We propose a method for MIMO decoding when channel state information (CSI) is unknown to both the transmitter and receiver. The proposed method requires some structure in the transmitted signal for the decoding to be effective, in particular that the underlying sources are drawn from a hypercubic space. Our proposed technique fits a minimum volume parallelepiped to the received samples. This problem can be expressed as a non-convex optimization problem that can be solved with high probability by gradient descent. Our blind decoding algorithm can be used when communicating over unknown MIMO wireless channels using either BPSK or MPAM modulation. We apply our technique to jointly estimate MIMO channel gain matrices and decode the underlying transmissions with only knowledge of the transmitted constellation and without the use of pilot symbols. Our results provide theoretical guarantees that the proposed algorithm is correct when applied to small MIMO systems. Empirical results show small sample size requirements, making this algorithm suitable for block-fading channels with coherence times typically seen in practice. Our approach has a loss of less than 3dB compared to zero-forcing with perfect CSI, imposing a similar performance penalty as space-time coding techniques without the loss of rate incurred by those techniques.
The problem of joint blind channel estimation and decoding is not new. For example, in @cite_2 , the authors apply MMSE techniques to the blind decoding of MIMO problems over small alphabets while simultaneously recovering the underlying channel gain matrix. The approach in @cite_2 requires the number of samples of received signals used by the algorithm to grow linearly with constellation size, which is exponential in @math , the number of transmit antennas. The approach in @cite_2 only requires the underlying constellation to be discrete; however, for constellations that are also hypercubic, our approach requires far fewer received samples than the approach of @cite_2 based on our simulation results.
@cite_2
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We consider the use of spatial diversity to improve the performance of analog joint source-channel coding in wireless fading channels. The communication system analyzed in this paper consists of discrete-time all-analog-processing joint source-channel coding where Maximum Likelihood (ML) and Minimum Mean Square Error (MMSE) detection are employed. By assuming a fast-fading Rayleigh channel, we show that MMSE performs much better than ML at high Channel Signal-to-Noise Ratios (CSNR) in single-antenna wireless systems. However, such performance gap can be significantly reduced by using multiple receive antennas, thus making low complexity ML decoding very attractive in the case of receive diversity. Moreover, we show that the analog scheme can be considerably robust to imperfect channel estimation. In addition, as an alternative to multiple antennas, we also consider spatial diversity through cooperative communications, and show that the application of the Amplify-and-Forward (AF) protocol with single antenna nodes leads to similar results than when two antennas are available at the receiver and Maximal Ratio Combining (MRC) is applied. Finally, we show that the MMSE implementation of the analog scheme performs very close to the unconstrained capacity of digital schemes using scalar quantization, while its complexity is much lower than that of capacity-approaching digital systems. Consider a MIMO interference channel whereby each transmitter and receiver are equipped with multiple antennas. The basic problem is to design optimal linear transceivers (or beamformers) that can maximize system throughput. The recent work [13] suggests that optimal beamformers should maximize the total degrees of freedom and achieve interference alignment in high SNR. In this paper we first consider the interference alignment problem in spatial domain and prove that the problem of maximizing the total degrees of freedom for a given MIMO interference channel is NP-hard. Furthermore, we show that even checking the achievability of a given tuple of degrees of freedom for all receivers is NP-hard when each receiver is equipped with at least three antennas. Moreover, in case where each transmitter and receiver use at most two antennas, the same problem is polynomial time solvable. Finally, we propose a distributed algorithm for transmit covariance matrix design, while assuming each receiver uses a linear MMSE beamformer. The simulation results show that the proposed algorithm outperforms the existing interference alignment algorithms in terms of system throughput. A new architecture called integer-forcing (IF) linear receiver has been recently proposed for multiple-input multiple-output (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be computed as a part of the decoding process. In this paper, we propose a method based on Hermite-Korkine-Zolotareff (HKZ) and Minkowski lattice basis reduction algorithms to obtain the integer coefficients for the IF receiver. We show that the proposed method provides a lower bound on the ergodic rate, and achieves the full receive diversity. Suitability of complex Lenstra-Lenstra-Lovasz (LLL) lattice reduction algorithm (CLLL) to solve the problem is also investigated. Furthermore, we establish the connection between the proposed IF linear receivers and lattice reduction-aided MIMO detectors (with equivalent complexity), and point out the advantages of the former class of receivers over the latter. For the 2 × 2 and 4× 4 MIMO channels, we compare the coded-block error rate and bit error rate of the proposed approach with that of other linear receivers. Simulation results show that the proposed approach outperforms the zero-forcing (ZF) receiver, minimum mean square error (MMSE) receiver, and the lattice reduction-aided MIMO detectors. We propose an efficient open-loop channel estimator for a millimeter-wave (mm-wave) hybrid multiple-input multiple-output (MIMO) system consisting of radio-frequency (RF) beamformers with large antenna arrays followed by a baseband MIMO processor. A sparse signal recovery problem exploiting the sparse nature of mm-wave channels is formulated for channel estimation based on the parametric channel model with quantized angles of departures arrivals (AoDs AoAs), called the angle grids. The problem is solved by the orthogonal matching pursuit (OMP) algorithm employing a redundant dictionary consisting of array response vectors with finely quantized angle grids. We suggest the use of non-uniformly quantized angle grids and show that such grids reduce the coherence of the redundant dictionary. The lower and upper bounds of the sum-of-squared errors of the proposed OMP-based estimator are derived analytically: the lower bound is derived by considering the oracle estimator that assumes the knowledge of AoDs AoAs, and the upper bound is derived based on the results of the OMP performance guarantees. The design of training vectors (or sensing matrix) is particularly important in hybrid MIMO systems, because the RF beamformer prevents the use of independent and identically distributed random training vectors, which are popular in compressed sensing. We design training vectors so that the total coherence of the equivalent sensing matrix is minimized for a given RF beamforming matrix, which is assumed to be unitary. It is observed that the estimation accuracy can be improved significantly by randomly permuting the columns of the RF beamforming matrix. The simulation results demonstrate the advantage of the proposed OMP with a redundant dictionary over the existing methods such as the least squares method and the OMP based on the virtual channel model.