The performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that encloses as special cases standard Gaussian, row-orthogonal, geometric, and so-called T-orthogonal constructions. Source vectors that have non-uniform sparsity are included in the system model. Regularization based on l(1)-norm and leading to LASSO estimation, or basis pursuit denoising, is given the main emphasis in the analysis. Extensions to l(2)-norm and zero-norm regularization are also briefly discussed. The analysis is carried out using the replica method in conjunction with some novel matrix integration results. Numerical experiments for LASSO are provided to verify the accuracy of the analytical results. The numerical experiments show that for noisy compressed sensing, the standard Gaussian ensemble is a suboptimal choice for the measurement matrix. Orthogonal constructions provide a superior performance in all considered scenarios and are easier to implement in practical applications. It is also discovered that for non-uniform sparsity patterns, the T-orthogonal matrices can further improve the mean square error behavior of the reconstruction when the noise level is not too high. However, as the additive noise becomes more prominent in the system, the simple row-orthogonal measurement matrix appears to be the best choice out of the considered ensembles.

This paper studies the asymptotic performance of multi-hop amplify-and-forward relay multiple-antenna communication channels. Each multi-antenna relay terminal in the considered network amplifies the received signal, sent by a source, and retransmits it upstream toward a destination. Achievable ergodic rates of the relay channel with both jointly optimal detection and decoding and practical separate-decoding receiver architectures for arbitrary signaling schemes, along with average bit error rates for various types of detectors are derived in the regime where the number of antennas at each terminal grows large without a bound. To overcome the difficulty of averaging over channel realizations, we apply a large-system analysis based on the replica method from statistical physics. The validity of the large-system analysis is further verified through Monte Carlo simulations of realistic finite-sized systems.

A subspace projection to improve channel estimation in massive multi-antenna systems is proposed and analyzed. Together with power-controlled hand-off, it can mitigate the pilot contamination problem without the need for coordination among cells. The proposed method is blind in the sense that it does not require pilot data to find the appropriate subspace. It is based on the theory of large random matrices that predicts that the eigenvalue spectra of large sample covariance matrices can asymptotically decompose into disjoint bulks as the matrix size grows large. Random matrix and free probability theory are utilized to predict under which system parameters such a bulk decomposition takes place. Simulation results are provided to confirm that the proposed method outperforms conventional linear channel estimation if bulk separation occurs.

Presence of multiple antennas on both sides of a communication channel promises significant improvements in system throughput and power efficiency. In effect, a new class of large multiple-input multiple-output (MIMO) communication systems has recently emerged and attracted both scientific and industrial attention. To analyze these systems in realistic scenarios one has to include such aspects as co-channel interference, multiple access and spatial correlation. In this paper, we study the properties of correlated MIMO multiple-access channels in the presence of external interference. Using the replica method from statistical physics, we derive the ergodic sum-rate of the communication for arbitrary signal constellations when the numbers of antennas at both ends of the channel grow large. Based on these asymptotic expressions, we also address the problem of sum-rate maximization using statistical channel state information and linear precoding. The numerical results demonstrate that when the interfering terminals use discrete constellations, the resulting interference becomes easier to handle compared to Gaussian signals. Thus, it may be possible to accommodate more interfering transmitter-receiver pairs within the same area as compared to the case of Gaussian signals. In addition, we demonstrate numerically for the Gaussian and QPSK signaling schemes that it is possible to design precoder matrices that significantly improve the achievable rates at low-to-mid range of signal-to-noise ratios when compared to isotropic precoding.

Motivation: Estimation of bacterial community composition from a high-throughput sequenced sample is an important task in metagenomics applications. As the sample sequence data typically harbors reads of variable lengths and different levels of biological and technical noise, accurate statistical analysis of such data is challenging. Currently popular estimation methods are typically time-consuming in a desktop computing environment.

Results: Using sparsity enforcing methods from the general sparse signal processing field (such as compressed sensing), we derive a solution to the community composition estimation problem by a simultaneous assignment of all sample reads to a pre-processed reference database. A general statistical model based on kernel density estimation techniques is introduced for the assignment task, and the model solution is obtained using convex optimization tools. Further, we design a greedy algorithm solution for a fast solution. Our approach offers a reasonably fast community composition estimation method, which is shown to be more robust to input data variation than a recently introduced related method.

Availability and implementation: A platform-independent Matlab implementation of the method is freely available at http://www.ee.kth.se/ctsoftware; source code that does not require access to Matlab is currently being tested and will be made available later through the above Web site.

A subspace method for channel estimation is pro- posed for asymmetric antenna array systems. The so-called pilot contamination problem reported in [1] is found to be due to the linearity of channel estimation in [2]. We show that it does not occur in cellular systems with power control and power-controlled handoff when the nonlinear channel estimation method proposed in this paper is used. Power-control hand-off is needed to guarantee separability between signal and interference subspaces. We derive the transmission conditions for subspace separability based on free probability and perturbation theory.

Bidirectional wireless communication between two multi-antenna terminals that operate in a full-duplex mode is considered. The effects of loopback self-interference and transmit-side noise due to radio front-end imperfections are analyzed in the asymptotic regime where the number of antennas at both terminals grows large. The study compares two transparent mitigation schemes by which conventional spatial multiplexing can operate without being aware of the self-interference issue: spatial-domain null-space projection and time-domain subtractive cancellation. Both schemes eliminate the information-bearing part of the self-interference perfectly, but due to transmitter noise, the subtractive cancellation suffers from residual self-interference. The receive-side null-space projection, on the other hand, suppresses also the transmit-side noise, but at the cost of reduction in the degrees of freedom available for data reception. The results indicate that suppression becomes preferred when the level of transmit-side noise increases and the receiver does not have instantaneous knowledge about the spatial structure of the self-interference. Exhaustive Monte Carlo simulations also show that the asymptotic analytical results are useful for evaluating the performance of practical not-so-large systems.

We propose a nonlinear channel estimation method based on a subspace projection that is suitable for asymmetric antenna array systems. We show that the so-called pilot contamination problem reported in [1], is an artefact of (inappropriate) linear channel estimation and does not occur in cellular systems with power-controlled handoff when the channel estimation method proposed in this paper is used. We intuitively explain our result by establishing an isomorphism between a massive MIMO system and a spread-spectrum system with unknown signature sequences.