. This work develops a novel low-complexity algorithm by which these potential gains are exploited. Invoking methods from fractional programming, the algorithm iteratively designs the digital precoder at the transmitter and tunes the IRS elements, such that the weighted secrecy sum-rate is maximized. It is shown that as the algorithm iterates, the weighted secrecy sum-rate evolves in a non-decreasing way. Numerical investigations confirm the efficiency of the proposed algorithm.

We introduce the new concept of computation coding. For linear functions, we present an algorithm to reduce the computational cost of multiplying an arbitrary given matrix with an unknown vector. It decomposes the given matrix into the product of codebook and wiring matrices whose entries are either zero or signed integer powers of two.For a typical implementation of deep neural networks, the proposed algorithm reduces the number of required addition units several times. To achieve the accuracy of 16-bit signed integer arithmetic for 4k-vectors, no multipliers and only 1.5 adders per matrix entry are needed.

We utilize recent results on the exact block error probability of Gaussian random codes in additive white Gaussian noise to analyze Gaussian random coding for massive multiple-access at finite message length. Soft iterative interference cancellation is found to closely approach the performance bounds recently found in [1]. The existence of two fundamentally different regimes in the trade-off between power and bandwidth efficiency reported in [2] is related to much older results in [3] on power optimization by linear programming. Furthermore, we tighten the achievability bounds of [1] in the low power regime and show that orthogonal constellations are very close to the theoretical limits for message lengths around 100 and above.

This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. The proposed method is applicable to various channels and ensembles. The focus is on both spherical and Gaussian random codes on the additive white Gaussian noise channel as well as binary random codes on both the binary symmetric channel and the binary erasure channel. While for the uniform spherical ensemble Shannon, in 1959, argued with solid angles in N-dimensional space, the presented approach projects the problem into two dimensions and applies standard trigonometry. This simplifies the derivation and also allows for the analysis of the independent identically distributed (i.i.d.) Gaussian ensemble which turns out to perform better for short blocklengths and high rates. Moreover, a new lower bound on the average block error probability of the uniform spherical ensemble is found. For codes with more than three codewords, it is tighter than the sphere packing bound, but requires exactly the same computing effort. Furthermore, tight approximations are proposed to simplify the computation of both the exact average error probability and the two bounds. For the binary symmetric channel and the binary erasure channel, bounds on the average block error probability for i.i.d. random coding are derived and compared to the exact calculations.

Passively overheard massive multiple-input multiple-output (MIMO) settings are capable of suppressing eavesdroppers via narrow beamforming towards legitimate receivers. This implies that secrecy is obtained almost for free in these settings. This study shows that this is a valid property for a large class of low-complexity massive MIMO transmitters. The investigations consider two dominant approaches for complexity reduction, namely antenna selection and hybrid analog-digital precoding. It is shown that using either approach, the information leakage per achievable sum-rate vanishes as the number of transmit antennas grows large. The results demonstrate that, as the transmit array size grows large, the normalized information leakage obtained by antenna selection and hybrid analog-digital precoding converges to zero double-logarithmically and logarithmically, respectively. The analytical results are confirmed for various benchmark architectures via numerical simulations.

This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. Deviating from Shannon's 1959 solid angle argument, we project the problem into two dimensions and apply standard trigonometry. This enables us to also analyze Gaussian random codes in additive white Gaussian noise and binary random codes for the binary symmetric channel. We find that the Voronoi regions harden doubly-exponential in the blocklength and utilize that to propose the new median bound that outperforms Shannon's 1959 sphere packing bound for the uniform spherical ensemble, whenever the code contains more than three codewords. Furthermore, we propose a very tight approximation to simplify computation of both exact error probability and the two bounds.

In this work, we propose a new single-RF MIMO architecture which enjoys high scalability and energy-efficiency. The transmitter in this proposal consists of a single RF illuminator radiating towards a reflecting surface. Each element on the reflecting surface re-transmits its received signal after applying a phase-shift, such that a desired beamforming pattern is obtained. For this architecture, the problem of beamforming is interpreted as linear regression and a solution is derived via the method of least-squares. Using this formulation, a fast iterative algorithm for tuning of the reflecting surface is developed. Numerical results demonstrate that the proposed architecture is fully compatible with current designs of reflecting surfaces.

Reliability-Based Hybrid Automated Repeat reQuest (RB-HARQ) strongly improves the throughput of a communications system by identifying and retransmitting the symbols deemed most unreliable after decoding the initial transmission. Additional soft-value processing, large feedback messages and many retransmissions are required to achieve a high throughput. We compare a variant of RB-HARQ designed for limited feedback with a new low-overhead, clustered Parity-Based Partial-Retransmission (PBPR) HARQ scheme. The new scheme selects symbols connected to unsatisfied parity checks and intersects this set with a subset of all symbols consisting of uniformly distributed information or parity symbols to improve the throughput. Since clustered HARQ schemes work best with codes exhibiting high intra-codeword correlations, we use Spatially-Coupled Low-Density Parity-Check (SC-LDPC) codes for evaluation.

In conventional Multiple-Input Multiple Output (MIMO) systems, each antenna requires its own Radio Frequency (RF) chain. Since each RF-chain includes several active components that have to be synchronised, costs and complexity become restrictive. The outphasing MIMO and the outphasing precoder architectures are possible approaches to mitigate this problem. The core of both architectures are Outphasing Elements (OEs), which are used to form a electronically controllable, passive antenna feed network. In this paper, these OEs are analysed with respect to component tolerances. The feasibility of the outphasing concept is demonstrated by the implementation of a hardware prototype OE. The performance of this prototype is measured and compared to theoretical predictions with good agreement.

Hybrid analog-digital architectures are considered as promising candidates for implementing millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems since they enable a considerable reduction of the required number of costly radio frequency (RF) chains by moving some of the signal processing operations into the analog domain. However, the analog feed network, comprising RF dividers, combiners, phase shifters, and line connections, of hybrid MIMO architectures is not scalable due to its prohibitively high power consumption for large numbers of transmit antennas. Motivated by this limitation, in this paper, we study novel massive MIMO architectures, namely reflect-array (RA) and transmit-array (TA) antennas. We show that the precoders for RA and TA antennas have to meet different constraints compared to those for conventional MIMO architectures. Taking these constraints into account and exploiting the sparsity of mmWave channels, we design an efficient precoder for RA and TA antennas based on the orthogonal matching pursuit algorithm. Furthermore, in order to fairly compare the performance of RA and TA antennas with conventional fully-digital and hybrid MIMO architectures, we develop a unified power consumption model. Our simulation results show that unlike conventional MIMO architectures, RA and TA antennas are highly energy efficient and fully scalable in terms of the number of transmit antennas.

Most detection algorithms in spatial modulation (SM) are formulated as linear regression via the regularized least-squares (RLS) method. In this method, the transmit signal is estimated by minimizing the residual sum of squares penalized with some regularization. This paper studies the asymptotic performance of a generic RLS-based detection algorithm employed for recovery of SM signals. We derive analytically the asymptotic average mean squared error and the error rate for the class of bi-unitarily invariant channel matrices. The analytic results are employed to study the performance of SM detection via the box-LASSO. The analysis demonstrates that the performance characterization for i.i.d. Gaussian channel matrices is valid for matrices with non-Gaussian entries, as well. This justifies the partially approved conjecture given in [1]. The derivations further extend the former studies to scenarios with non-i.i.d. channel matrices. Numerical investigations validate the analysis, even for practical system dimensions.

Joint user selection and precoding in multiuser MIMO settings can be interpreted as group sparse recovery in linear models. In this problem, a signal with group sparsity is to be reconstructed from an underdetermined system of equations. This paper utilizes this equivalent interpretation and develops a computationally tractable algorithm based on the method of group LASSO. Compared to the state of the art, the proposed scheme shows performance enhancements in two different respects: higher achievable sum-rate and lower interference at the non-selected user terminals.

The large-system performance of maximum-a-poste-rior estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix to be chosen from the large class of rotationally invariant random matrices. We take a statistical mechanical approach by introducing a spin glass corresponding to the estimator, and employing the replica method for the large-system analysis. In contrast to earlier replica based studies, our analysis evaluates the general replica ansatz of the corresponding spin glass and determines the asymptotic distortion of the estimator for any structure of the replica correlation matrix. Consequently, the replica symmetric as well as the replica symmetry breaking ansatz with$b$steps of breaking is deduced from the given general replica ansatz. The generality of our distortion function lets us derive a more general form of the maximum-a-posterior decoupling principle. Based on the general replica ansatz, we show that for any structure of the replica correlation matrix, the vector-valued system decouples into a bank of equivalent decoupled scalar systems followed by maximum-a-posterior estimators. The structure of the decoupled system is further studied under both the replica symmetry and the replica symmetry breaking assumptions. For$b$steps of symmetry breaking, the decoupled system is found to be an additive system with anon-Gaussiannoise term given as the sum of an independent Gaussian random variable with$b$non-Gaussian impairment terms which depend on the input symbol. The general decoupling property of the maximum-a-posterior estimator leads to the idea of a replica simulator which represents the replica ansatz through the state evolution of a transition system described by its corresponding decoupled system. As an application of our study, we investigate large compressive sensing systems by considering the$\ell _{p}$norm minimization recovery schemes. Our numerical investigations show that the replica symmetric ansatz for$\ell _{0}$norm recovery fails to give an accurate approximation of the mean square error as the compression rate grows, and therefore, the replica symmetry breaking ansätze are needed in order to assess the performance precisely.

This paper proposes the class of generalized least-square-error (GLSE) precoders for multiuser massive multiple-input multiple-output (MIMO) systems. For a generic transmit constellation, the GLSE precoders minimize the interference at user terminals assuring that some given constraints on the transmit signals are satisfied. The general form of these precoders enables us to impose multiple restrictions at the transmit signal, such as limited peak power and restricted number of active transmit antennas. The performance of these precoders is analyzed in the large-system limit. It is shown that the output symbols are identically distributed, and their statistics are described with an equivalent scalar GLSE precoder. To demonstrate the applications of the proposed framework, we employ the GLSE precoding to form transmit signals over a discrete alphabet and to select an effective subset of transmit antennas. Our investigations show that a computationally efficient GLSE precoder requires 41% less active transmit antennas than the conventional selection protocols in order to achieve a given level of input-output distortion.

In massive MIMO wiretap settings, the base station can significantly suppress eavesdroppers by narrow beamforming toward legitimate terminals. Numerical investigations show that by this approach, secrecy is obtained at no significant cost. We call this property of massive MIMO systems "secrecy for free" and show that it not only holds when all the transmit antennas at the base station are employed, but also when only a single antenna is set active. Using linear precoding, the information leakage to the eavesdroppers can be sufficiently diminished, when the total number of available transmit antennas at the base station grows large, even when only a fixed number of them are selected. This result indicates that passive eavesdropping has no significant impact on massive MIMO systems, regardless of the number of active transmit antennas.

This paper studies the asymptotic performance of maximum-a-posteriori estimation in the presence of prior information. The problem arises in several applications such as recovery of signals with non-uniform sparsity pattern from underdetermined measurements. With prior information, the maximum-a-posteriori estimator might have asymmetric penalty. We consider a generic form of this estimator and study its performance via the replica method. Our analyses demonstrate an asymmetric form of the decoupling property in the large-system limit. Employing our results, we further investigate the performance of weighted zero-norm minimization for recovery of a non-uniform sparse signal. Our investigations illustrate that for a given distortion, the minimum number of required measurements can be significantly reduced by choosing weighting coefficients optimally.

The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior is proportional to the regularization term. In this paper, we study distributed sensing networks in which a set of spatially correlated signals are measured individually at separate terminals, but recovered jointly via a generic maximum-a-posterior estimator. Using the replica method, it is shown that the setting exhibits the decoupling property. For the case with jointly sparse signals, we invoke Bayesian inference and propose the “multi-dimensional soft thresholding” algorithm which is posed as a linear programming. Our investigations depict that the proposed algorithm outperforms the conventional l2,1-norm regularized least squares scheme while enjoying a feasible computational complexity.

The iterative algorithms employed to decode Low-Density Parity-Check (LDPC) codes are not guaranteed to converge to a valid code word for every receive word. The goal of Early Termination (ET) is to prevent the waste of resources in such cases. In this paper, we conduct an analysis of the suitability of ET criteria by tracking the evolution of parameters available from decoder-internal states. We find that the commonly selected parameters, e.g., the mean Log-Likelihood Ratio (LLR) magnitude or the fraction of satisfied parity checks, result in similar probabilities of detecting non-converging receive words. We propose a novel criterion for Early Give-Up (EGU) and evaluate its performance using a cost metric based on the retransmission of individual code blocks initiated by higher-layer protocols.

In this paper, we study the impacts of transmit antenna selection on the secrecy performance of massive MIMO systems. We consider a wiretap setting in which a fixed number of transmit antennas are selected and then confidential messages are transmitted over them to a multi-antenna legitimate receiver while being overheard by a multi-antenna eavesdropper. For this setup, we derive an accurate approximation of the instantaneous secrecy rate. Using this approximation, it is shown that in some wiretap settings under antenna selection the growth in the number of active antennas enhances the secrecy performance of the system up to some optimal number and degrades it when this optimal number is surpassed. This observation demonstrates that antenna selection in some massive MIMO settings not only reduces the RF-complexity, but also enhances the secrecy performance. We then consider various scenarios and derive the optimal number of active antennas analytically using our large-system approximation. Numerical investigations show an accurate match between simulations and the analytic results.

We investigate the capacity scaling of multiple-input-multiple-output systems with the system dimensions. To that end, we quantify how the mutual information varies when the number of antennas (at either the receiver or transmitter side) is altered. For a system comprising R receive and T transmit antennas with R > T, we find the following: by removing as many receive antennas as needed to obtain a square system (provided the channel matrices before and after the removal have full rank) the maximum resulting loss of mutual information over all signal-to-noise ratios (SNRs) depends only on R, T, and the matrix of left-singular vectors of the initial channel matrix, but not on its singular values. In particular, if the latter matrix is Haar distributed the ergodic rate loss is given by Σt=1TΣr=T+1R1/r-t nats. Under the same assumption, if T, R → ∞ with the ratio φ=ΔT/R fixed, the rate loss normalized by R converges almost surely to H(φ) bits with H(·) denoting the binary entropy function. We also quantify and study how the mutual information as a function of the system dimensions deviates from the traditionally assumed linear growth in the minimum of the system dimensions at high SNR.

Antenna selection is an effective means to address the cost and complexity issues in massive MIMO systems. This paper studies the performance limits of massive MIMO systems under practical antenna selection algorithms. A massive MIMO system is considered in which the transmitter employs only a fixed-size subset of the available antennas with the strongest channel gains. For this setup, the input-output mutual information of the system is shown to be well-approximated by a normal random variable when the number of transmit antennas is large. The mean of this random variable grows proportional to the number of antennas and its variance vanishes in the large-system limit. This behavior of the mutual information generalizes the well-known channel hardening property in massive MIMO systems to the cases with antenna selection. Our investigations show that 90% of the ergodic rate achieved by full antenna selection can be achieved by selecting less than 30% of the transmit antennas. Using large-system analysis, we drive an analytical expression for the number of selected antennas that maximizes the energy efficiency. This number is also derived for the case where a certain fraction of the totally achievable rate is aimed to be achieved. Our numerical investigations demonstrate a close match between the analytical and simulation results even for scenarios with not-so-large dimensions.

This paper proposes nonlinear least square error (LSE) precoders for multiuser MIMO broadcast channels. The LSE precoders are designed such that the discrete output signals are from a predefined set. This predefined set allows us to model several signal constraints such as peak power constraint, constant envelope, and discrete constellations. We study the large-system performance of these precoders via the replica method from statistical physics, and derive a closed-form expression for the asymptotic distortion. Our results demonstrate that an LSE precoder with the output peak-to-average power ratio of 3 dB can perform similar to the regularized zero forcing (RZF) precoder. As the peak-to-average power ratio reduces to one, the constant envelope precoder is recovered. The investigations show that the performance of the RZF precoder is achieved by a constant envelope precoder with 20% additional transmit antennas. For M-phase shift keying constellations, our analysis gives a lower bound on the asymptotic distortion which is tight for moderate antenna-to-user ratios and deviates as the ratio grows. We improve this bound by deriving the replica solution under one-step of replica symmetry breaking. Our numerical investigations for this case show that the bound is tight for antenna-to-user ratios less than 5.

User pairing in non-orthogonal multiple-access (NOMA) uplink is investigated considering some predefined power allocation schemes. The base station divides the set of users into disjunct pairs and assigns the available resources to these pairs. The combinatorial problem of user pairing to achieve the maximum sum rate is analyzed in the large system limit for various scenarios, and some optimum and sub-optimum algorithms with a polynomial-time complexity are proposed. In the first scenario, 2 M users and the base station have a singleantenna and communicate over M subcarriers. The performance of optimum pairing is derived for M → ∞ and shown to be superior to random pairing and orthogonal multiple access techniques. In the second setting, a novel NOMA scheme for a multi-antenna base station and single carrier communication is proposed. In this case, the users need not be aware of the pairing strategy. Furthermore, the proposed NOMA scheme is generalized to multi-antenna users. It is shown that for the considered power allocation scheme, random and optimum user pairing perform similarly in the large system limit, but optimum pairing is significantly better in finite dimensions. It is shown that NOMA with the proposed user pairing scheme outperforms a previously proposed NOMA with signal alignment.

This paper studies the impact of transmit antenna selection on the secrecy performance of massive MIMO wiretap channels. We consider a scenario in which a multi-antenna transmitter selects a subset of transmit antennas with the strongest channel gains. Confidential messages are then transmitted to a multi-antenna legitimate receiver while the channel is being overheard by a multi-antenna eavesdropper. For this setup, we approximate the distribution of the instantaneous secrecy rate in the large-system limit. The approximation enables us to investigate the optimal number of selected antennas which maximizes the asymptotic secrecy throughput of the system. We show that increasing the number of selected antennas enhances the secrecy performance of the system up to some optimal value, and that further growth in the number of selected antennas has a destructive effect. Using the large-system approximation, we obtain the optimal number of selected antennas analytically for various scenarios. Our numerical investigations show an accurate match between simulations and the analytic results even for not so large dimensions.

Consider a fading Gaussian MIMO channel with Nttransmit and Nrreceive antennas. The transmitter selects Ltantennas corresponding to the strongest channels. For this setup, we study the distribution of the input-output mutual information when Ntgrows large. We show that, for any Nrand Lt, the distribution of the input-output mutual information is accurately approximated by a Gaussian distribution whose mean grows large and whose variance converges to zero. Our analysis depicts that, in the large limit, the gap between the expectation of the mutual information and its corresponding upper bound, derived by applying Jensen's inequality, converges to a constant which only depends on Nrand Lt. The result extends the scope of channel hardening to the general case of antenna selection with multiple receive and selected transmit antennas. Although the analyses are given for the large-system limit, our numerical investigations indicate the robustness of the approximated distribution even when the number of antennas is not large.

We introduce π/2-shifted Phase Shift Keying on the Hypersphere (π/2-PSKH), a new modulation scheme for Multiple-Input Multiple-Output (mIMO) systems. π/2-PSKH is a multidimensional extension of shifted QAM which allows to use load-modulated MIMO transmitters with a highly efficient power amplifier with reduced backoff. We propose π/2-PSKH constellations and explain how a π/2-PSKH signal is generated. The signal point sequence for π/2-PSKH is time-varying and as such has an inherent code. For the receiver, three algorithms are introduced and numerical simulations are used to examine their performance. These algorithms are further modified in order to reduce their complexity. We discuss the effect of this complexity reduction and the trade-off between receiver complexity and performance. It is shown that due to its inherent code, π/2-PSKH shows excellent performance in terms of power efficiency even if used with conventional amplifiers.

A general class of nonlinear Least Square Error (LSE) precoders in multi-user multiple-input multiple-output systems is analyzed using the replica method from statistical mechanics. A single cell downlink channel with N transmit antennas at the base station and K single-antenna users is considered. The data symbols are assumed to be iid Gaussian and the precoded symbols on each transmit antenna are restricted to be chosen from a predefined set X. The set X encloses several well-known constraints in wireless communications including signals with peak power, constant envelope signals and finite constellations such as Phase Shift Keying (PSK). We determine the asymptotic distortion of the LSE precoder under both the Replica Symmetry (RS) and the one step Replica Symmetry Breaking (1-RSB) assumptions. For the case of peak power constraint on each transmit antenna, our analyses under the RS assumption show that the LSE precoder can reduce the peak to average power ratio to 3dB without any significant performance loss. For PSK constellations, as N/K grows, the RS assumption fails to predict the performance accurately and therefore, investigations under the 1-RSB assumption are further considered. The results show that the 1-RSB assumption is more accurate.

This paper studies the large-system performance of Least Square Error (LSE) precoders which minimize the input-output distortion over an arbitrary support subject to a general penalty function. The asymptotics are determined via the replica method in a general form which encloses the Replica Symmetric (RS) and Replica Symmetry Breaking (RSB) ansätze. As a result, the “marginal decoupling property” of LSE precoders for b-steps of RSB is derived. The generality of the studied setup enables us to address special cases in which the number of active transmit antennas are constrained. Our numerical investigations depict that the computationally efficient forms of LSE precoders based on “li-norm” minimization perform close to the cases with “zero-norm” penalty function which have a considerable improvements compared to the random antenna selection. For the case with BPSK signals and restricted number of active antennas, the results show that RS fails to predict the performance while the RSB ansatz is consistent with theoretical bounds.

We analyze the performance of Bit-Interleaved Coded Modulation (BICM) for MIMO systems employing Phase Shift Keying on the Hypersphere (PSKH), an extension of conventional PSK to higher dimensions. Because the quality of BICM relies on the bit-mapping between coded bits and signal points, PSKH constellations with superior distance properties and capacities might have poor power efficiency. In this paper, we analyze these losses in power efficiency and propose a new method to generate PSKH constellations, i.e., spherical codes, together with a BICM optimized bit-mapping. It turns out that for one bit per real dimension, individual QPSK per antenna is optimal, whereas for other constellation sizes notable gains can be achieved.

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 distribution of mutual information assuming the block fading channels and the uniform power transmission scheme. Using techniques of free probability theory, the asymptotic variance of mutual information is derived when the dimensions of the channel matrices approach infinity. In this asymptotic regime, the mutual information is rigorously proven to be Gaussian distributed. Using the obtained results, a fundamental tradeoff between multiplexing gain and diversity gain of Rayleigh product channels under the uniform power transmission can be characterized by the closed-form expression at any finite signal-to-noise ratio. Numerical results are provided to compare the outage performance between the Rayleigh product channels and the conventional Rayleigh MIMO channels.

In this paper we propose a novel robust channel estimation algorithm exploiting path diversity in both angle and power domains, relying on a suitable combination of the spatial filtering and amplitude based projection. The proposed approach is able to cope with a wide range of system and topology scenarios, including those where interference channel may overlap with desired channels in terms of multipath angles of arrival (AoA) or exceed them in terms of received power. We establish the analytical conditions under which the proposed channel estimator is fully decontaminated.

The large-system decoupling property of a MAP estimator is studied when it estimates the i.i.d. vector x from the observation y = Ax + z with A being chosen from a wide range of matrix ensembles, and the noise vector z being i.i.d. and Gaussian. Using the replica method, we show that the marginal joint distribution of any two corresponding input and output symbols converges to a deterministic distribution which describes the input-output distribution of a single user system followed by a MAP estimator. Under the bRSB assumption, the single user system is a scalar channel with additive noise where the noise term is given by the sum of an independent Gaussian random variable and b correlated interference terms. As the bRSB assumption reduces to RS, the interference terms vanish which results in the formerly studied RS decoupling principle.

We introduce phase modulation on the hypersphere (PMH) for load-modulated multiple-input multiple-output (MIMO) transmitters with a single central power amplifier. In PMH, the peak to average ratio of the sum power before pulse shaping is 1; thus, the central power amplifier of load-modulated MIMO transmitters does not require any back-off. We derive the capacity of PMH on an additive white Gaussian noise channel and show that the input signal should be uniformly distributed on a hypersphere. The mutual information of uniformly distributed PMH input is derived in an uplink multiple-access independent identically distributed Gaussian MIMO channel using the replica method from statistical physics. Furthermore, discrete PMH is introduced using spherical codes and also generalizing minimum shift keying from the complex unit circle to the hypersphere. We investigate different pulse shaping methods for PMH including a novel spherical filtering. Using spherical pulse shaping, the signal stays on the hypersphere. Various filters are investigated, and a tradeoff between spectral shape and peak-to-average-sum-power ratio (PASPR) is found. For as few as four antennas, good spectral properties (similar to root-raised cosine pulses) can be achieved at very low PASPR. Both former and latter further improve with increasing the number of antennas.

The paper analyzes the performance of an advanced random access scheme for the return channel of a satellite communication link. The scheme is an evolution of the E-SSA scheme proposed in [1], [2] that couples an asynchronous Spread Spectrum Aloha access with Successive Interference Cancellation (SIC) at the central Gateway (GW) receiver to increase the channel throughput. Main feature of the proposed scheme is the exploitation of an approximate linear Minimum Mean Square Error (MMSE) detector in place of the conventional Single User Matched Filter (SUMF) detector used in E-SSA. A gain of 50% in terms of spectral efficiency is achieved over E-SSA in most typical scenarios.

The Diversity-Multiplexing Tradeoff (DMT) is studied for the large Rayleigh product channel at non-asymptotic SNRs. The first result is that, as matrix dimensions growing to infinity, the channel capacity converges to a Gaussian random variable. Based on this, we derive a compact expression for the finite-SNR DMT. From the analytical and numerical results, we gain useful insight into the fundamental tradeoff of the considered channel model in the realistic SNR regime.

The performance of short block length low-density parity-check (LDPC) codes (both binary and nonbinary) and convolutional codes is compared under the constraint of tight structural delay constraints. Additionally, we use fundamental bounds on block codes and low rate turbo codes to evaluate our results in a broader context. It turns out that-depending on the code rate and given delay-convolutional codes are able to outperform fundamental lower bounds for block codes, yielding a definite result on the question, which codes are superior in this regime. From a break-even point onward, convolutional codes cannot compete with block codes anymore and nonbinary LDPC codes show the best performance. Turbo codes with a short interleaver length show competitive results.

We extend the result by Tse and Verdú on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access (CDMA) with binary phase shift keying input. Random Gaussian and random binary antipodal spreading are considered. We obtain the optimum asymptotic multiuser efficiency of a K-user system with spreading gain N when K and N → ∞ and the loading factor, (K/N), grows logarithmically with K under some conditions. It is shown that the optimum detector in a Gaussian randomly spread CDMA system has a performance close to the single user system at high signal-to-noise ratio when K and N → ∞ and the loading factor, (K/N), is kept less than (log3K/2). Random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained. Furthermore, we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency. We obtain a condition such that for any binary input, an N × K random matrix, whose entries are chosen randomly from a finite set, is a detecting matrix as K and N → ∞.

In this paper, we focus on throughput performance of multiuser communications systems over fading channels. More specifically, we consider the uplink where multiuser detection under asynchronous transmissions is exploited for random-access management and iterative receivers are considered for practical issues. Normalized throughput is evaluated through a semi-analytic procedure in order to avoid time-consuming simulations. Power randomization is explored as a means for improving performance through system asymmetries. It is found beneficial, particularly in case of overloaded systems operating at low-to-medium signal-to-noise ratio, where it allows reducing significantly the number of iterations at the receiver.

Virtually rotating antennas, which rotate once or several times during a symbol interval, have been considered in recent years as a compact (in volume) alternative for achieving additional degrees of freedom compared to standard multiple antenna receivers. Antenna rotation effectively induces bandwidth expansion at the receiver, which in turn increases the effective dimensionality, and may potentially allow for spatial multiplexing. However, in a licensed spectrum such bandwidth expansion also introduces interference from signals transmitted in adjacent frequency bands. This paper investigates to what extent such adjacent channel interference can be mitigated by appropriate signal processing. The potentially achievable throughput of systems employingmultiplevirtually rotating antennas is examined analytically in a multiuser setting, while considering the large system limit, and employing random matrix theory tools. The analysis focuses on the linear minimum mean-square error (MMSE) receiver, and a receiver that optimally decodes the transmissions of desired users, while being unaware of the codebooks of interferers. The achievable throughput is compared to the corresponding throughputs of standard multiple antenna receivers employing the same number of physicalactiveantenna elements. Conditions for virtually rotating antennas to be beneficial are identified, which when met are shown to lead to significant performance enhancement over standard multiple antenna receivers.

We design a new precoding scheme for massive multiple-input multiple-output (MIMO) systems subject to an instantaneous total power constraint. Unlike the classical way of designing precoders, we use a more realistic model for power amplifiers by considering their maximum power. The considered power constraint is applicable in the single-RF MIMO transmitter which has been proposed recently for massive MIMO systems. For sake of analysis, i.i.d. Gaussian signals are considered. It is shown that the designed precoding scheme results in a good performance in terms of signal to interference plus noise ratio (SINR) at the receivers and power efficiency at the transmitter. It is shown that the power efficiency utilizing this precoding scheme is almost equal to the case of constant envelope signals. Since the proposed precoding limits the total transmit power, there is no need for peak-to-average power ratio (PAPR) reduction algorithms.

We derive some bounds on the Optimum Asymptotic Multiuser Efficiency (OAME) of randomly spread CDMA as extensions of the result by Tse and Verdú. To this end, random Gaussian and random binary antipodal spreading are considered. Furthermore, the input signal is assumed to be Binary Phase Shift Keying (BPSK). It is shown that in a CDMA system with K-user and N chips when K and N → 8 and the loading factor, K over N, grows logarithmically with K, the OAME converges to 1 almost surely under some condition. It is also shown that a Gaussian randomly spread CDMA system has a performance close to the single user system at high Signal to Noise Ratio (SNR) when the loading factor is kept less than log3K over 2. Moreover, for random binary antipodal matrices, we show that the loading factor cannot grow faster than equation.

In this study, the performance of a spectral‐amplitude‐coding optical code division multiple access (SAC‐OCDMA) system in the asynchronous regime is evaluated using a Gaussian approximation of the decision variable for codes with fixed cross‐correlation used in SAC‐OCDMA systems. The authors consider the effect of phase‐induced intensity noise (PIIN), thermal noise and shot noise. Moreover, the validity of the Gaussian approximation is confirmed by a Kolmogorov–Smirnov fitness test. For sake of comparison, the bit error rate (BER) of the asynchronous SAC‐OCDMA system is also plotted numerically in comparison with the BER of the synchronous SAC‐OCDMA. They show that a SAC‐OCDMA system without any time management for the users, that is, the asynchronous regime, has a better performance than the synchronous SAC‐OCDMA when PIIN effect exists.

In this work, we present a low-complexity linear precoding scheme for downlink large-scale multiple-input multiple-output (MIMO) systems. The proposed scheme can achieve near minimum mean square error (MMSE) precoding performance in terms of the sum rate and is based on a matrix polynomial instead of matrix inversion. Simulation results show that matrix polynomials consisting of only a few terms are sufficient to closely approach the sum rate of the classical MMSE precoder and to perform orders of magnitude better than the simple conjugate beamforming (BF) precoder. We derive exact expressions for the computational complexity of the proposed scheme in terms of the number of additions and multiplications and compare it to the complexity of the BF and MMSE precoders. Our complexity analysis shows that for large number of base station antennas N compared to the number of generated transmit symbols τ per channel estimate and large number of users K, the proposed polynomial precoder has a lower complexity than the classical MMSE precoder.

A subspace method for channel estimation is proposed for asymmetric antenna array systems. The so-called pilot contamination problem reported in [1] is found to be due to the linearity of channel estimation in [2]. We show that it does not occur in cellular systems with power control and power-controlled handoff when the nonlinear channel estimation method proposed in this paper is used. Power-control hand-off is needed to guarantee separability between signal and interference subspaces. We derive the transmission conditions for subspace separability based on free probability and perturbation theory.

Iterative channel estimation and decoding based on probabilistic bias is investigated. In order to control the occurrence probability of transmitted symbols, biased convolutional codes (CCs) are proposed. A biased CC is obtained by puncturing the parity bit of a conventional (unbiased) CC and by inserting a fixed bit at the punctured position when the state is contained in a certain subset of all possible states. A priori information about the imposed bias is utilized for the initial linear minimum mean-squared error (LMMSE) channel estimation. This paper focuses on biased turbo codes that are constructed as the parallel concatenation of two biased CCs with interleaving, and proposes an iterative LMMSE channel estimation and decoding scheme based on approximate belief propagation. The convergence property of the iterative LMMSE channel estimation and decoding scheme is analyzed via density evolution (DE). The DE analysis allows one to design the magnitude of the bias according to the coherence time, in terms of the decoding threshold. The proposed scheme is numerically shown to outperform conventional pilot-based schemes in the moderate signal-to-noise ratio (SNR) regime, at the expense of a performance degradation in the high SNR regime.

Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all SNRs. The comparison between the obtained bound and a high-SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high-SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low-SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.

This paper studies the asymptotic eigenvalue distribution (AED) and the mutual information of a multiuser (MU) multiple-input multiple output (MIMO) channel with a certain fraction of users experiencing line-of-sight. It shows that the AED of the channel matrix decomposes into two separate bulks for practically relevant parameter choices and differs very much from the common assumption of independent identically distributed (iid) entries which induces the quarter circle law. This happens even without antenna correlation at either side of the channel. In order to tackle this problem the paper makes use of recent developments in free probability theory which allow to deal with complex-valued eigenvalue distributions of non-Hermitian matrices by means of quaternions.

We consider the total capacity of a Gaussian multiple-access MIMO channel with a linear array of R receive antennas and T distributed transmit antennas. If the spatial distribution of transmit antennas weighed by their path loss and marginalized to a sphere around the receive array is proportional to the ratio of receive antenna directivity to transmit antenna directivity, the capacity is shown to approach Rlog(1 + SNR) as T → ∞, irrespective of the inter-element distance at the receiver.We further show that the capacity for other distributions of transmit antennas can be even greater, as the inter-element distance approaches zero.

This paper presents a large-system analysis of the performance of joint channel estimation, multiuser detection, and per-user decoding (CE-MUDD) for randomly-spread multiple-input multiple-output (MIMO) direct-sequence code-division multiple-access (DS-CDMA) systems. A suboptimal receiver based on successive decoding in conjunction with linear minimum mean-squared error (LMMSE) channel estimation is investigated. The replica method, developed in statistical mechanics, is used to evaluate the performance in the large-system limit, where the number of users and the spreading factor tend to infinity while their ratio and the number of transmit and receive antennas are kept constant. The performance of the joint CE-MUDD based on LMMSE channel estimation is compared to the spectral efficiencies of several receivers based on one-shot LMMSE channel estimation, in which the decoded data symbols are not utilized to refine the initial channel estimates. The results imply that the use of joint CE-MUDD significantly reduces rate loss due to transmission of pilot signals, especially for multiple-antenna systems. As a result, joint CE-MUDD can provide significant performance gains, compared to the receivers based on one-shot channel estimation.

The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of input alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

There are a number of corrections for the above titled paper (ibid., vol. 58, no. 3, pp. 1413-1440, Mar. 2012). They are presented here.

A novel signaling scheme for iterative channel estimation and data decoding is proposed. In the proposed scheme, the occurrence probability of transmitted symbols is biased. A priori information about the bias is utilized for the initial channel estimation. The proposed scheme is based on parallel concatenation of two biased convolutional codes (BCCs), which are constructed as systematic recursive convolutional codes with state-dependent puncturing. The BCCs can be regarded as a joint coding scheme that determines the insertion positions of pilot symbols according to information bits. The proposed scheme is numerically shown to outperform conventional pilot-based schemes in the waterfall region, while it is inferior to the conventional schemes in the error-floor region.

This paper studies the design of random code-division multiple-access (CDMA) with continuous-time constant envelope. The proposed scheme is compatible with linear CDMA and allows for standard methods of linear multiuser detection while avoiding phase jumps at all times. The proposed algorithm finds a set of spreading waveforms with approximately rectangular power spectral density and stop-band attenuation of more than 60 dB at exactly constant envelope. Alternatively, the algorithm can provide perfect stop-band attenuation at a peak-to-average power ratio of 0.04 dB at spreading factor 512.

In this work an opportunistic scheduling scheme is presented and analyzed for a multiuser system. The objective of the proposed scheme is to minimize the system transmit energy in the presence of a hard deadline delay constraint for the individual packets. In the large system limit, the scheme is modeled and analyzed in the scenario when arriving packets have associated deadlines which vary from packet to packet. We introduce transmission thresholds that depend on channel quality and number of time slots left before a packet reaches its hard deadline. These thresholds are optimized such that they reflect the interaction of deadline delay and channel variation, and result in a minimum system energy. The results demonstrate the saving in energy for a system where the applications have individual packet deadline delay constraints.

In this work, an opportunistic scheduling scheme for a large multiuser system is proposed. A group of users with good channels are scheduled simultaneously for data transmission and separated by means of superposition coding. The proposed scheduling scheme is analyzed in the large system limit. Random packet arrivals are modeled as constant arrivals with random content size. Transmission thresholds are optimized in such a way that the system energy is minimized while obeying a strict upper bound on the packet delay. We find that the state space representations of systems with either constant or random arrivals are equivalent. Thus, the thresholds optimized for constant arrivals in earlier work are valid for systems with random arrivals as well. Furthermore, we address the option of intentional packet dropping and the trade-off between packet drop rate and required system energy.

In this paper, we investigate the spectral efficiency of vector precoding with minimum mean square error (MMSE) linear preprocessing. We restrict the discussion to the spectral efficiency of MMSE vector precoding with quadrature phase-shift keying (QPSK) signaling. Spectral efficiency is investigated by numerical simulations, and plotted as a function of the energy per bit divided by the noise spectral density Eb/N0. The optimum system load α, given as the ratio of the number of transmit and receive antennas, that maximizes spectral efficiency is obtained. Previously obtained spectral efficiency results for: Dirty paper coding (DPC), linear zero forcing (ZF), ZF vector precoding, and linear MMSE precoding are provided for comparison. We quantify the performance enhancement that MMSE vector precoding obtains in comparison to vector precoding with ZF linear preprocessing, in the low to medium Eb/N0region. We also find that MMSE vector precoding does not significantly outperform its linear counterpart.

The large system analysis of randomly spread MIMO DS-CDMA systems is provided. Correlated Rayleigh fading MIMO channels are assumed for all users. Linear multiuser detection with separate decoding and pilot-aided channel estimation are used. The results imply that with channel estimation, the performance can improve significantly as the correlation between the transmit antennas increases. No channel information at the transmitter is required, but the channel estimator needs knowlegde of the long term transmit correlation in advance. The numerical results demonstrate that in a 4 × 4 MIMO DS-CDMA system with two users per chip, high antenna correlation at the transmitter can double the ergodic spectral efficiency compared to the case of uncorrelated transmit antennas.

In this paper we propose a modification of the Hopfield neural networks for vector precoding, based on Lenstra, Lenstra, and Lovasz lattice basis reduction. This precoding algorithm controls the energy penalty for system loads α = K/N close to 1, with N and K denoting the number of transmit and receive antennas, respectively. Simulation results for the average transmit energy as a function of α show that our algorithm improves performance within the range 0.9 ≤ α ≤ 1, between 0.4 dB and 2.6 dB in comparison to standard HNN precoding. The proposed algorithm performs close to the sphere encoder (SE) while requiring much lower complexity, and thus, can be applied as an efficient suboptimal precoding method.

A Rayleigh block-fading multiple-input multiple-output (MIMO) channel with channel state information (CSI) available neither to the transmitter nor to the receiver is considered. A lower bound on the capacity is formulated based on a successive decoding (SD) scheme. An analytical expression of the lower bound is derived in the large-system limit, by using the replica method. Furthermore, the achievable rate of the linear minimum mean-squared error (LMMSE) receiver with SD is also evaluated in the large-system limit. The lower bound is superior to the lower bound derived by Hassibi and Hochwald for all signal-to-noise ratios (SNRs).

Spectral efficiency for asynchronous code division multiple access (CDMA) with random spreading is calculated in the large system limit allowing for arbitrary chip waveforms and frequency-flat fading. Signal-to-interference and noise ratios (SINRs) for suboptimal receivers, such as the linear minimum mean square error (MMSE) detectors, are derived. The approach is general and optionally allows even for statistics obtained by undersampling the received signal. All performance measures are given as a function of the chip waveform and the delay distribution of the users in the large system limit. It turns out that synchronizing users on a chip level impairs performance for all chip waveforms with bandwidth greater than the Nyquist bandwidth, e.g., positive roll-off factors. For example, with the pulse shaping demanded in the UMTS standard, user synchronization reduces spectral efficiency up to 12% at 10 dB normalized signal-to-noise ratio. The benefits of asynchronism stem from the finding that the excess bandwidth of chip waveforms actually spans additional dimensions in signal space, if and only if the users are desynchronized at chip-level. The analysis of linear MMSE detectors shows that the limiting interference effects can be decoupled both in the user domain and in the frequency domain such that the concept of effective interference spectral density arises. This generalizes and refines Tse and Hanly's concept of effective interference. In Part II, the analysis is extended to any linear detector that admits a representation as multistage detector and guidelines for the design of low complexity multistage detectors with universal weights are provided.

Totally asynchronous code-division multiple-access (CDMA) systems are addressed. In Part I, the fundamental limits of asynchronous CDMA systems are analyzed in terms of spectral efficiency and SINR at the output of the optimum linear detector. The focus of Part II is the design of low-complexity implementations of linear multiuser detectors in systems with many users that admit a multistage representation, e.g., reduced rank multistage Wiener filters, polynomial expansion detectors, weighted linear parallel interference cancellers. The effects of excess bandwidth, chip-pulse shaping, and time delay distribution on CDMA with suboptimum linear receiver structures are investigated. Recursive expressions for universal weight design are given. The performance in terms of SINR is derived in the large-system limit and the performance improvement over synchronous systems is quantified. The considerations distinguish between two ways of forming discrete-time statistics: chip-matched filtering and oversampling.

We address the possibility of overloaded vector precoding in single user MIMO channels, i.e. the number of data streams is larger than the minimum of the number of antennas at transmitter and receiver side.We find that the convex vector precoding introduced in [1] allows for overloading while, with a certain probability, keeping the received signal free of interference. We find that the probability that overloading is not possible decays exponentially with the size of the system as long as the number of data streams is less than twice the minimum number of antennas. We give an explicit formula to calculate this probability for any antenna configuration in presence of correlated Rayleigh fading. Although overloading comes with the need for increased transmitted power, we show by means of the replica method that overloading up to 22% yields better spectral and power efficiency than without overload and spatial matched filter processing at the receiver.

This paper proposes a low-complexity two-dimensional channel estimator for MIMO-OFDM systems derived from a time-frequency variant channel estimator previously proposed. The estimator exploits both time and frequency correlations of the wireless channel via use of Slepian-basis expansions. The computational saving comes from replacing a two-dimensional Slepian-basis expansion with two serially-concatenated one-dimensional Slepian-basis expansions. Performance in terms of normalized mean square error (NMSE) vs. signal-to-noise ratio (SNR) have been analyzed via numerical simulations and compared with the original estimator. The analysis of the performance takes into account the impact of both system and channel parameters.

This paper studies large randomly spread direct-sequence code-division multiple-access system operating over a block fading multipath channel. Channel knowledge is obtained by a linear estimator whose initial decisions are iteratively refined by using a soft feedback from the single-user decoders. In addition to the traditional training symbol based signaling scheme, we study a novel method that utilizes a random bias in the symbol probabilities of the transmitted signal to construct the initial channel estimates. The numerical results suggest that in the large system limit, appropriate selection of the channel code and signaling method allows for successful communication with vanishing training overhead in overloaded systems if iterative channel and data estimation is performed at the receiver.

We propose a randomly-biased quadrature phase shift keying (QPSK) signaling scheme for a noncoherent Rayleigh block-fading multiple-input multiple-output (MIMO) channel. In order to optimize a prior of bias, we evaluate a lower bound of the spectral efficiency of the noncoherent MIMO channel with randomly-biased QPSK signaling in the large-system limit, by using the replica method. Our main result is that randomly-biased QPSK signaling with vanishing bias is optimal in the large-system limit for any signal-to-noise ratio.

The large system analysis of a randomly spread direct-sequence code-division multiple-access system operating over a frequency-selective fading channel is considered. Iterative multiuser detection and decoding based on generalized posterior mean estimation and interference cancellation is assumed. The channel is mismatched and provided by a linear estimator whose initial pilot-based decisions are iteratively refined by using a feedback from the single-user decoders. By an application of the replica method, a tool from statistical physics, and density evolution with Gaussian approximation, we show that the performance metrics of the considered multiuser system converge in distribution at the large system limit to that of a simple single-user system operating over a flat fading channel. We also give the exact result of the hard decision feedback based channel estimator analyzed approximately by Li et al. (2007).

We propose a novel signaling scheme for wireless communication systems without channel state information (CSI). In that scheme, a bias of the occurrence probabilities of constellation points is utilized as pilot information known to the receiver, whereas pilot signals known to the receiver are sent in conventional pilot-based approaches. We evaluate the performance of the new scheme and conventional pilot-based schemes for a large direct-sequence code-division multiple-access (DS-CDMA) system, by using the replica method. It is shown that the new scheme outperforms the conventional pilot-based scheme when the amount of pilot information is large.

We study the spectral efficiency of large random direct-sequence code-division multiple-access systems utilizing linear minimum mean square error (LMMSE) channel estimation and iterative multiuser detection and decoding (MUDD). Iterative MUDD based on non-linear data estimation and single-user decoding is considered as a benchmark for the more practical iterative LMMSE data estimator with soft parallel interference cancellation. The results showed that the channel parameters and the choice of error correction code have a great impact on the achievable spectral efficiency. It was also found that for the considered setups, the iterative LMMSE based channel estimator is near optimal for slowly time-varying multipath fading channels.

This paper aims at validation of an iterative receiver for multiple-input multiple-output with orthogonal frequency division multiplexing (MIMO-OFDM) systems using real-measurement channel data from an indoor scenario. The receiver performs iterative multi-user detection (MUD) and Channel Estimation (CE) via soft information from the single- user decoders. The channel measurements were performed for a dynamic dual MIMO link scenario. The case with two users with multiple antennas interfering each other is considered. CE at the receiver exploits the frequency correlation of the MIMO link. Simulation results for the performance are shown in terms of bit- error rate (BER) vs. signal-to-noise ratio (SNR). Performance for the whole system are provided and compared with respect to the case of perfect channel-state information (PCSI) at the receiver, as well as for the single user. We also provide an analysis of BER with respect to signal-to-interference ratio (SIR). CE performance are evaluated in terms of normalized mean square error (NMSE).

We consider impacts of channel estimation errors on performance of general multiuser detectors in MIMO DS-CDMA channels. We evaluate their performance in terms of asymptotic spectral efficiency, which is obtained via decoupling structure, by using the replica method. Numerical results imply that the performance of LMMSE detection is very close to that of MMSE detection for small system loads. Furthermore, we find that the spectral efficiency of MMSE detection grows discontinuously with the length of pilot sequences for large system loads, and that the critical length is close to the optimal length. While it is indistinguishable from that of LMMSE detection for short pilot sequences, the gap between the two is significantly large if the length of pilot sequences is longer than the critical length.

Multiuser diversity scheduling is studied in a single cell system with a limited scatterers channel. The scheduler implements the proportional fairness algorithm with infinite time constant, serving at each scheduling instant the user with the maximum short term fading coefficient. The limits of multiuser diversity gains due to the bounded support of the limited scatterers channel are explored by evaluating the average system capacity and the corresponding required transmitted energy per transmitted bit. The bounded support of the limited scatterers channel results in a capacity saturation as user population size grows even though the number of channel scatterers - the channel richness - is assumed to grow proportionally with the number of users.

Recently Muller et al. (IEEE J. Select. Areas Commun. 2008) used asymptotic methods from statistical physics to analyze non-linear vector precoding for MIMO broadcast channels. They proposed to extend BPSK input alphabets onto both real and complex supersets of the original constellation points. They showed that, as the optimization space is greater, lower energies are achieved when the extended alphabets are complex. In this work we use similar asymptotic methods and propose an alternative channel inversion technique which makes purely real alphabets perform as well as their complex extensions, which results in reduced complexity in the optimization process.

This paper studies a nonlinear vector precoding scheme which inverts the wireless multiple-input multiple-output (MIMO) channel at the transmitter so that simple symbol-by-symbol detection can be used in lieu of sophisticated multiuser detection at the receiver. In particular, the transmit energy is minimized by relaxing the transmitted symbols to a larger alphabet for precoding, which preserves the minimum signaling distance. The so-called replica method is used to analyze the average energy savings with random MIMO channels in the large-system limit. It is found that significant gains can be achieved with complex-valued alphabets. The analysis applies to a very general class of MIMO channels, where the statistics of the channel matrix enter the result via the R-transform of the asymptotic empirical distribution of its eigenvalues. Moreover, we introduce polynomial-complexity precoding schemes for binary and quadrature phase-shift keying in complex channels by using convex rather than discrete relaxed alphabets. In case the number of transmit antennas is more than twice the number of receive antennas, we show that a convex precoding scheme, despite its polynomial complexity, outperforms NP-hard precoding using the popular Tomlinson-Harashima signaling.

A linear channel estimator for multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO- OFDM) systems, based on a two-dimensional Slepian expansion, is presented. The estimator is meant to be part of an iterative receiver. We consider both estimation based on pilots only and on pilots and data, the latter considered as a reference for the case when feedback from decoders is exploited. Performances are analyzed via computer simulations comparing the relative minimum square error (RMMSE) of an analogous one-dimensional estimator and the proposed extension.

We consider a new concept of a multiple-input-multiple-output (MIMO) receiver which uses one active receiving antenna and multiple parasitic elements. The parasitic elements give the possibility of creating a directive antenna beam which is rotated 360 degrees around within the duration of a symbol period. The received signal which is accessed at the antenna connector of the active antenna is expanded in frequency bandwidth compared to the transmitted signal. We show that each sub-band of the received signal consists of linearly independent combinations of the transmitted signals, and thus we have obtained a MIMO receiver. We give a few examples on how to implement this receiver and also explain the effects of sampling the wave-field at discrete angular directions.

This paper presents an iterative receiver for Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems over time-variant wireless channels. The receiver performs joint decoding, channel estimation, and multiuser detection, with soft information iteratively provided by the single-user decoders. Time-variance is effectively taken into account exploiting the properties of the Discrete Prolate Spheroidal (DPS) sequences, being the bandlimited sequences with maximum energy concentration in time. Turbo codes are used for each transmit antenna, thus the receiver presents an iterative structure also in the single-user case. Simulation results for the performance are presented in terms of Bit Error Rate (BER) and Normalized Mean Square Error (NMSE) vs Signalto- Noise Ratio (SNR). The effects of the number of external and internal iterations as well as the number of pilots on the performance of the system are investigated.

This paper presents an iterative receiver for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The receiver performs channel estimation and multi-user detection, with soft information iteratively provided by the single-user decoders. Time- variance is effectively taken into account exploiting the properties of the discrete prolate spheroidal (DPS) sequences. Simulation results for the performance are presented in terms of bit error rate (BER) vs signal-to-noise ratio (SNR), showing how the single-user bound (SUB) is approached in a few iterations.

A power optimal scheduling algorithm that guarantees desired throughput and bounded delay to each user is developed for fading multi-access multi-band channels that can model many important practical systems including OFDM system and flat and frequency selective multi-access channels. The optimization is over the joint space of all rate allocation and coding strategies. The proposed scheduling assigns rates on each band based only on the current system state, and subsequently uses optimal multi-user signaling to achieve these rates. The scheduling is computationally simple, and hence scalable. Due to uplink-downlink duality, all the results extend in straightforward fashion to the broadcast channels.

We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization (i) 2-point lattice pre-coding and (ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.

The design and analysis of multistage detectors with universal weights for asynchronous CDMA systems is presented. The use of a front-end that enables joint detection and provides sufficient statistics is proposed. With such a front end the proposed multistage detector has the same complexity order per bit as the matched filter. The proposed approach can also take into account other suboptimum statistics and the non-ideality of the chip pulse waveforms. In such a way, the universal weights can be designed and the performance can be computed for very realistic scenarios.

We consider a wireless communication system formed by a single cell with one base station and K user terminals. User channels are characterized by frequency-selective fading due to small-scale effects, modeled as a set of M parallel block-fading channels, and a frequency-flat distance-dependent path loss. We compare delay-limited systems with variable-rate systems under fairness constraints, in terms of the achieved system spectral efficiency C (bit/s/Hz) versus Eb/N0. The considered delay-limited systems impose "hard-fairness": every user transmits at its desired rate on all blocks, independently of its fading conditions. The variable-rate system imposes "proportional fairness" via the popular Proportional Fair Scheduling (PFS) algorithm, currently implemented in 3G wireless for data (delay-tolerant) applications. We find simple iterative resource allocation algorithms that converge to the optimal delay-limited throughput for orthogonal (frequency-division multiple access (FDMA)/time-division multiple access (TDMA)) and optimal (superposition/interference cancellation) signaling. In the limit of large K and finite M we find closed-form expressions for C as a function of Eb/N0. We show that in this limit, the optimal allocation policy consists of letting each user transmit on its best subchannel only. Also, we find a simple closed-form expression for the throughput of PFS in a cellular environment, that holds for any K and M. Finally, we obtain closed-form expressions for C versus Eb/N0in the low and high spectral efficiency regimes. The conclusions of our analysis in terms of system design guidelines are as follows: a) if hard fairness is a requirement, orthogonal access incurs a large throughput penalty with respect to the optimal (superposition coding) strategy, especially in the regime of high spectral efficiency; b) for high spectral efficiency, PFS does not provide any significant gain and may even perform worse than the optimal delay-limited system, despite the fact that the imposed fairness constraint is laxer; c) for low to moderate spectral efficiency, the stricter hard-fairness constraint incurs in a large throughput penalty with respect to PFS

This correspondence analyzes the behavior of code-division multiple-access (CDMA) systems with correlated spatial diversity. The users transmit to one or more antenna arrays. The centralized receiver employs a linear multiuser detector. We derive the performance of a large system with random spreading sequences and weak assumptions on the flat-fading channel gains—the fading may be correlated and contain line-of-sight components. We show that, as the number of users and the spreading factor grow large with fixed ratio, the performance of the system is fully characterized by a square matrix with size equal to the number of receiving antennas and multiuser efficiencies are not identical for all users. Our general result includes the analysis of CDMA systems with spatial diversity discussed by Hanly and Tse ('01) for independent channel gains in case of both micro-diversity and macro-diversity and provides a rigorous proof for the macro-diversity case missing in their work. We also show that to any scenario with correlated Rayleigh fading, there exists a macro-diversity scenario with independent Rayleigh fading which is characterized by the same signal-to-interference-and-noise ratio (SINR). Furthermore, sufficient conditions are given which force the multiuser efficiencies of all users to become identical also in case of statistically dependent channel gains.

We consider the uplink and the downlink of a multiuser wireless system with one base station and K user terminals (single-cell case). Each user is affected by a position-dependent path loss, fixed in time, and by a slowly time-varying frequency-selective fading channel modeled as M parallel block-fading channels. We study the system throughput (sum rate) versus Eb/N0under hard fairness and proportional fairness constraints. We obtain closed-form expressions for the throughput in the limit of a large number of users, as well as for the asymptotics in the low and high SNR regions

The large system performance analysis of linear multiuser detectors (e.g. MMSE, MSWF, multistage detectors) for asynchronous CDMA systems is provided. While the performance of synchronous systems with square-root waveforms is independent of the chip bandwidth, the performance of asynchronous systems depends on the pulse shape and the bandwidth. It increases as the bandwidth increases beyond half on the chip rate and, in such a case, asynchronous systems outperform the synchronous ones.

Joint time-variant channel estimation and multi-user detection are key building-blocks for wireless broadband communication for mobile users at vehicular speed. We propose an iterative receiver for a multi-carrier (MC) code division multiple access (CDMA) system in the uplink. Multi-user detection is implemented through iterative parallel interference cancellation and conditional linear minimum mean square error (MMSE) filtering. MC-CDMA is based on orthogonal frequency division multiplexing (OFDM), thus time-variant channel estimation can be performed for every subcarrier individually. The variation of a subcarrier over the duration of a data block is upper bounded by the maximum Doppler bandwidth which is determined by the maximum velocity of the users. We exploit results from the theory of time-concentrated and bandlimited sequences and apply a Slepian basis expansion for time-variant subcarrier estimation. This approach enables time-variant channel estimation without complete knowledge of the second-order statistics of the fading process. The square bias of the Slepian basis expansion is one order of magnitude smaller compared to the Fourier basis expansion. The square bias of the basis expansion is the determining factor for the performance of the iterative joint channel estimation and data detection. We present an iterative linear MMSE estimation algorithm for the basis expansion coefficients in a multi-user system. The consistent performance of the iterative receiver using the Slepian basis expansion is validated by simulations for a wide range of velocities

We determine the maximum transport capacity of a Gaussian broadcast channel and of a Gaussian multiple access channel. Transport capacity is defined as the sum, over all simultaneous transmissions, of the product of the transmission rate with a reward r(x), where x is the distance between the receiver and the transmitter. In the case of the broadcast channel, the optimization is performed over all allocations of the transmitter power to the signals intended for the different receivers. In the case of the multiple access channel, the optimization is performed over all allocations of power at the transmitters that satisfy a sum constraint. Our approach is to assume a large number of receivers (or transmitters) and formulate the problem within the framework of the calculus of variations

We consider the uplink and the downlink of a multiuser wireless system with one base station and K user terminals. We model wideband transmission by considering M parallel subchannels, each of which is affected by fading. The fading processes in each subchannel are slowly time-varying with respect to the coding block length. Hence, in order to maintain given rate requirements for each user and each channel state, power control is used. We study the delay-limited achievable sum rate (throughput) versus the system E/sub b//N/sub O/, under orthogonal and optimal signaling. We show that for both the orthogonal and the optimal schemes, in the limit of large K and finite M, the optimal allocation strategy consists of allocating each user to its best subchannel only. Hence, we are able to quantify the multiuser diversity gain by comparing the case K /spl rarr/ /spl infin/ with the single-user delay-limited case. Finally, we show that the limits of optimal signaling can be approached by relatively simple convolutional codes and iterative joint multiuser decoding with appropriate power control. The proposed scheme can be regarded as a practical version of the optimal successive decoding approach, that mitigates the error propagation due to the suboptimality of the user channel codes.

We study the transport capacity of a Gaussian multiple access channel, which consists of a set of transmitters and a single receiver. The transport capacity is defined as the sum, over all transmitters, of the product of the transmission rate with a reward r(x), which is a function of the distance x between the transmitter and the receiver, and quantifies the usefulness of the transmitting information over a distance x. Assuming that the sum of the transmitter powers is upper bounded, we present in closed form the optimal power allocation among the transmitters, that maximizes the transport capacity. We then present simple expressions for the optimal power allocation and induced transport capacity, as the number of transmitters approaches infinity. We also study the transport capacity of a Gaussian broadcast channel, which consists of a single transmitter and multiple receivers. Here, the transport capacity is defined as the sum, over all receivers, of the product of the transmission rate with a reward r(x). We determine in closed form the maximum possible transport capacity and the distribution of the available transmitter power among the receivers that achieve it. Although this result has already been reported in the literature, our derivation is shorter, and leads to simpler expressions. Our results can be used to gain intuition and develop good design principles in a variety of settings. For example, they apply to the uplink and downlink channel of cellular networks, and also to sensor networks which consist of multiple sensors that communicate with a single central station.

We consider linear multistage detectors with universal (large system) weighting for synchronous code-division multiple access (CDMA) in multipath fading channels with many users. A convenient choice of the basis of the projection subspace allows a joint projection of all users. Taking advantage of this property, the complexity per bit of multistage detectors with universal weights scales linearly with the number of users on the uplink CDMA channel, while other known multistage detectors with universal weights and different bases of the projection subspace keep the same quadratic complexity order per bit as the linear minimum mean-square error (LMMSE) detector. We focus on the design of two kinds of detectors with linear complexity. The detector of Type I is obtained as an asymptotic approximation of the polynomial expansion detector proposed by Moshavi et al. The detector of Type II has the same performance as the multistage Wiener filter (MSWF) in large systems. Additionally, general performance expressions for large systems, applicable to any multistage detector with the same basis of the projection subspace (e.g., linear parallel interference canceling detectors), are derived. As a by-product, the performance analysis disproves the widespread belief that the MSWF and the polynomial expansion detector are equivalent. We show that, in general, the MSWF outperforms the latter one and they are equivalent only asymptotically in the case of equal received powers.

We devise theoretical grounds for constructing channel models for multiple-input multiple-output (MIMO) systems based on information-theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we give here has already been fruitfully explored with success in the context of Bayesian spectrum analysis and parameter estimation. For each channel model, we conduct an asymptotic analysis (in the number of antennas) of the achievable transmission rate using tools from random matrix theory. A central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations. The results are useful both in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks.

In this work we compare the channel estimation algorithms for use in an iterative CDMA receiver in a block fading environment. The receiver consists of a soft multiuser data estimator, a bank of single user decoders, und a multiuser channel estimator. The multiuser data estimator is implemented as parallel interference canceler with unconditional post-MMSE filtering (PIC-MMSE) and the decoder is a soft-in soft-out MAP decoder. In the channel estimator we make use of dedicated pilot symbols and fed back soft-code symbols which are exploited as additional soft pilot symbols when the iterations proceed. We show that using extrinsic information increases the receiver performance significantly compared to using a posteriori information in the feedback for channel estimation. We introduce a linear MMSE (LMMSE) estimator which takes into account the variances of fed back code symbols and compare it to approximations of the least-squares (ALS) estimator and the linear minimum-mean-square-error (ALMMSE) estimator. Performance results are illustrated in terms of bit error rate (BER) and average normalized square error (ANSE) of the channel estimators. They show that the newly proposed LMMSE algorithm outperforms the ALS and ALMMSE algorithms.

The asymptotic performance of the linear MMSE detector for any finite observation window and any symbol impinging the observed signal is derived for asynchronous but chip synchronous CDMA systems with random spreading. Additionally, a multistage detector that does not suffer from windowing effects and performs as well as the correspondent detector in synchronous systems is proposed. In contrast to the synchronous case, considering a sufficient large delay, the proposed multistage detector can even outperform the full rank linear MMSE detector constrained to a finite fixed observation window.

We consider a canonical model for coded code-division multiple access (CDMA) with random spreading, where the receiver makes use of iterative belief-propagation (BP) joint decoding. We provide simple density-evolution analysis in the large-system limit (large number of users) of the performance of the BP decoder and of some suboptimal approximations based on interference cancellation (IC). Based on this analysis, we optimize the received user signal-to-noise ratio (SNR) distribution in order to maximize the system spectral efficiency for given user channel codes, channel load (users per chip), and target user bit-error rate (BER). The optimization of the received SNR distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms. Remarkably, under the optimized SNR assignment, the suboptimal minimum mean-square error (MMSE) IC-based decoder performs almost as well as the more complex BP decoder. Moreover, for a large class of commonly used convolutional codes, we observe that the optimized SNR distribution consists of a finite number of discrete SNR levels. Based on this observation, we provide a low-complexity approximation of the MMSE-IC decoder that suffers from very small performance degradation while attaining considerable savings in complexity. As by-products of this work, we obtain a closed-form expression of the multiuser efficiency (ME) of power-mismatched MMSE filters in the large-system limit, and we extend the analysis of the symbol-by-symbol maximum a posteriori probability (MAP) multiuser detector in the large-system limit to the case of nonconstant user powers and nonuniform symbol prior probabilities.

The performance loss due to separation of detection and decoding on the binary-input additive white Gaussian noise (AWGN) channel is quantified in terms of mutual information. Results are reported for both the code-division multiple-access (CDMA) channel in the large system limit and the intersymbol interference (ISI) channel. The results for CDMA rely on the replica method developed in statistical mechanics. It is shown that a previous result of Shamai and Verdu found for Gaussian input alphabet holds also for binary input alphabets. For the ISI channel, the performance loss is calculated via the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. Comparisons are made to the capacity of separate detection and decoding using suboptimum detectors such as a decision-feedback equalizer.

In iterative receiver structures, soft information becomes available after the decoding stage. This information is used to enhance the quality of the channel estimates for the next iteration. We derive a generalized estimator based on the linear minimum mean square error (LMMSE) principle for deterministic pilot information combined with soft information. We present the special case of multi-carrier code division multiple access (MC-CDMA) in detail and provide simulation results. The presented channel estimation algorithm can be also applied to direct sequence (DS)-CDMA and multiple-input multiple-output (MIMO) systems.

Multi-carrier code division multiple access (MC-CDMA) systems are under intense investigation for high bit rate wireless communications systems. Their equalization is based on the fast Fourier transform, allowing for an efficient implementation. Iterative receivers with joint detection and decoding have been shown to achieve very good performance for direct-sequence (DS)-CDMA systems. We apply this concept to MC-CDMA, the multiuser detector is implemented as parallel interference canceller with post-minimum mean squared error filtering. In this contribution a new pilot based channel estimation scheme based on random time sequences is developed. The presented simulation results for a multi path scenario show, that in a fully loaded system with 64 users the single user bound can be approached up to 1 dB. A bit error rate (BER) of 10/sup -3/ is reached already at an E/sub b//N/sub 0/ of 12 dB with a 4 state, rate 1/2 convolutional code.

In this work we provide equations to precisely calculate the asymptotic weighting of multistage detectors satisfying the individually and jointly LMMSE criteria in the projection subspace for scenarios with unequal powers. Additionally, a general expression of the SINR achievable at the filter output as system size grows large is derived. Such an equation can be applied to any multistage detector. We specialize this result to both the individually and jointly LMMSE multistage detector with asymptotic weighting. We show that the individually LMMSE detector outperforms the other detector in the case of unequal received powers while both the detectors are equivalent in the case of equal received powers.

The performance loss due to separation of detection and decoding on the binary-input Gaussian CDMA channel is calculated in the large system limit. It is shown that a previous result found for the Gaussian input alphabet holds also for the binary input alphabet.

The linear vector-valued channel x |/spl rarr/ /spl Pi//sub n/ M/sub n/x + z with z and M/sub n/ denoting additive white Gaussian noise and independent random matrices, respectively, is analyzed in the asymptotic regime as the dimensions of the matrices and vectors involved become large. The asymptotic eigenvalue distribution of the channel's covariance matrix is given in terms of an implicit equation for its Stieltjes transform as well as an explicit expression for its moments. Additionally, almost all eigenvalues are shown to converge toward zero as the number of factors grows over all bounds. This effect cumulates the total energy in a vanishing number of dimensions. The channel model addressed generalizes the model introduced Muller (see IEEE Trans. Inform. Theory) for communication via large antenna arrays to N-fold scattering per propagation path. As a byproduct, the multiplicative free convolution is shown to extend to a certain class of asymptotically large non-Gaussian random covariance matrices.

A random matrix model is introduced that probabilistically describes the spatial and temporal multipath propagation between a transmitting and receiving antenna array with a limited number of scatterers for mobile radio and indoor environments. The model characterizes the channel by its richness delay profile which gives the number of scattering objects as a function of the path delay. Each delay is assigned the eigenvalue distribution of a random matrix that depends on the number of scatterers, receiving antennas, and transmitting antennas. The model allows one to calculate signal-to-interference-and-noise ratios (SINRs) and channel capacities for large antenna arrays analytically and quantifies to what extent rich scattering improves performance.

A random matrix model is introduced that probabilistically describes the multi--path propagation between a transmitting and receiving antenna array with a limited number of scatterers for indoor environments. The model allows to analytically calculate signal--to--interference-- and--noise ratios and channel capacities for communication systems that apply, similar to the BLAST [1] proposal, antenna arrays at both ends of the wireless link to boost spectral efficiency. I.

The random matrix model for multipath propagation on the antenna array channel is generalised to decaying power delay profiles. Results are given in terms of Stieltjes transforms of the eigenvalue distributions of the channel's space-time covariance matrix.

Linear multiuser detectors for vector channels with crosstalk are approximated by weighted matrix polynomials. The weight optimization problem is overcome using convergence results from random matrix theory. The results are also extended to receivers with subsequent successive decoding. In the case of subsequent successive decoding, a novel low-complexity implementation is found for the first-order approximation that is based on matched filter banks only and does not require matrix algebra. Spectral efficiency is obtained analytically and found to be fairly close to the optimum. The paper is focussed on multiuser detection for CDMA, but the results can be easily extended to communication via antenna arrays.

Synchronous code-division multiple-access (CDMA) communication systems with randomly chosen spreading sequences and capacity-achieving forward error correction coding are analyzed in terms of spectral efficiency. Emphasis is on the penalties paid by applying single-user coding in conjunction with suboptimal multiuser receivers as opposed to optimal joint decoding which involves complexity that is exponential in the number of users times the code word length. The conventional, the decorrelating, and the (re-encoded) decorrelating decision-feedback detectors are analyzed in the nonasymptotic case for spherical random sequences. The re-encoded minimum mean-squared error (MMSE) decision-feedback receiver achieving the same performance as joint multiuser decoding for equal power users is shown to be suboptimal in the case of equal rates.

In this letter, a novel equalization algorithm applying soft-decision feedback and designed for binary transmission is introduced. In contrast to conventional decision-feedback equalization (DFE), iterations are necessary, because a simple matched filter serves as feedforward filter, which collects signal energy, but creates noncausal intersymbol interference. The rule for generating soft decisions is adapted continuously to the current state of the algorithm. In most cases, standard DFE methods are clearly outperformed. For a class of certain channel impulse responses, performance of maximum-likelihood sequence estimation is attained, in principle. The high performance of the scheme is explained using results from neural network theory.

Code-division multiple-access is a promising technique for communication systems. Many demodulation schemes have been proposed which take account of inherent multiple-access interference. In this paper, linear interference suppression as proposed by for example Madhow and Honig (194), is compared with conventional demodulation based on power-bandwidth plane. This approach is much more general than the comparison of error rates for specific scenarios as used previously. In case of interference suppression, the spectral efficiency is calculated by a combination of analysis and simulation. The coding and modulation scheme used is characterized within the power-bandwidth plane for a single-cell scenario as well as for a cellular system. In the latter case, some statements which are valid for the single-cell scenario have to be revised.

The loss due to imperfect channel estimation is derived for pilot symbol assisted binary phase-shift keying (BPSK) on fading channels with diversity. The presented approach, which holds for both narrow-band and spread spectrum communication, further provides an analytical optimization of pilot symbol spacing. The loss due to channel estimation is demonstrated to be low if the maximum Doppler frequency is significantly less than the bit rate.