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In downlink multi-user beamforming, a single basestation is serving a number of users simultaneously. However, energy intended for one user may leak to other unintended users, causing interference. With signal-to-interference-plus-noise ratio (SINR) being one of the most crucial quality metrics to users, beamforming design with SINR guarantee has always been an important research topic. However, when the channel state information is not accurate, the SINR requirements become probabilistic constraints, which unfortunately are not tractable analytically for general uncertainty distribution. Therefore, existing probabilistic beamforming methods focus on the relatively simple Gaussian and uniform channel uncertainties, and mainly rely on probability inequality based approximated solutions, resulting in conservative SINR outage realizations. In this paper, based on the local structure of the feasible set in the probabilistic beamforming problem, a systematic method is proposed to realize tight SINR outage control for a large class of channel uncertainty distributions. With channel estimation and quantization errors as examples, simulation results show that the SINR outage can be realized tightly, which results in reduced transmit power compared to the existing inequality based probabilistic beamformers.

This paper investigates the problem of interference among the simultaneous multiuser transmissions in the downlink of multiple antennas systems. Using symbol level precoding, a new approach towards the multiuser interference is discussed along this paper. The concept of exploiting the interference between the spatial multiuser transmissions by jointly utilizing the data information (DI) and channel state information (CSI), in order to design symbol-level precoders, is proposed. In this direction, the interference among the data streams is transformed under certain conditions to useful signal that can improve the signal to interference noise ratio (SINR) of the downlink transmissions. We propose a maximum ratio transmission (MRT) based algorithm that jointly exploits DI and CSI to glean the benefits from constructive multiuser interference. Subsequently, a relation between the constructive interference downlink transmission and physical layer multicasting is established. In this context, novel constructive interference precoding techniques that tackle the transmit power minimization (min power) with individual SINR constraints at each user's receivers is proposed. Furthermore, fairness through maximizing the weighted minimum SINR (max min SINR) of the users is addressed by finding the link between the min power and max min SINR problems. Moreover, heuristic precoding techniques are proposed to tackle the weighted sum rate problem. Finally, extensive numerical results show that the proposed schemes outperform other state of the art techniques., Submitted to IEEE Transactions on Signal Processing

Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of interference distributions in large-scale networks modeled as point processes. Interference is a major performance-limiting factor in most wireless networks, thus it is important to characterize its statistics. Since closed-form results for the distribution of interference for such networks are only available in limited cases, it is of interest to compare network interference using stochastic orders, for two different point processes with different fading or path-loss scenarios between the interferers and the receiver. In this paper, conditions on the fading distribution and path-loss model are given to establish stochastic ordering between interferences. Moreover, Laplace functional ordering is defined between point processes and applied for comparing interference. Monte-Carlo simulations are used to supplement our analytical results. The useful applications of this research are also provided.

We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequential optimization procedures to maximize the Signal to Interference plus Noise Ratio (SINR), accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties (e.g., in terms of pulse compression and ambiguity). The presented sequential optimization algorithms, based on a relaxation method, yield solutions with good accuracy. Their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length. Finally, we evaluate the proposed techniques, by considering their SINR performance, beam pattern as well as pulse compression property, via numerical simulations.

This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the non-convex maximin optimization problem can be transformed into a quasiconvex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied via geometric programming. We also study the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, for the global power constraint scenario, although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper's CSI, we show that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at Eve in the presence of channel mismatches between the transmitters and the eavesdropper., Comment: 28 pages, 5 figures

This paper is concerned with the game theoretical approach in designing the multiuser downlink beamformers in multicell systems. Sharing the same physical resource, the base-station of each cell wishes to minimize its transmit power subject to a set of target signal-to-interference-plus-noise ratios (SINRs) at the multiple users in the cell. In this context, at first, the paper considers a strategic noncooperative game (SNG) where each base-station greedily determines its optimal downlink beamformer strategy in a distributed manner, without any coordination between the cells. Via the game theory framework, it is shown that this game belongs to the framework of standard functions. The conditions guaranteeing the existence and uniqueness of a Nash Equilibrium (NE) in this competitive design are subsequently examined. The paper then makes a revisit to the fully coordinated design in multicell downlink beamforming, where the optimal beamformers are jointly designed between the base-stations. A comparison between the competitive and coordinated designs shows the benefits of applying the former over the latter in terms of each design's distributed implementation. Finally, in order to improve the efficiency of the NE in the competitive design, the paper considers a more cooperative game through a pricing mechanism. The pricing consideration enables a base-station to steer its beamformers in a more cooperative manner, which ultimately limits the interference induced to other cells. The study on the existence and uniqueness of the new game's NE is then given. The paper also presents a condition on the pricing factors that allow the new NE point to approach the performance established by the coordinated design, while retaining the distributed nature of the multicell game.

In various applications, the effect of errors in gradient-based iterations is of particular importance when seeking saddle points of the Lagrangian function associated with constrained convex optimization problems. Of particular interest here are problems arising in power control applications, where network utility is maximized subject to minimum signal-to-interference-plus-noise ratio (SINR) constraints, maximum interference constraints, maximum received power constraints, or simultaneous minimum and maximum SINR constraints. Especially when the gradient iterations are executed in a disributed fashion, imperfect exchanges among the link nodes may result in erroneous gradient vectors. In order to assess and cope with such errors, two running averages (ergodic sequences) are formed from the iterates generated by the perturbed saddle point method, each with complementary strengths. Under the assumptions of problem convexity and error boundedness, bounds on the constraint violation and the suboptimality per iteration index are derived. The two types of running averages are tested on a spectrum sharing problem with minimum and maximum SINR constraints, as well as maximum interference constraints., Submitted to IEEE Transactions on Signal Processing

A discretized version of a continuous optimization problem is considered for the case where data is obtained from a set of dispersed sensor nodes and the overall metric is a sum of individual metrics computed at each sensor. An example of such a problem is maximum-likelihood estimation based on statistically independent sensor observations. By ordering transmissions from the sensor nodes, a method for achieving a saving in the average number of sensor transmissions is described. While the average number of sensor transmissions is reduced, the approach always yields the same solution as the optimum approach where all sensor transmissions occur. The approach is described first for a general optimization problem. A maximum-likelihood target location and velocity estimation example for a multiple node noncoherent multiple-input multiple-output (MIMO) radar system is later described. In particular, for cases with N good quality sensors with ideal signals and sufficiently large signal-to-interference-plus-noise ratio (SINR), the average percentage of transmissions saved approaches 100% as the number of discrete grid points in the optimization problem Q becomes significantly large. In these same cases, the average percentage of transmissions saved approaches (Q-1)/ Q × 100 % as the number of sensors N in the network becomes significantly large. Similar savings are illustrated for general optimization (or estimation) problems with some sufficiently well-designed sensors. Savings can be even larger in some cases for systems with some poor quality sensors.

In this paper, low-complexity joint power assignment algorithms are developed for multi-source multi-destination relay networks where multiple sources share a common relay that forwards all received signals simultaneously to destinations. In particular, we consider the following power optimization strategies: (i) Minimization of the total transmission power of the sources and the relay under the constraint that the signal-to-interference-plus-noise ratio (SINR) requirement of each source-destination pair is satisfied, and (ii) Maximization of the minimum SINR among all source-destination pairs subject to any given total power budget. Both optimization problems involve K power variables, where K is the number of source-destination pairs in the network, and an exhaustive search is prohibitive for large K. In this work, we develop a methodology that allows us to obtain an asymptotically tight approximation of the SINR and reformulate the original optimization problems to single-variable optimization problems, which can be easily solved by numerical search of the single variable. Then, the corresponding optimal transmission power at each source and relay can be calculated directly. The proposed optimization schemes are scalable and lead to power assignment algorithms that exhibit the same optimization complexity for any number (K) of source-destination pairs in the network. Moreover, we apply the methodology that we developed to solve a related max-min SINR based optimization problem in which we determine power assignment for the sources and the relay to maximize the minimum SINR among all source-destination pairs subject to any given total power budget. Extensive numerical studies illustrate and validate our theoretical developments.

This paper investigates the possibility of having convex or concave formulations of optimization problems for interference coupled wireless systems. An axiomatic framework for interference functions proposed by Yates in 1995 is used to model interference coupling in our paper. The paper shows that under certain natural assumptions, the exponential transformation is the unique transformation (up to a positive constant) for “convexification” of resource allocation problems for linear interference functions. Furthermore, it is shown that under certain intuitive assumptions, it is sufficient to check for the joint concavity (convexity) of sum of weighted functions of SINR (inverse SINR) with respect to s (p=es , where p is the power vector of the users), if we would like the resulting resource allocation problem to be concave (convex). This paper characterizes the largest class of utility functions and the largest class of interference functions (respectively), which allow a convex and concave formulation of a problem for interference coupled wireless systems. It extends previous literature on log-convex interference functions and provides boundaries on the class of problems in wireless systems, which can be algorithmically tackled by convex optimization techniques.

The employment of forward-backward (FB) processing to both batch and adaptive beamformers provides a superior performance than the forward only (FO) algorithm. Based on the finite-sample minimum variance distortionless response (MVDR) beamformer, a set of closed-form expressions for the variance of the weight vector, the output signal-to-interference-plus-noise ratio (SINR) and the mean-square error (MSE) is derived, for both FB and FO algorithms. As shown in our analysis, all errors of the FB algorithm are only approximately half of the FO case.

In this paper we aim to solve the multiuser multi-input multi-output (MIMO) downlink beamforming problem where one multi-antenna base station broadcasts data to many users. Each user is assigned multiple data streams and has multiple antennas at its receiver. Efficient solutions to the joint transmit-receive beamforming and power allocation problem based on iterative methods are proposed. We adopt the group maximum signal-to-interference-plus-noise-ratio (SINR) filter bank (GSINR-FB) as our beamformer which exploits receiver diversity through cooperation between the data streams of a user. The data streams for each user are subject to an average SINR constraint, which has many important applications in wireless communication systems and serves as a good metric to measure the quality of service (QoS). The GSINR-FB also optimizes the average SINR of its output. Based on the GSINR-FB beamformer, we find an SINR balancing structure for optimal power allocation which simplifies the complicated power allocation problem to a linear one. Simulation results verify the superiority of the proposed algorithms over previous works with approximately the same complexity., 29 pages, 7 figures

Based on worst-case performance optimization, the recently developed adaptive beamformers utilize the uncertainty set of the desired array steering vector to achieve robustness against steering vector mismatches. In the presence of large steering vector mismatches, the uncertainty set has to expand to accommodate the increased error. This degrades the output signal-to-interference-plus-noise ratios (SINRs) of these beamformers since their interference-plus-noise suppression abilities are weakened. In this paper, an iterative robust minimum variance beamformer (IRMVB) is proposed which uses a small uncertainty sphere (and a small flat ellipsoid) to search for the desired array steering vector iteratively. This preserves the interference-plus-noise suppression ability of the proposed beamformer and results in a higher output SINR. Theoretical analysis and simulation results are presented to show the effectiveness of the proposed beamformer.

Secure transmission techniques have been receiving growing attention in recent years, as a viable, powerful alternative to blocking eavesdropping attempts in an open wireless medium. This paper proposes a secret transmit beamforming approach using a quality-of-service (QoS)-based perspective. Specifically, we establish design formulations that: i) constrain the maximum allowable signal-to-interference-and-noise ratios (SINRs) of the eavesdroppers, and that ii) provide the intended receiver with a satisfactory SINR through either a guaranteed SINR constraint or SINR maximization. The proposed designs incorporate a relatively new idea called artificial noise (AN), where a suitable amount of AN is added in the transmitted signal to confuse the eavesdroppers. Our designs advocate joint optimization of the transmit weights and AN spatial distribution in accordance with the channel state information (CSI) of the intended receiver and eavesdroppers. Our formulated design problems are shown to be NP-hard in general. We deal with this difficulty by using semidefinite relaxation (SDR), an approximation technique based on convex optimization. Interestingly, we prove that SDR can exactly solve the design problems for a practically representative class of problem instances; e.g., when the intended receiver's instantaneous CSI is known. Extensions to the colluding-eavesdropper scenario and the multi-intended-receiver scenario are also examined. Extensive simulation results illustrate that the proposed AN-aided designs can yield significant power savings or SINR enhancement compared to some other methods.

This paper studies distributed optimization schemes for multicell joint beamforming and power allocation in time-division-duplex (TDD) multicell downlink systems where only limited-capacity intercell information exchange is permitted. With an aim to maximize the worst-user signal-to-interference-and-noise ratio (SINR), we devise a hierarchical iterative algorithm to optimize downlink beamforming and intercell power allocation jointly in a distributed manner. The proposed scheme is proved to converge to the global optimum. For fast convergence and to reduce the burden of intercell parameter exchange, we further propose to exploit previous iterations adaptively. Results illustrate that the proposed scheme can achieve near-optimal performance even with a few iterations, hence providing a good tradeoff between performance and backhaul consumption. The performance under quantized parameter exchange is also examined.

A simple linear precoding technique is proposed for multiple input multiple output (MIMO) broadcast systems using phase shift keying (PSK) modulation. The proposed technique is based on the fact that, on an instantaneous basis, the interference between spatial links in a MIMO system can be constructive and can contribute to the power of the useful signal to improve the performance of signal detection. In MIMO downlinks this co-channel interference (CCI) can be predicted and characterised prior to transmission. Contrary to common practice where knowledge of the interference is used to eliminate it, the main idea proposed here is to use this knowledge to influence the interference and benefit from it, thus gaining advantage from energy already existing in the communication system that is left unexploited otherwise. The proposed precoding aims at adaptively rotating, rather than zeroing, the correlation between the MIMO substreams depending on the transmitted data, so that the signal of interfering transmissions is aligned to the signal of interest at each receive antenna. By doing so, the CCI is always kept constructive and the received signal to interference-plus-noise ratio (SINR) delivered to the mobile units (MUs) is enhanced without the need to invest additional signal power per transmitted symbol at the MIMO base station (BS). It is shown by means of theoretical analysis and simulations that the proposed MIMO precoding technique offers significant performance and throughput gains compared to its conventional counterparts.

In this paper, we investigate methods for reducing the likelihood that a message transmitted between two multiantenna nodes is intercepted by an undetected eavesdropper. In particular, we focus on the judicious transmission of artificial interference to mask the desired signal at the time it is broadcast. Unlike previous work that assumes some prior knowledge of the eavesdropper's channel and focuses on maximizing secrecy capacity, we consider the case where no information regarding the eavesdropper is available, and we use signal-to-interference-plus-noise-ratio (SINR) as our performance metric. Specifically, we focus on the problem of maximizing the amount of power available to broadcast a jamming signal intended to hide the desired signal from a potential eavesdropper, while maintaining a prespecified SINR at the desired receiver. The jamming signal is designed to be orthogonal to the information signal when it reaches the desired receiver, assuming both the receiver and the eavesdropper employ optimal beamformers and possess exact channel state information (CSI). In practice, the assumption of perfect CSI at the transmitter is often difficult to justify. Therefore, we also study the resulting performance degradation due to the presence of imperfect CSI, and we present robust beamforming schemes that recover a large fraction of the performance in the perfect CSI case. Numerical simulations verify our analytical performance predictions, and illustrate the benefit of the robust beamforming schemes., 10 pages, 5 figures; to appear, IEEE Transactions on Signal Processing, 2010

In this paper, we propose algorithms to jointly optimize the multiple multiantenna relays which assist multipoint-to-multipoint communications in wireless networks. Assuming that the knowledge of the second order statistics of the channels such as covariance matrices are available, the multiple-input-multiple-output (MIMO) relays are designed using two different methods: (1) minimize the sum of the powers of the relays while fulfilling the signal-to-interference-plus-noise ratio (SINR) requirements for all destinations and (2) maximize the minimum of the SINRs of all destinations satisfying the transmit power constraint of each MIMO relay. Furthermore, considering the fact that the covariance matrices of the channels between the MIMO relays and destinations are subject to uncertainty due to feedback and quantization errors, the robust versions of the aforementioned methods based on worst-case concept are proposed. It is shown that the proposed nonrobust as well as robust designs are nonconvex optimization problems but they can be solved accurately and efficiently using the standard semidefinite relaxation and randomization techniques. Computer simulations verify the improved performance of the robust designs over nonrobust methods.

A practical approach for detecting packet-based orthogonal-frequency-division multiplexing (OFDM) signals in the presence of phase noise is presented. An OFDM packet consists of several OFDM symbols with full-pilot symbols at the beginning followed by consecutive data symbols. Based on the full-pilot OFDM symbol, a frequency-domain joint phase noise and channel vector estimator is first derived. It is shown that the phase noise vector can be estimated by maximizing a constrained quadratic form without requiring knowledge of the channel vector. This estimated phase noise vector is then used to compute the least squares channel estimator. Assuming that the channel is constant during each packet, the estimated channel is used in subsequent data OFDM symbols for equalization and data detection. Since phase noise changes from one OFDM symbol to the next, the scattered pilots in each data OFDM symbol are used to non-iteratively estimate and mitigate the phase noise induced interference. A significant improvement in the signal-to-interference-plus-noise ratio is achieved using the proposed algorithm.

In this correspondence, a novel robust adaptive beamformer is proposed based on the worst-case semi-definite programming (SDP). A recent paper has reported that a beamformer robust against large steering direction error can be constructed by using linear constraints on magnitude response in SDP formulation. In practice, however, array system also suffers from many other array imperfections other than steering direction error. In order to make the adaptive beamformer robust against all kinds of array imperfections, the worst-case optimization technique is proposed to reformulate the beamformer by minimizing the array output power with respect to the worst-case array imperfections. The resultant beamformer has the mathematical form of a regularized SDP problem and possesses superior robustness against arbitrary array imperfections. Although the formulation of robust beamformer uses weighting matrix, with the help of spectral factorization approach, the weighting vector can be obtained so that the beamformer can be used for both signal power and waveform estimation. Simple implementation, flexible performance control, as well as significant signal-to-interference-plus-noise ratio (SINR) enhancement, support the practicability of the proposed method.

The sample matrix inversion (SMI) beamformer suffers from performance degradation due to the finite sample size effect and the arrival angle mismatch problem. A simple technique to provide robustness to the conventional SMI beamformer is to block the desired signal from the received data before calculating the beamformer's weight vector, which leads to the subtraction-based SMI (S-SMI) beamformer. In this correspondence, closed-form approximations of the expected value of the signal-to-interference-plus-noise ratio (SINR) for the S-SMI beamformer and the SMI beamformer are derived, where the effect of both finite sample size and arrival angle mismatch are considered. Simulations show that the derived approximations are close enough to represent the true values of the SINR, when the sample size is small and the arrival direction mismatch exists.

We propose a novel suboptimum detection method for spatially multiplexed multicarrier code division multiplexing (SM-MC-CDM) communications. Compared to the spatially multiplexed OFDM (SM-OFDM), the frequency domain spreading in SM-MC-CDM systems results in an additional diversity gain. To take advantage of diversity and multiplexing while mitigating interference, we design a low complexity efficient detector called unified successive interference cancellation (SIC) detector for SM-MC-CDM communications. Further performance improvement is achieved by adopting in conjunction with the unified SIC the iterative subcarrier reconstruction-detection algorithm originally proposed for single antenna systems. The results demonstrate significant performance improvement over other existing methods of comparable complexity. A close approximation for the probability density function (pdf) of the proposed detector's output signal-to-interference plus noise ratio (SINR) is found and used to obtain error bounds for the bit error rate (BER). Performance of the coded SM-MC-CDM transmission is also discussed in the paper.

We introduce an iterative procedure for design of adaptive KL-variate linear beamformers that are structured as the Kronecker product of K-variate (transmit) and L-variate (receive) beamformers. We focus on MIMO radar applications for scenarios where only joint transmit and receive adaptive beamforming can efficiently mitigate multi-mode propagated backscatter interference. This is because the direction-of-departure (DoD) on one interference mode, and the direction-of-arrival (DoA) on the other, coincide with those of a target, respectively. We introduce a Markov model for the adaptive iterative routine, specify its convergence condition, and derive final (stable) signal-to-interference-plus-noise ratio (SINR) performance characteristics. Simulation results demonstrate high accuracy of the analytical derivations. In addition, we demonstrate, that for the considered class of multiple-input multiple-output (MIMO) radar interference scenarios, the diagonally loaded sample matrix inversion (SMI) algorithm provides additional performance improvement and convergence rate for this iterative adaptive Kronecker beamformer.

We characterize the complete quality-of-service (QoS) feasibility region and present a simple feasibility test for given QoS requirements in the Gaussian vector broadcast channel. While most contributions in the literature recast the QoS constraints into requirements for the signal-to-interference-and-noise ratios (SINRs), we convert them into upper bounds for the minimum mean square errors (MMSEs) instead and test feasibility in the MMSE domain. Our main contribution is a complete description of the feasible MMSE region. Its closure is shown to be a polytope and we find the complete set of its bounding half-spaces noniteratively after a finite number of steps. The polytope can easily be converted into any other QoS domain like SINR or rate. However, the simple geometry of the MMSE domain is lost in other domains. Once the bounding half-spaces are determined, any target MMSE tuple can quickly be checked for feasibility by verifying its membership to the interior of the polytope. For nondegenerate channels, the only relevant bounding half-space is essentially the lower bound on the sum mean square error. No further computations are necessary contrary to existing feasibility checks which iteratively solve eigenproblems in an alternating optimization framework for every single QoS requirement to test. For two particular user/antenna configurations, we find a noniterative closed form solution for the optimum power allocation of the signal-to-interference ratio (SIR) balancing.

A random beamforming scheme for the Gaussian MIMO broadcast channel with channel quality feedback is investigated and extended. Considering the case where the n receivers each have N receive antennas, the effects of feeding back various amounts of signal-to-interference-plus-noise ratio (SINR) information are analyzed. Using the results from order statistics of the ratio of a linear combination of exponential random variables, the distribution function of the maximum order statistic of the SINR observed at the receiver is found. The analysis from viewing each antenna as an individual user is extended to allow combining at the receivers, where it is known that the linear MMSE combiner is the optimal linear receiver and the CDF for the SINR after optimal combining is derived. Analytically, using the Delta Method, the asymptotic distribution of the maximum order statistic of the SINR with and without combining is shown to be, in the nomenclature of extreme order statistics, of type 3. The throughput of the feedback schemes are shown to exhibit optimal scaling asymptotically in the number of users. Finally, to further reduce the amount of feedback, a hard threshold is applied to the SINR feedback. The amount of feedback saved by implementing a hard threshold is determined and the effect on the system throughput is analyzed and bounded.

This paper studies the robust beamforming design for a multi-antenna cognitive radio (CR) network, which transmits to multiple secondary users (SUs) and coexists with a primary network of multiple users. We aim to maximize the minimum of the received signal-to-interference-plus-noise ratios (SINRs) of the SUs, subject to the constraints of the total SU transmit power and the received interference power at the primary users (PUs) by optimizing the beamforming vectors at the SU transmitter based on imperfect channel state information (CSI). To model the uncertainty in CSI, we consider a bounded region for both cases of channel matrices and channel covariance matrices. As such, the optimization is done while satisfying the interference constraints for all possible CSI error realizations. We shall first derive equivalent conditions for the interference constraints and then convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation, which leads to iterative algorithms for obtaining the robust optimal beamforming solution. Results demonstrate the achieved robustness and the performance gain over conventional approaches and that the proposed algorithms can obtain the exact robust optimal solution with high probability.

The concept of multiple-input multiple-output (MIMO) radar allows each transmitting antenna element to transmit an arbitrary waveform. This provides extra degrees of freedom compared to the traditional transmit beamforming approach. It has been shown in the recent literature that MIMO radar systems have many advantages. In this paper, we consider the joint optimization of waveforms and receiving filters in the MIMO radar for the case of extended target in clutter. A novel iterative algorithm is proposed to optimize the waveforms and receiving filters such that the detection performance can be maximized. The corresponding iterative algorithms are also developed for the case where only the statistics or the uncertainty set of the target impulse response is available. These algorithms guarantee that the SINR performance improves in each iteration step. Numerical results show that the proposed methods have better SINR performance than existing design methods.

In wireless networks, implementing cooperative beamforming (CB) can enable long-range communications in an energy efficient manner. By appropriately weighting and forwarding message signals, the cooperating nodes form one or more beams to cooperatively transmit one or more message signals to the desired destinations. In this paper, a cross-layer CB framework recently proposed by the authors is revisited and optimal weight design is considered. For single-beam beamforming, closed-form optimal weights that maximize the received signal-to-noise ratio (SNR) or signal-to-interference-plus-noise ratio (SINR) under a transmit power constraint are derived. It is shown that these weights also achieve maximal spectral efficiency. For multibeam beamforming, determining the weights that maximize spectral efficiency is in general a difficult problem, and two suboptimal weight designs (co-phasing weights and nulling weights) are proposed. Co-phasing weights allow desired signals to combine coherently at destinations and require local channel state information (CSI); nulling weights completely cancel interference at destinations and require global CSI.

We consider an ad hoc wireless network consisting of d source-destination pairs communicating, in a pairwise manner, via R relaying nodes. The relay nodes wish to cooperate, through a decentralized beamforming algorithm, in order to establish all the communication links from each source to its respective destination. Our communication strategy consists of two steps. In the first step, all sources transmit their signals simultaneously. As a result, each relay receives a noisy faded mixture of all source signals. In the second step, each relay transmits an amplitude- and phase-adjusted version of its received signal. That is each relay multiply its received signal by a complex coefficient and retransmits the so-obtained signal. Our goal is to obtain these complex coefficients (beamforming weights) through minimization of the total relay transmit power while the signal-to-interference-plus-noise ratio (SINR) at the destinations are guaranteed to be above certain predefined thresholds. Although such a power minimization problem is not convex, we use semidefinite relaxation to turn this problem into a semidefinite programming (SDP) problem. Therefore, we can efficiently solve the SDP problem using interior point methods. Our numerical examples reveal that for high network data rates, our space division multiplexing scheme requires significantly less total relay transmit power compared to other orthogonal multiplexing schemes, such as time-division multiple access schemes.

In this paper, we perform the prediction of the signal-to-interference-plus-noise ratio (SINR) root mean square (RMS) in the IEEE 802.16 system. We obtain the time series of the SINR RMS using system-level simulations. The SINR RMS is a heteroscedastic stochastic process. We propose a nonlinear transform of the SINR RMS that generates a linear homoscedastic stochastic process, which may be considered Gaussian in practice. We construct the prediction model of this Gaussian stochastic process using the linear autoregressive process. We propose three predictions of the SINR RMS, that is, the minimum mean square, the median, and the maximum-likelihood predictions, using the prediction of the linear autoregressive process. Our minimum mean-square error (MMSE) prediction of the SINR RMS is more reliable than the prediction based on averaging of the SINR RMS.

The problem of designing multiple-input-multiple-output (MIMO) relay for multipoint to multipoint communication in wireless networks has been dealt with by considering the fact that only the imperfect channel state information (CSI) is available at the MIMO relay. In particular, assuming that the second-order terms of the uncertainties of the source-relay and relay-destination channels are negligible, we design an amplify-and-forward (AF) MIMO relay that provides robustness against channel uncertainties. In our proposed robust method, the objective is to design the MIMO relay in which the worst-case relay transmit power is minimized by keeping the worst-case signal-to-interference-and-noise ratio (SINR) for all destinations above a certain threshold value. This paper shows that the aforementioned problem is nonconvex but it can be relaxed to a convex problem consisting of second-order cone (SOC) and semidefinite cone constraints using the semidefinite relaxation technique. The optimal solution of the relaxed problem is utilized to generate the best approximate solution of the original nonconvex problem using the well-known randomization technique. Computer simulations verify the robustness of the proposed MIMO relay when compared to the nonrobust MIMO relay.

In this paper, novel robust adaptive beamformers are proposed with constraints on array magnitude response. With the transformation from the array output power and the magnitude response to linear functions of the autocorrelation sequence of the array weight, the optimization of an adaptive beamformer, which is often described as a quadratic optimization problem in conventional beamforming methods, is then reformulated as a linear programming (LP) problem. Unlike conventional robust beamformers, the proposed method is able to flexibly control the robust response region with specified beamwidth and response ripple. In practice, an array has many imperfections besides steering direction error. In order to make the adaptive beamformer robust against all kinds of imperfections, worst-case optimization is exploited to reconstruct the robust beamformer. By minimizing array output power with the existence of the worst-case array imperfections, the robust beamforming can be expressed as a second-order cone programming (SOCP) problem. The resultant beamformer possesses superior robustness against arbitrary array imperfections. With the proposed methods, a large robust response region and a high signal-to-interference-plus-noise ratio (SINR) enhancement can be achieved readily. Simple implementation, flexible performance control, as well as significant SINR enhancement, support the practicability of the proposed methods.

We consider the downlink of a cellular system in which the base station employs multiple transmit antennas, each receiver has a single antenna, and the users specify certain quality of service (QoS) requirements. We study the design of robust broadcasting schemes that minimize the transmission power necessary to guarantee that the QoS requirements are satisfied for all channels within bounded uncertainty regions around the transmitter's estimate of each user's channel. Each user's QoS requirement is formulated as a constraint on the mean square error (MSE) in its received signal, and we show that these MSE constraints imply constraints on the received signal-to-interference-plus-noise ratio. Using the MSE constraints, we present a unified approach to the design of linear and nonlinear transceivers with QoS requirements that must be satisfied in the presence of bounded channel uncertainty. The proposed designs overcome the limitations of existing approaches that provide conservative designs or are only applicable to the case of linear precoding. Furthermore, we provide computationally efficient design formulations for a rather general model of bounded channel uncertainty that subsumes many natural choices for the uncertainty region. We also consider the problem of the robust counterpart to precoding schemes that maximize the fidelity of the weakest user's signal subject to a power constraint. For this problem, we provide quasi-convex formulations, for both linear and nonlinear transceivers, that can be efficiently solved using a one-dimensional bisection search. Our numerical results demonstrate that in the presence of bounded uncertainty in the transmitter's knowledge of users' channels, the proposed designs provide guarantees for a larger range of QoS requirements than the existing approaches that are based on bounded channel uncertainty models and require less transmission power to provide these guarantees.

This paper discusses the constrained stochastic gradient (CSG) algorithm used for controlling antenna arrays, aiming to maximize the signal-to-interference-plus-noise ratio (SINR) in mobile communications. Firstly, analytical expressions for the first moment of the weight vector and the SINR characteristic of the standard CSG algorithm are derived for two interferer signals, considering small step-size conditions and assuming Gaussian signal, interference, and noise. From these model expressions, the CSG algorithm performance is assessed, which predicts undesired behavior (termed here unbalanced behavior, pertaining to an unbalance between maximizing signal power and minimizing interference power) when one or more interference angles-of-arrival are close to the signal angle-of-arrival and the angle-of-arrival spreads of the involved signals are small. Finally, by using the model expressions, an improved CSG (ICSG) algorithm is proposed to compensate the unbalanced behavior of the standard CSG algorithm. The accuracy of the proposed model and the effectiveness of the modified algorithm are assessed through numerical simulations.

In this paper, the performance of the cooperative multiuser direct-sequence code-division multiple-access (DS-CDMA) system is analyzed in the asymptotic regime where both the spreading codes and the number of users grow unboundedly large with the same ratio. Assuming that each terminal is paired with another user which, in addition to transmitting its own data, estimates and relay the information transmitted from its partner, a simple approximate signal-to-interference-plus-noise ratio (SINR) expression is derived that is independent from the spreading codes and explicitly accounts for the effects of the multiple-access interference (MAI) and the relay noise. The so-obtained SINR expression is then computed based entirely on the available local information and without any knowledge about the interfering users. The results obtained above are then used to optimally design the cooperative system. In particular, it is shown how the amount of cooperation between each collaborating pair can be adjusted to simultaneously achieve a preassigned target SINR for both users. Based on the local information, the globally optimal amount of the relay power is obtained that maximizes the achieved SINR at the access point. It is shown that increasing the relay power does not necessarily result in improving the quality of reception at the access point and, to maximize each user's SINR, its relay power should be carefully adjusted based on the environmental parameters such as the interpartner channel link and the powers of MAI and the relay noise. The connection between the cooperative and the conventional multiuser systems is also studied and simulations are used to demonstrate the validity of the analytical results.

We present a mean-square-error (MSE) duality between the broadcast channel and the multiple access channel for multiantenna users communicating with a single base station. We introduce three levels of the duality which allow for a problem specific customization with different computational complexities and resolutions. The first level preserves the sum-MSE during the conversion from the uplink to the downlink and vice versa, whereas the second level not only keeps the sum-MSE constant but also ensures the preservation of the individual users' MSEs. The third level involves the finest resolution and preserves the individual streams' MSEs and the individual streams' signal-to-interference-and-noise ratio (SINR) simultaneously. In contrast with hitherto existing MSE-dualities, the proposed sort of duality features a lower complexity since no MSE computation detouring is necessary during the conversion to the dual domain and is capable of handling all combinations of active and passive transmitters and receivers. Moreover, we show how two of these three dualities can be exploited to solve the unweighted total sum-MSE minimization problem and the weighted sum-MSE minimization in the broadcast channel in an efficient way by revealing the hidden convexity in the first case and drastically reducing the computational complexity in the latter case.

This paper studies the two-hop relay broadcast channel (BC) for a relay-assisted wireless cellular network where the multiuser independent downlink signals from the base station (BS) are first transmitted to a fixed relay station (RS), and then forwarded by the RS to multiple mobile users. Assuming both the BS and RS are equipped with multiantennas, we study the joint optimization of linear beamforming and power control at the BS and RS so as to minimize their weighted sum-power consumption under the user minimum signal-to-interference-noise-ratio (SINR) - quality-of-service (QoS) - constraints. We apply two well-known criteria in the literature, namely, the ldquoSINR balancingrdquo and the ldquochannel-inversion,rdquo for the design of linear precoding in the traditional nonrelay-assisted multiantenna BC to the relay-assisted multiantenna BC. First, a convergence-ensured iterative SINR-balancing algorithm is proposed to successively in turn optimize the transmit parameters at one station (BS or RS) with those at the other station being fixed. Second, a joint BS and RS channel-inversion algorithm is proposed together with a novel technique, termed ldquoeigenmode switching,rdquo at the RS to reduce the power penalty of the channel inversion. Simulation results show that the proposed joint beamforming and power control schemes provide substantial power savings to achieve the assigned user QoS constraints.

Many resource allocation problems can be studied within the framework of interference functions. Basic properties of interference functions are non-negativity, scale-invariance, and monotonicity. In this paper, we study interference functions with additional properties, namely convexity, concavity, and log-convexity. Such interference functions occur naturally in various contexts, e.g., adaptive receive strategies, robust power control, or resource allocation over convex utility sets. We show that every convex (resp. concave) interference function can be expressed as a maximum (resp. minimum) over a weighted sum of its arguments. This analytical insight provides a link between the axiomatic interference framework and conventional interference models that are based on the definition of a coupling matrix. We show how the results can be used to derive best-possible convex/concave approximations for general interference functions. The results have further application in the context of feasible sets of multiuser systems. Convex approximations for general feasible sets are derived. Finally, we show how convexity can be exploited to solve the problem of signal-to-interference-plus-noise ratio (SINR)-constrained power minimization with super-linear convergence.

A minimum mean-square error (MMSE)-based iterative soft interference cancellation (MMSE-SIC) receiver has been proposed to mitigate the interferences of the multiple-input multiple-output (MIMO) channels, with reduced complexity as compared to maximum-likelihood (ML) detection. On the other hand, the block-iterative generalized decision-feedback equalizer (BI-GDFE) attains close to the performance of the MMSE-SIC receivers with further reduced complexity. The BI-GDFE, however, requires an accurate estimate of the input-decision correlation (IDC), which is a statistical reliability metric of earlier-made decisions. To date, the BI-GDFE receiver is applicable only to phase-shift-keying (PSK) modulations due to the absence of a method to estimate the IDC for higher order quadrature amplitude modulations (QAMs). In this paper, we establish the relationship between the MMSE-SIC and BI-GDFE receivers and propose an algorithm to determine the IDC for BI-GDFE from the unconditional MMSE-SIC (U-MMSE-SIC). We further analyze and compare the asymptotic performances of the two receivers for large random MIMO channels and prove that for the limiting case, the output signal-to-interference-plus-noise ratios (SINRs) at each iteration for both receivers converge in probability to their respective deterministic limits. Our simulation results have shown that the bit error rate (BER) performance of the BI-GDFE receiver with the proposed IDC selection method achieves close to that of the U-MMSE-SIC receiver with similar convergence behavior and reaches the single-user matched filter bound (MFB) with several iterations for high enough signal-to-noise ratio (SNR).

Consider a downlink multicast scenario where a base station equipped with multiple antennas wishes to simultaneously broadcast a number of signals to some given groups of users over a common bandwidth. The goal of the base station is to select appropriate beamforming vectors so as to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among all users under a power budget constraint. Since this max-min-fair transmit beamforming problem is NP-hard in general, a randomized polynomial time approximation approach based on semidefinite relaxation (SDR) has been proposed recently where excellent performance in both simulated and measured wireless channels has been reported. This paper shows that the SDR-based approach can provide at least an O(1/M) approximation to the optimum solution, where M is the total number of users. This estimate implies that the SDR solution achieves an SINR that is at most (logM+O(1)) dB away from the highest possible value. The existence of such a data independent bound certifies the worst-case approximation quality of the SDR algorithm for any problem instance and any number of transmit antennas. For real-valued problems, the corresponding approximation ratio is shown to be O(1/M2), while the SINR loss due to SDR approximation is at most (2logM+O(1)) dB.

Joint design of linear multiuser multiple-input-multiple-output (MIMO) transceiver subject to different quality of service (QoS) constraints per user and with per-antenna or antenna group power constraints is considered. Solutions for two linear transceiver optimization problems are proposed, i.e., balancing the weighted signal-to-interference-plus-noise ratio (SINR) per data stream and balancing the weighted rate for each scheduled user with minimum rate requirements per user. The proposed joint transceiver optimization algorithms are compared to corresponding optimal nonlinear transmission methods as well as to generalized zero-forcing transmission solutions. Unlike the optimal nonlinear schemes, the optimization problems employed in the linear multiuser MIMO transceiver design are not convex in general. However, the proposed algorithms are shown to provide very efficient solutions despite of the fact that the global optimum cannot be guaranteed due to nonconvexity of the problems.

High signal-to-noise ratio (SNR) properties of the minimum output energy (MOE) receiver and the Capon channel estimation technique are analyzed in the case of large direct-sequence code-division multiple-access (DS-CDMA) systems. It is shown that if the noise power tends to zero and the system load is less than one, then the signal-to-interference-plus-noise ratio (SINR) of the MOE receiver tends to infinity and the Capon channel estimate converges to a scaled version of the channel vector of the user-of-interest. For the case when the system load is larger than one, an asymptotic SINR expression is obtained. Furthermore, expressions for the efficiency and asymptotic efficiency of the MOE receiver are derived. Simple approximations of (and upper/lower bounds on) these expressions are found and the effects of the system physical parameters on the performance of the MOE receiver are discussed.

Minimum variance beamforming, which uses a weight vector that maximizes the signal-to-interference-plus-noise ratio (SINR), is often sensitive to estimation error and uncertainty in the parameters, steering vector and covariance matrix. Robust beamforming attempts to systematically alleviate this sensitivity by explicitly incorporating a data uncertainty model in the optimization problem. In this paper, we consider robust beamforming via worst-case SINR maximization, that is, the problem of finding a weight vector that maximizes the worst-case SINR over the uncertainty model. We show that with a general convex uncertainty model, the worst-case SINR maximization problem can be solved by using convex optimization. In particular, when the uncertainty model can be represented by linear matrix inequalities, the worst-case SINR maximization problem can be solved via semidefinite programming. The convex formulation result allows us to handle more general uncertainty models than prior work using a special form of uncertainty model. We illustrate the method with a numerical example.

The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signal-to-interference-plus-noise ratio (SINR) at each receiver; and a "fair" approach maximizing the overall minimum SINR under a total power budget. The core problem is a multicast generalization of the multiuser downlink beamforming problem; the difference is that each transmitted stream is directed to multiple receivers, each with its own channel. Such generalization is relevant and timely, e.g., in the context of the emerging WiMAX and UMTS-LTE wireless networks. The joint problem also contains single-group multicast beamforming as a special case. The latter (and therefore also the former) is NP-hard. This motivates the pursuit of computationally efficient quasi-optimal solutions. It is shown that Lagrangian relaxation coupled with suitable randomization/cochannel multicast power control yield computationally efficient high-quality approximate solutions. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Extensive numerical results using both simulated and measured wireless channels are presented to corroborate our main findings. ©2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Eleftherios Karipidis, Nicholas Sidiropoulos and Zhi-Quan Luo, Quality of Service and Max-Min Fair Transmit Beamforming to Multiple Cochannel Multicast Groups, 2008, IEEE Transactions on Signal Processing, (56), 3, 1268-1279.http://dx.doi.org/10.1109/TSP.2007.909010

The random matrix theory is used to analyze the asymptotic performance of the blind minimum output energy (MOE) receiver in direct-sequence code division multiple-access (DS-CDMA) systems in the presence of unknown multipath channel under the condition that the spreading factor and the number of users go to infinity with the same rate. As a special case, the asymptotic properties of the blind Capon receiver are also studied and the conditions of convergence of the signal-to-interference-plus-noise ratio (SINR) of this receiver to that of the optimal minimum-mean-square error (MMSE) receiver are discussed. In particular, it is shown that the SINR performances of the Capon and MMSE receivers are nearly identical in the uplink scenario, while the performance of the Capon receiver may be considerably inferior to that of the MMSE receiver in the downlink transmission case. As the performance of the Capon receiver is closely related to the performance of the Capon channel estimator, the asymptotic properties of the latter estimator are also studied and the conditions of convergence of the Capon channel estimate to a scaled version of the channel vector of the user-of-interest are obtained.

We consider sample-matrix-inversion (SMI)-type estimates of the minimum-mean-square-error (MMSE) and the linearly constrained-minimum-variance (LCMV) linear filters obtained from data records of limited size. We quantify theoretically the (detrimental) effect of the desired-signal energy level on the mean square (MS) filter estimation error and the normalized output signal-to-interference-plus-noise ratio (SINR) by deriving a new exact analytical expression and a lower bound, respectively. For cases where accumulation of pure disturbance observations is not possible, we show theoretically how certain intuitive, pilot-assisted, and decision-directed adaptive filter implementations that utilize desired-signal-present data/observations perform close to their desired-signal-absent counterparts. Simulation studies illustrate our theoretical developments in the context of spread-spectrum communications over multipath fading channels under perfect and nonperfect synchronization.

For communication over doubly dispersive channels, we consider the design of multicarrier modulation (MCM) schemes based on time-frequency shifts of prototype pulses. We consider the case where the receiver knows the channel state and the transmitter knows the channel statistics (e.g., delay spread and Doppler spread) but not the channel state. Previous work has examined MCM pulses designed for suppression of inter-symbol/inter-carrier interference (ISI/ICI) subject to orthogonal or biorthogonal constraints. In doubly dispersive channels, however, complete suppression of ISI/ICI is impossible, and the ISI/ICI pattern generated by these (bi)orthogonal schemes can be difficult to equalize, especially when operating at high bandwidth efficiency. We propose a different approach to MCM pulse design, whereby a limited expanse of ISI/ICI is tolerated in modulation/demodulation and treated near-optimally by a downstream equalizer. Specifically, we propose MCM pulse designs that maximize a signal-to-interference-plus-noise ratio (SINR) which suppresses ISI/ICI outside a target pattern. In addition, we propose two low-complexity turbo equalizers, based on minimum mean-squared error and maximum likelihood criteria, respectively, that leverage the structure of the target ISI/ICI pattern. The resulting system exhibits an excellent combination of low complexity, low bit-error rate, and high spectral efficiency.