Robust Sum MSE Optimization for Downlink Multiuser MIMO Systems with Arbitrary Power Constraint: Generalized Duality Approach

This paper considers linear minimum meansquare- error (MMSE) transceiver design problems for downlink multiuser multiple-input multiple-output (MIMO) systems where imperfect channel state information is available at the base station (BS) and mobile stations (MSs). We examine robust sum mean-square-error (MSE) minimization problems. The problems are examined for the generalized scenario where the power constraint is per BS, per BS antenna, per user or per symbol, and the noise vector of each MS is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel duality based iterative solution. Each of these problems is solved as follows. First, we establish a novel sum average meansquare- error (AMSE) duality. Second, we formulate the power allocation part of the problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. To solve robust sum MSE minimization constrained with per BS antenna and per BS power problems, we have established novel downlink-uplink duality. On the other hand, to solve robust sum MSE minimization constrained with per user and per symbol power problems, we have established novel downlink-interference duality. For the total BS power constrained robust sum MSE minimization problem, the current duality is established by modifying the constraint function of the dual uplink channel problem. And, for the robust sum MSE minimization with per BS antenna and per user (symbol) power constraint problems, our duality are established by formulating the noise covariance matrices of the uplink and interference channels as fixed point functions, respectively.Comment: IEEE TSP Journa

Linear Transceiver design for Downlink Multiuser MIMO Systems: Downlink-Interference Duality Approach

This paper considers linear transceiver design for downlink multiuser multiple-input multiple-output (MIMO) systems. We examine different transceiver design problems. We focus on two groups of design problems. The first group is the weighted sum mean-square-error (WSMSE) (i.e., symbol-wise or user-wise WSMSE) minimization problems and the second group is the minimization of the maximum weighted mean-squareerror (WMSE) (symbol-wise or user-wise WMSE) problems. The problems are examined for the practically relevant scenario where the power constraint is a combination of per base station (BS) antenna and per symbol (user), and the noise vector of each mobile station is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel downlink-interference duality based iterative solution. Each of these problems is solved as follows. First, we establish a new mean-square-error (MSE) downlink-interference duality. Second, we formulate the power allocation part of the problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. For the first group of problems, we have established symbol-wise and user-wise WSMSE downlink-interference duality.Comment: IEEE TSP Journa

Pilot Optimization and Channel Estimation for Multiuser Massive MIMO Systems

This paper proposes novel pilot optimization and channel estimation algorithm for the downlink multiuser massive multiple input multiple output (MIMO) system with $K$ decentralized single antenna mobile stations (MSs), and time division duplex (TDD) channel estimation which is performed by utilizing $N$ pilot symbols. The proposed algorithm is explained as follows. First, we formulate the channel estimation problem as a weighted sum mean square error (WSMSE) minimization problem containing pilot symbols and introduced variables. Second, for fixed pilot symbols, the introduced variables are optimized using minimum mean square error (MMSE) and generalized Rayleigh quotient methods. Finally, for $N=1$ and $N=K$ settings, the pilot symbols of all MSs are optimized using semi definite programming (SDP) convex optimization approach, and for the other settings of $N$ and $K$, the pilot symbols of all MSs are optimized by applying simple iterative algorithm. When $N=K$, it is shown that the latter iterative algorithm gives the optimal pilot symbols achieved by the SDP method. Simulation results confirm that the proposed algorithm achieves less WSMSE compared to that of the conventional semi-orthogonal pilot symbol and MMSE channel estimation algorithm which creates pilot contamination.Comment: Accepted in CISS 2014 Conferenc

Max-Min SNR Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks with Noise Variance Uncertainty

This paper proposes novel spectrum sensing algorithms for cognitive radio networks. By assuming known transmitter pulse shaping filter, synchronous and asynchronous receiver scenarios have been considered. For each of these scenarios, the proposed algorithm is explained as follows: First, by introducing a combiner vector, an over-sampled signal of total duration equal to the symbol period is combined linearly. Second, for this combined signal, the Signal-to-Noise ratio (SNR) maximization and minimization problems are formulated as Rayleigh quotient optimization problems. Third, by using the solutions of these problems, the ratio of the signal energy corresponding to the maximum and minimum SNRs are proposed as a test statistics. For this test statistics, analytical probability of false alarm ($P_f$) and detection ($P_d$) expressions are derived for additive white Gaussian noise (AWGN) channel. The proposed algorithms are robust against noise variance uncertainty. The generalization of the proposed algorithms for unknown transmitter pulse shaping filter has also been discussed. Simulation results demonstrate that the proposed algorithms achieve better $P_d$ than that of the Eigenvalue decomposition and energy detection algorithms in AWGN and Rayleigh fading channels with noise variance uncertainty. The proposed algorithms also guarantee the desired $P_f(P_d)$ in the presence of adjacent channel interference signals

Sensing Throughput Tradeoff for Cognitive Radio Networks with Noise Variance Uncertainty

This paper proposes novel spectrum sensing algorithm, and examines the sensing throughput tradeoff for cognitive radio (CR) networks under noise variance uncertainty. It is assumed that there are one white sub-band, and one target sub-band which is either white or non-white. Under this assumption, first we propose a novel generalized energy detector (GED) for examining the target sub-band by exploiting the noise information of the white sub-band, then, we study the tradeoff between the sensing time and achievable throughput of the CR network. To study this tradeoff, we consider the sensing time optimization for maximizing the throughput of the CR network while appropriately protecting the primary network. The sensing time is optimized by utilizing the derived detection and false alarm probabilities of the GED. The proposed GED does not suffer from signal to noise ratio (SNR) wall (i.e., robust against noise variance uncertainty) and outperforms the existing signal detectors. Moreover, the relationship between the proposed GED and conventional energy detector (CED) is quantified analytically. We show that the optimal sensing times with perfect and imperfect noise variances are not the same. In particular, when the frame duration is 2s, and SNR is -20dB, and each of the bandwidths of the white and target sub-bands is 6MHz, the optimal sensing times are 28.5ms and 50.6ms with perfect and imperfect noise variances, respectively.Comment: Accepted in CROWNCOM, June 2014, Oulu, Finlan