Multiple-antenna Channels Research Articles

Transactions letters - Combining long-term and low-rate short-term channel state information over correlated mimo channels

A simple structure to exploit both long-term and partial short-term channel state information at the transmitter (CSIT) over a family of correlated multiple-antenna channels is proposed. Partial short-term CSIT in the form of a weighting matrix is combined with a unitary transformation based on the long-term channel statistics. The heavily quantized feedback link is directly optimized to maximize the expected achievable rate under different power constraints, using vector quantization and convex optimization techniques on a sample channel distribution. Robustness against errors in the feedback link is also pursued with tools in channel optimized vector quantization. Simulations indicate the benefits of the proposed scheme.

Performance Analysis of Multiuser Diversity under Transmit Antenna Correlation

In this paper, we investigate the effect of spatial correlation on throughput performance of downlink multi-antenna transmission schemes exploiting multiuser diversity, in which partial channel information such as signal-to-interference plus noise power ratio (SINR) is available at the transmitter. The asymptotic analysis is performed based on the extreme value theory. From this analysis, we demonstrate that the throughput optimal transmission scheme depends on the degree of the antenna correlation and the operating SNR. Especially, the multiuser spatial multiplexing known as the asymptotically optimal transmission scheme is no longer optimal in highly correlated multiple antenna channels.

MIMO capacity and multipath scaling in ultra-wideband channels

Generalising previous results for narrowband multiple-antenna channels, a quadratic growth in multipath with the array size is reported for ultra-wideband indoor channels, based on experimental analysis. It is shown that the observed increase in multipath is sufficient to guarantee multiple-antenna capacity growth linearly with the array size, facilitating multi-gigabit future wireless systems.

Transmitter Layering for Multiuser MIMO Systems

A novel structure for multiple antenna transmissions utilizing space-time dispersion is proposed, where the original data stream is divided into substreams which are modulated onto all available transmit antennas using stream-specific transmit signature sequences. In order to achieve this, the transmit antennas are partitioned into groups of antennas, called partitions. The signals from the data streams are independently interleaved by partition over the entire transmission frame. The interleaved partitions are then added over all substreams prior to transmission over the MIMO channel. At the receiver, a low-complexity iterative detector adapted from recent CDMA multiuser detection research is used. It is shown that with careful substream power assignments this transmission methodology can efficiently utilize the capacity of rank-deficient channels as it can approach the capacity limits of the multiple antenna channel closely over the entire range of available signal-to-noise ratios and system sizes. This transmission methodology and receiver structure are then applied to multiuser MIMO systems where several multiple antenna terminals communicate concurrently to a joint receiver. It is shown that different received power levels from the different MIMO terminals can be beneficial and that higher spectral efficiencies can be achieved than in the single-terminal case.

Delay-limited capacity: multiple antennas, moment constraints, and fading statistics

Different performance measures are an important mean in order to analyze and design wireless communications systems. Examples of common performance measures are the ergodic capacity, the outage capacity, and the average mean-square error (MSE). In this work, we study the delay-limited capacity (DLC). The DLC depends on the properties of the fading channel, e.g. on the spatial correlation and on the line-of-sight (LOS) component. In this letter, we derive the DLC for the general class of parallel fading channels, including the multiple antenna channels under moment and long-term power constraint. We prove that the DLC is Schur-concave with respect to the spatial correlation in single-input multiple-output (SIMO), and multiple-input single-output (MISO). Bounds for the DLC of multiple-input multiple-output (MIMO) and parallel fading channels are derived and the impact of the the mean component and spatial correlation on these bounds is characterized.

Optimization-Theoretic Analysis of Stability-Optimal Transmission Policy for Multiple-Antenna Multiple-Access Channel

The philosophy of scheduler design in modern wireless data networks exposes the tendency towards layer-spanning optimization (cross-layer design). An important particular goal of joint design of the physical and (data) link layer appears to be the achievement of the entire stability region of the network. In this work, we provide the optimization-theoretic analysis of the corresponding policy, referred to as stability-optimal policy, in the multiple-antenna multiple-access channel. We characterize some useful features of the policy. In particular, we state the conditions for optimality of link subset transmission and expose essential differences to the established scheduling approaches, such as sum-rate maximization. This further allows for the statement of necessary and sufficient conditions for the overall stability optimality of successive interference cancellation order. Finally, we present the approach of splitting of the multilink stability problem into the set of single-link optimization problems. We propose a corresponding iterative optimization method, which is an extension of the known concept of iterative waterfilling from

Accurate Approximation of QAM Error Probability on Quasi-Static MIMO Channels and Its Application to Adaptive Modulation

An accurate approximation for the conditional error probability on quasi-static multiple-input multiple-output (MIMO) antenna channels is proposed. For a fixed channel matrix, it is possible to accurately predict the performance of quadrature amplitude modulations (QAM) transmitted over the MIMO channel in presence of additive white Gaussian noise. The tight approximation is based on a simple Union bound for the point error probability in the n-dimensional real space. Instead of making an exhaustive evaluation of all pairwise error probabilities (intractable in many cases), a Pohst or a Schnorr-Euchner lattice enumeration is used to limit the local theta series inside a finite radius sphere. The local theta series is derived from the original lattice theta series and the point position within the finite multidimensional QAM constellation. In particular, we take into account the number of constellation facets (hyperplanes) that are crossing the sphere center. As a direct application to the accurate approximation for the conditional error probability, we describe a new adaptive QAM modulation for quasi-static multiple antenna channels

Outage Capacity of Spatially Correlated Multipath Fading Channels

In this paper, we study the effect of the scattering environment on the capacity of a single carrier linear modulation used in a multipath, multiple antenna channel. The work incorporates detailed 3D geometric channel models to assess the effect of spatial correlation. The analysis techniques, based on the pioneering work of Hirt and Massey (1988), provide a method to evaluate outage capacity. Channels that are derivatives of the ETSI standard hilly terrain and typical urban are considered in detail. The results quantify the loss of capacity produced by higher spatial correlation. When comparing signals of different bandwidth, wideband systems produce more diversity due to better temporal resolution. Surprisingly, narrowband systems gain some diversity back by being less susceptible to loss of diversity from spatial correlation

Achieving the Optimal Diversity-Versus-Multiplexing Tradeoff for MIMO Flat Channels With QAM Space–Time Spreading and DFE Equalization

The use of multiple transmit (Tx) and receive (Rx) antennas allows to transmit multiple signal streams in parallel and hence to increase communication capacity. We have previously introduced simple convolutive linear precoding schemes that spread transmitted symbols in time and space, involving spatial spreading, delay diversity and possibly temporal spreading. In this paper we show that the use of the classical multiple-input-multiple-output (MIMO) decision feedback equalizer (DFE) (but with joint detection) for this system allows to achieve the optimal diversity-versus-multiplexing tradeoff introduced in Zheng and Tse, Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels, IEEE Trans. Inf. Theory, May 2003, when a minimum mean squared error (MMSE) design is used. One of the major contributions of this work is the diversity analysis of a MMSE equalizer without the Gaussian approximation. Furthermore, the tradeoff is discussed for an arbitrary number of transmit and receive antennas. We also show the tradeoff obtained for a MMSE zero forcing (ZF) design. So, another originality of this paper is to show that the MIMO optimal tradeoff can be attained with a suboptimal receiver, in this case a DFE, as opposed to optimal maximum likelihood sequence estimation (MLSE)

Spectrally efficient differential space-time coding using non-full-diverse constellations

In this paper, a method is proposed to construct spectral-efficient unitary space–time codes for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods, which are designed to maximize the diversity product (the minimum determinant distance), our objective is to increase the spectral efficiency. The simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the existing alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum-likelihood decoding algorithm. Also, we demonstrate that similar ideas can be applied for designing codes for more than two transmit antennas. As an example, we present a construction for a 4 $times$ 4 unitary constellations which has a good performance, as compared with the other known codes.

Impact of signal constellation expansion on the achievable diversity of pragmatic bit-interleaved space-time codes

This letter studies the effect of signal constellation expansion on the achievable diversity of pragmatic bit-interleaved space-time codes in quasistatic multiple antenna channels. Signal constellation expansion can be obtained either by increasing the size of the constellation in the complex plane or by using multidimensional linear mappings. By means of two simple constructions, we provide a comparison of the two options with message passing decoding. We show that multidimensional expansion achieves some performance advantage over complex-plane expansion at the cost of significantly higher decoding complexity and larger peak-to-average power ratio of the transmitted signals.

An induced additive-noise model for memoryless Rayleigh-fading channels

This correspondence investigates a noncoherent discrete-time memoryless Rayleigh-fading channel. A logarithmic transform converts it into an induced channel with additive noise that is independent of the channel input. From this perspective, it is natural and convenient for us to revisit several known results and gain new insights. In particular, we specify a class of simple, log-scale uniform channel input distributions that performs well for moderate to high signal-to-noise ratio (SNR). Furthermore, a continuous-amplitude log-scale uniform distribution is asymptotically capacity-achieving in the sense that the difference between the resulting mutual information and the channel capacity approaches zero as SNR becomes large. We also extend the induced additive-noise channel approach to memoryless multiple-antenna channels possibly with transmit, but without receive, spatial correlation.

Impact of scattering on the capacity, diversity, and propagation range of multiple-antenna channels

The impact of scattering condition and array configuration on performances are inseparable in early analyses of multiple-antenna systems. An array-independent scattering model is introduced where three basic scattering mechanisms are modeled. Performance results become more intrinsic property of the scattering channel itself. For linear arrays of length L in an environment of total angle spread |Omega|, the ergodic capacity is shown to increase linearly with L|Omega| for large arrays. When antenna arrays reduce to practical sizes, the capacity scaling depends on the signal-to-noise ratio (SNR) as well. This implies that the number of antennas used should also depend on the SNR. In terms of outage capacity, the tradeoff between spatial multiplexing gain and diversity gain is shown to be very sensitive to the underlying scattering mechanisms. Finally, as |Omega| varies with the propagation range, the tradeoff among multiplexing gain, diversity gain, and propagation range is studied

Spatially correlated multiple-antenna channel capacity distributions

The capacity of multiple-input multiple-output (MIMO) wireless communication systems over spatially correlated Rayleigh distributed flat fading channels with complex Gaussian additive noise is investigated. Specifically, the probability density function of the mutual information between transmitted and received complex signals of MIMO systems is derived. Using this density the closed-form ergodic capacity (mean), delay-limited capacity, capacity variance and outage capacity formulas for spatially correlated channels are derived and then these formulas are evaluated numerically. Numerical results show how the channel correlation degrades the capacity of MIMO communication systems. It is also shown that the density of mutual information of correlated/uncorrelated MIMO systems can be approximated by a Gaussian density with derived mean and variance, even for a finite number of inputs and outputs.

The Asymptotic Capacity of Multiple-Antenna Rayleigh-Fading Channels

We consider the asymptotic behavior of the capacity of multiple-antenna Rayleigh-fading channels in the limit as the transmit and receive arrays become large. We show that the capacity converges in distribution to a Gaussian random variable, and give closed-form formulas for its mean and variance. These results enable us to derive the first asymptotic formula for outage rates, as well as a sharper estimate of the error in previously reported asymptotic formulas for ergodic capacity. Although these formulas are asymptotic, we show by simulation that they are often quite accurate, even for relatively small arrays.

Multidimensional Mappings for Iteratively Decoded BICM on Multiple-Antenna Channels

Multidimensional binary mappings for bit-interleaved coded modulations (BICMs) on ergodic multiple-antenna channels with iterative decoding are presented. After derivation of a closed-form expression for the pairwise error probability under ideal maximum-likelihood (ML) decoding, the design criterion for mapping optimization is established from the ML performance of the ideally interleaved channel. It coincides with the figure of merit derived from the genie condition when the iterative receiver converges to perfect a priori information. Multidimensional mapping constructions that exhibit high signal-to-noise ratio (SNR) gains without increasing the complexity of the a posteriori probability (APP) detection are proposed. They allow for a reduced decoding complexity as they achieve near turbo code performance with a single convolutional code.

Factor-Graph-Based Soft Self-Iterative Equalizer for Multipath Channels

We consider factor-graph-based soft self-iterative equalization in wireless multipath channels. Since factor graphs are able to characterize multipath channels to per-path level, the corresponding soft self-iterative equalizer possesses reduced computational complexity in sparse multipath channels. The performance of the considered self-iterative equalizer is analyzed in both single-antenna and multiple-antenna multipath channels. When factor graphs of multipath channels have no cycles or mild cycle conditions, the considered self-iterative equalizer can converge to optimum performance after a few iterations; but it may suffer local convergence in channels with severe cycle conditions.

On the capacity of MIMO broadcast channels with partial side information

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.

Degrees of Freedom in Multiple-Antenna Channels: A Signal Space Approach

Multiple-antenna systems that are limited by the area and geometry of antenna arrays, are considered. Given these physical constraints, the limit on the available number of spatial degrees of freedom is derived. The commonly used statistical multiple-input multiple-output (MIMO) model is inadequate. Antenna theory is applied to take into account the area and geometry constraints, and to define the spatial signal space so as to interpret experimental channel measurements in an array-independent but manageable description of the physical environment. Based on these modeling strategies, for a spherical array of effective aperture A in a physical environment of angular spread |/spl Omega/| in solid angle, the number of spatial degrees of freedom is shown to be A|/spl Omega/| for uni-polarized antennas and 2A|/spl Omega/| for tri-polarized antennas. Together with the 2WT degrees of freedom for a system of bandwidth W transmitting in an interval T, the total degrees of freedom of a multiple-antenna channel is therefore 4WTA|/spl Omega/|.

Adaptive blind estimation algorithm for OFDM-MIMO radio systems over multipath channels

This paper investigates the blind algorithm for channel estimation of Orthogonal Frequency Division Multiplexing-Multiple Input Multiple Output (OFDM-MIMO) wireless communication system using the subspace decomposition of the channel received complex baseband signals and proposes a new two-stage blind algorithm. Exploited the second-order cyclostationarity inherent in OFDM with cyclic prefix and the characteristics of the phased antenna, the practical HIPERLAN/2 standard based OFDM-MIMO simulator is established with the sufficient consideration of statistical correlations between the multiple antenna channels under wireless wideband multipath fading environment, and a new two-stage blind algorithm is formulated using rank reduced subspace channel matrix approximation and adaptive Constant Modulus (CM) criterion. Simulation results confirm the theoretical analysis and illustrate that the proposed algorithm is capable of tracking matrix channel variations with fast convergence rate and improving acceptable overall system performance over various common wireless and mobile communication links.