Minimum achievable complexity (MAC) for a maximum likelihood (ML) performance-achieving detection algorithm is derived. Using the derived MAC, we prove that the conventional sphere decoding (SD) ...algorithms suffer from an inherent weakness at low SNRs. To find a solution for the low SNR deficiency, we analyze the effect of zero-forcing (ZF) and minimum mean square error (MMSE) linearly detected symbols on the MAC and demonstrate that although they both improve the SD algorithm in terms of the computational complexity, the MMSE linearly detected point has a vital difference at low SNRs. By exploiting the information provided by the MMSE of linear method, we prove the existence of a lossless dimension reduction which can be interpreted as the feasibility of a detection method which is capable of detecting the ML symbol without visiting any nodes at low and high SNRs. We also propose a lossless dimension reduction-aided detection method which achieves the promised complexity bounds marginally and reduces the overall computational complexity significantly, while obtaining the ML performance. The theoretical analysis is corroborated with numerical simulations.
A new approach to the design of robust adaptive beamforming is introduced. The essence of the new approach is to estimate the difference between the actual and presumed steering vectors and to use ...this difference to correct the erroneous presumed steering vector. The estimation process is performed iteratively where a quadratic convex optimization problem is solved at each iteration. Contrary to the worst-case performance-based and the probability-constrained-based approaches, our approach does not make any assumptions on either the norm of the mismatch vector or its probability distribution. Hence, it avoids the need for estimating their values.
The robust adaptive beamforming (RAB) problem for general-rank signal model with an additional positive semi-definite constraint is considered. Using the principle of the worst-case performance ...optimization, such RAB problem leads to a difference-of-convex functions (DC) optimization problem. The existing approaches for solving the resulted non-convex DC problem are based on approximations and find only suboptimal solutions. Here, we aim at finding the globally optimal solution for the non-convex DC problem and clarify the conditions under which the solution is guaranteed to be globally optimal. Particularly, we rewrite the problem as the minimization of a one-dimensional optimal value function (OVF). Then, the OVF is replaced with another equivalent one, for which the corresponding optimization problem is convex. The new one-dimensional OVF is minimized iteratively via polynomial time DC (POTDC) algorithm. We show that the POTDC converges to a point that satisfies Karush-Kuhn-Tucker (KKT) optimality conditions, and such point is the global optimum under certain conditions. Towards this conclusion, we prove that the proposed algorithm finds the globally optimal solution if the presumed norm of the mismatch matrix that corresponds to the desired signal covariance matrix is sufficiently small. The new RAB method shows superior performance compared to the other state-of-the-art general-rank RAB methods.
The worst-case robust adaptive beamforming problem for general-rank signal model is considered. Its formulation is to maximize the worst-case signal-to-interference-plus-noise ratio, incorporating a ...positive semidefinite constraint on the actual covariance matrix of the desired signal. In the literature, semidefinite program (SDP) techniques, together with others, have been applied to approximately solve this problem. Herein, an inner second-order cone program (SOCP) approximate algorithm is proposed to solve it. In particular, a sequence of SOCPs are constructed and solved, while the SOCPs have the nonincreasing optimal values and converge to a locally optimal value (it is in fact a globally optimal value through our extensive simulations). As a result, our algorithm does not use computationally heavy SDP relaxation technique. To validate our inner approximation results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformer in terms of the averaged cpu-time (indicating how fast the algorithms converge) in a high signal-to-noise region.
Traditional compressed sensing considers sampling a 1D signal. For a multidimensional signal, if reshaped into a vector, the required size of the sensing matrix becomes dramatically large, which ...increases the storage and computational complexity significantly. To solve this problem, the multidimensional signal is reshaped into a 2D signal, which is then sampled and reconstructed column by column using the same sensing matrix. This approach is referred to as parallel compressed sensing, and it has much lower storage and computational complexity. For a given reconstruction performance of parallel compressed sensing, if a so-called acceptable permutation is applied to the 2D signal, the corresponding sensing matrix is shown to have a smaller required order of restricted isometry property condition, and thus, lower storage and computation complexity at the decoder are required. A zigzag-scan-based permutation is shown to be particularly useful for signals satisfying the newly introduced layer model. As an application of the parallel compressed sensing with the zigzag-scan-based permutation, a video compression scheme is presented. It is shown that the zigzag-scan-based permutation increases the peak signal-to-noise ratio of reconstructed images and video frames.
This paper studies the impact of additional pilot overhead for covariance matrix estimation in a time-division duplexed (TDD) massive multiple-input multiple-output (MIMO) system. We choose average ...uplink (UL) and downlink (DL) spectral efficiencies (SEs) as performance metrics for the massive MIMO system, and derive closed form expressions for them in terms of the additional pilot overhead. The expressions are derived by considering linear minimum mean squared error (LMMSE)-type and element-wise LMMSE-type channel estimates that represent LMMSE and element-wise LMMSE with estimated covariance matrices, respectively. Using these expressions, a detailed theoretical analysis of SE behavior as a function of pilot overhead for both LMMSE-type and element-wise LMMSE-type channel estimation are presented, followed by simulations, which also demonstrate and validate theoretical results.
Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC ...programming problems occur also in other signal processing applications and are typically solved using different modifications of the branch-and-bound method which, however, does not have any polynomial time complexity guarantees. In this paper, we develop two efficient polynomial time algorithms for the sum-rate maximization in two-way AF MIMO relaying. The first algorithm guarantees to find at least a Karush-Kuhn-Tucker (KKT) solution. There is a strong evidence, however, that such a solution is actually globally optimal. The second algorithm that is based on the generalized eigenvectors shows the same performance as the first one with reduced computational complexity. The objective function of the problem is represented as a product of quadratic fractional ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative Newton-type search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We derive an upper-bound for the optimal value of the corresponding optimization problem and show by simulations that this upper-bound is achieved by both algorithms. It provides an evidence that the algorithms find a global optimum. The proposed methods are also superior to other state-of-the-art algorithms.
In this paper, we propose a two-dimensional joint transmit array interpolation and beamspace design for planar array mono-static multiple-input-multiple-output radar for direction-of-arrival (DOA) ...estimation via tensor modeling. Our underlying idea is to map the transmit array to a desired array and suppress the transmit power outside the spatial sector of interest. In doing so, the signal-to-noise ratio is improved at the receive array. Then, we fold the received data along each dimension into a tensorial structure and apply tensor-based methods to obtain DOA estimates. In addition, we derive a closed-form expression for DOA estimation bias caused by interpolation errors and argue for using a specially designed look-up table to compensate for the bias. The corresponding Cramér-Rao bound (CRB) is also derived. Simulation results are provided to show the performance of the proposed method and compare its performance to CRB.
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