This paper analyzes the impact of spatially correlated additive noise on the minimum mean-square error (MMSE) estimation of multiple-input multiple-output (MIMO) channels from one-bit quantized observations. Although additive noise can be correlated in practical scenarios, e.g., due to jamming, clutter, or other external disturbances, the effect of such correlation on the MMSE channel estimator in this setting remains unexplored in prior work. Against this backdrop, we derive a novel analytical expression for the general MIMO MMSE channel estimator, which is inherently nonlinear in one-bit observations, and accommodates arbitrary channel and noise correlation structures. To further characterize the impact of noise correlation, we subsequently specialize the general MMSE expression to certain tractable multi antenna configurations in which both the channel and the noise assume single-parameter constant correlation structures. Our analyses reveal nontrivial, noise-correlation-induced scenarios in which the estimator remains linear despite non-zero channel and noise correlation parameters. Moreover, the results indicate that, at low-to-medium signal-to-noise ratio, noise correlation improves the MMSE performance when channels are uncorrelated, but degrades performance when channels are strongly correlated.

This paper investigates a three-layer IoT-fog-cloud computing system to determine the optimum workload and power allocation at each layer. The objective is to minimize maximum per-layer latency (including both data processing and transmission delays) with individual power constraints. The resulting optimum resource allocation problem is a mixed-integer optimization problem with exponential complexity. Hence, the problem is first relaxed under appropriate modeling assumptions, and then an efficient iterative method is proposed to solve the relaxed but still non-convex problem. The proposed algorithm is based on an alternating optimization approach, which yields close-to-optimum results with significantly reduced complexity. Numerical results are provided to illustrate the performance of the proposed algorithm compared to the exhaustive search method. The latency gain of three-layer distributed IoT-fog-cloud computing is quantified with respect to fog-only and cloud-only computing systems.

This work focuses on the design and analysis of distributed stochastic precoding algorithms for multiple-input single-output (MISO) interference channels, where each transmitter is provided with mean information of its intended channel and that of interfering channels. Unlike in cases where exact channel gains are known as in most existing works, here generalrank precoding is required for optimality instead of the rank-one beamforming. An efficient algorithm for the distributed implementation of the Nash equilibrium precoding is first proposed. A sufficient condition for this algorithm to converge to the unique equilibrium is derived for the two-user case based on stochastic ordering, and is valid for a wide range of system parameters. To improve the sum-rate performance under medium to strong interference, a pricing-based algorithm is also provided and its convergence analyzed. The two algorithms are compared in terms of sum-rate and system overhead.

This work considers linear precoding strategies for multiple-input single-out (MISO) interference channels with channel mean feedback at transmitters, where the interference at each receiver is treated as additive noise. The challenge here is that previous precoder designs with perfect channel state information (CSI) at transmitters do not apply and new approaches are required. Based on the Laplace transform order, an altruistic non-equilibrium strategy, i.e., the stochastic zero forcing, is first proposed under practical assumptions, generalizing the traditional zero forcing which requires perfect CSI. Interestingly, the precoding matrices here are all rank-one beamformers as in the traditional zero forcing. The competitive use of the common physical media in MISO interference channels is also formulated as a strategic noncooperative game. In contrast to the perfect CSI case with a unique rank-one Nash equilibrium, with channel mean feedback, the Nash equilibria here are not necessarily rank-one in general. Nevertheless, when achieved by the rank-one beamforming, the equilibrium is unique and convenient for implementation. Accordingly, the condition for beamforming to achieve the equilibrium is derived. Comparisons of the above two strategies reveal no overall dominance of one over the other, thereby establishing stochastic zero forcing as an alternative to the Nash equilibrium designs.

This paper investigates the optimal source transmit precoding to maximize the ergodic mutual information between the input and the output of a noncoherent amplify-and-forward relay channel, with multiple antennas at the source and with a single antenna at both the relay and the destination. It is assumed that only the source-relay channel mean information is available at the source. The challenge here is that relaying introduces a nonconvex structure in the objective function. Therefore, previous methods dealing with channel mean feedback, which generally require the concavity of the objective function, cannot be applied. To circumvent the difficulty at hand, a different approach based on stochastic ordering is employed. The stochastic optimization problem here is ultimately transformed into the comparison of two nonnegative random variables in the Laplace transform order. It is shown that the optimal source transmit strategy is to transmit along the known channel mean and its orthogonal eigen-channels. Our result subsumes as an asymptotic case the optimal precoding for multiple-input single-output (MISO) channels without relaying under mean feedback. Furthermore, the analysis can be partially extended to the case with multiple antennas at the relay. Numerical examples are provided to complement and corroborate the analysis.

Two linear precoding strategies are investigated for multiple-input single-out (MISO) interference channels with channel mean feedback at transmitters. The interference at each receiver is treated as additive noise. The challenge here is that previous analysis with perfect channel state information (CSI) at transmitters does not apply. Based on stochastic ordering, the altruistic non-equilibrium stochastic zero forcing strategy is first proposed, generalizing traditional zero forcing which requires perfect CSI. Interestingly, the precoding matrices here are all rank-one as in traditional zero forcing. The competitive use of the common channel is also formulated as a strategic game. Different from the perfect CSI case, with channel mean feedback, infinitely many Nash equilibria exist in general, which are not necessarily rank-one. Comparisons of the above two precoding strategies reveal no overall dominance of one over the other, thereby establishing stochastic zero forcing as an appealing alternative to the prevailing Nash equilibrium strategies.

Stochastic optimization arising from precoding in a multi-antenna fading channel with channel mean feedback to maximize data rates is important but challenging. The use of relaying further complicates the situation, as it may induce a nonconvex structure in the objective function, thereby excluding the use of existing approaches which re quire convexity or concavity. To deal with challenges as such, this paper presents a new framework for solving a class of stochastic optimization problems. The analysis here involves the comparison of two nonnegative random variables in the Laplace transform order. Our framework is particularized to optimal precoding for maximum ergodic or effective capacity in multi-antenna channels with or with out relaying assuming channel mean feedback, where the objectives may or may not have convexity or concavity. The application to stochastic power allocation is also discussed.

This paper investigates the optimum source transmission strategy to maximize the capacity of a multiple-input single-output (MISO) amplify-and-forward relay channel, assuming source-relay channel mean feedback at the source. The challenge here is that relaying introduces a nonconvex structure in the objective function, thereby excluding the possible use of previous methods dealing with mean feedback that generally rely on the concavity of the objective function. A novel method is employed, which divides the feasible set into two subsets and establishes the optimum from one of them by comparison. As such, the optimization is transformed into the comparison of two nonnegative random variables in the Laplace Transform order, which is one of the stochastic orders. It turns out that the optimum transmission strategy is to transmit along the known channel mean and its orthogonal eigenchannels. The condition for rank-one precoding (beamforming) to achieve capacity is also determined. Our results subsume those for traditional MISO precoding with mean feedback.

In this paper, the aggregate interference in a finite-area multi-antenna wireless ad hoc network is statistically characterized. While most of the existing studies model the spatial distribution of transmit nodes as a Poisson point process in an infinite plane, a binomial point process is adopted here to better characterize the node distribution in a finite area. In the test link, maximum-ratio combining (MRC) is employed at the receiver, whereas spatial multiplexing or transmit antenna selection is employed at the transmitter depending on the availability of limited feedback. Moments of aggregate interference as well as outage probability formulas are obtained. Interestingly, for a finite network, our analysis establishes the optimality of single-stream transmissions in spatial multiplexing with a MRC test receiver, and justifies the use of transmit antenna selection for further enhancing the outage performance with limited feedback. Simulations are provided to corroborate the analysis.

New results on maximum mutual information design for multiple-input multiple-output (MIMO) systems are presented, assuming that both transmitter and receiver know only an estimate of the channel state as well as the transmit and receive correlation. Since an exact capacity expression is difficult to obtain for this case, a tight lower-bound on the mutual information between the input and the output of a MIMO channel has been previously formulated as a design criterion. However, in the previous literature, there has been no analytical expression of the optimum transmit covariance matrix for this lower-bound. Here it is shown that for the general case with channel correlation at both ends, there exists a unique and globally optimum transmit covariance matrix whose explicit expression can be conveniently determined. For the special case with transmit correlation only, the closed-form optimum transmit covariance matrix is presented. Interestingly, the optimal transmitters for the maximum mutual information design and the minimum total mean-square error design share the same structure, as they do in the case with perfect channel state information. Simulation results are provided to demonstrate the effects of channel estimation errors and channel correlation on the mutual information.

Assuming perfect channel state information (CSI), linear precoding/decoding for multiple-input multiple-output (MIMO) systems has been considered in the literature under various performance criteria, such as minimum total mean-square error (MSE), maximum mutual information, and minimum average bit error rate (BER). It has been shown that these criteria belong to a set of reasonable Schur-concave or Schur-convex objective functions of the diagonal entries of the system mean-square error (MSE) matrix. In this paper, assuming only the knowledge of channel mean and transmit correlation at both ends, a general theoretical framework is presented to derive the optimum precoder and decoder for MIMO systems using these objective functions. It is shown that for all these objective functions the optimum transceivers share a similar structure. Compared to the case with perfect CSI, a linear filter is added to both ends to balance the suppression of channel noise and the additional noise induced from channel estimation error. Simulation results are provided.

Joint linear minimum sum mean-squared error (referred to as MSMSE) transmitter and receiver (transceiver) optimization problems are formulated for multiuser MIMO systems under a sum power constraint assuming imperfect channel state information (CSI). Both the uplink and the dual downlink are considered. Based on the Karush-Kuhn-Tucker (KKT) conditions associated with both problems, a relation between the two problems is discovered, which is termed the uplinkdownlink duality in sum MSE under imperfect CSI. As a result, the MSMSEs in both links are the same and any admissible uplink design satisfying the KKT conditions can be translated for application to the downlink, and vice versa. Simulation results are provided to demonstrate the duality and show the impact of imperfect CSI.

Duality between the multi-antenna multi-user uplink and the downlink has been discovered in terms of sum rate, capacity region, signal-to-interference-plus-noise-ratio (SINR) region or normalized mean-squared error (MSE) region. Previous work on duality has assumed perfect channel knowledge. However, channel estimation is never perfect in practice. In this paper, channel estimation error as well as antenna correlation at the base station (BS) is taken into account. A multi-user system with multiple antennas at the BS and with single-antenna users is studied. Joint detection and transmission are used in the uplink and the downlink, respectively. It is analytically shown that with imperfect channel state information (CSI), under the same sum power constraint, the achievable SINR regions or the normalized MSE regions in both links are the same, as in the case with perfect CSI. Monte Carlo simulation results and discussions are also provided to complement the analysis.

This paper presents a new result on minimum total mean squared error (MSE) joint transceiver design for multiple-input multiple-output (MIMO) systems, with imperfect channel state information (CSI) at both ends and subject to a total power constraint. The channel knowledge here is the channel mean and transmit correlation information. The joint design is formulated into an optimization problem, to which the closed-form optimum solution is found. The optimum precoder consists of a linear filter, a matrix which collects effective channel eigenmodes, and a diagonal power allocation matrix. The linear filter balances the suppression of channel noise and the additional noise induced by channel estimation error. Given the precoder, the optimum decoder is simply a linear minimum MSE (LMMSE) data estimator. The performance degradations due to imperfect channel estimation and/or transmit correlation are demonstrated by simulation results. The relation between the minimum total MSE design and the maximum mutual information design is determined as well, under the above mentioned imperfect CSI.