arXiv subjects

Mikko Vehkapera

Publications and source records attributed to Mikko Vehkapera.

6 recordsLinked to original sources

arXiv2018

Downlink Performance of Superimposed Pilots in Massive MIMO systems

In this paper, we investigate the downlink throughput performance of a massive multiple-input multiple-output (MIMO) system that employs superimposed pilots for channel estimation. The component of downlink (DL) interference that results from transmitting data alongside pilots in the uplink (UL) is shown to decrease at a rate proportional to the square root of the number of antennas at the BS. The normalized mean-squared error (NMSE) of the channel estimate is compared with the Bayesian Cramér-Rao lower bound that is derived for the system, and the former is also shown to diminish with increasing number of antennas at the base station (BS). Furthermore, we show that staggered pilots are a particular case of superimposed pilots and offer the downlink throughput of superimposed pilots while retaining the UL spectral and energy efficiency of regular pilots. We also extend the framework for designing a hybrid system, consisting of users that transmit either regular or superimposed pilots, to minimize both the UL and DL interference. The improved NMSE and DL rates of the channel estimator based on superimposed pilots are demonstrated by means of simulations.

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arXiv2017

Superimposed Pilots are Superior for Mitigating Pilot Contamination in Massive MIMO

In this paper, superimposed pilots are introduced as an alternative to time-multiplexed pilot and data symbols for mitigating pilot contamination in massive multiple-input multiple-output (MIMO) systems. We propose a non-iterative scheme for uplink channel estimation based on superimposed pilots and derive an expression for the uplink signal-to-interference-plus-noise ratio (SINR) at the output of a matched filter employing this channel estimate. Based on this expression, we observe that power control is essential when superimposed pilots are employed. Moreover, the quality of the channel estimate can be improved by reducing the interference that results from transmitting data alongside the pilots, and an intuitive iterative data-aided scheme that reduces this component of interference is also proposed. Approximate expressions for the uplink SINR are provided for the iterative data-aided method as well. In addition, we show that a hybrid system with users utilizing both time-multiplexed and superimposed pilots is superior to an optimally designed system that employs only time-multiplexed pilots, even when the non-iterative channel estimate is used to build the detector and precoder. We also describe a simple approach to implement this hybrid system by minimizing the overall inter and intra-cell interference. Numerical simulations demonstrating the performance of the proposed channel estimation schemes and the superiority of the hybrid system are also provided.

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arXiv2016

Analysis of Regularized LS Reconstruction and Random Matrix Ensembles in Compressed Sensing

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 l1-norm and leading to LASSO estimation, or basis pursuit denoising, is given the main emphasis in the analysis. Extensions to l2-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.

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arXiv2014

Signal recovery using expectation consistent approximation for linear observations

A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica theory, which is supposed to be exact in the large system limit, when each entry of the observation matrix is independently generated from an identical distribution. However, this is not necessarily the case for general matrices. We show that EC recovery exhibits consistency with the replica theory for a wider class of random observation matrices. This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.

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arXiv2013

Statistical Mechanics Approach to Sparse Noise Denoising

Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the possibility of perfect and imperfect reconstruction. Conditions characterizing this threshold are derived and the mean square error of the estimate is obtained for the case when perfect reconstruction is not possible. Detailed calculations are provided to expose the mathematical tools to a wide audience.

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arXiv2012

Typical $l_1$-recovery limit of sparse vectors represented by concatenations of random orthogonal matrices

We consider the problem of recovering an $N$-dimensional sparse vector $\vm{x}$ from its linear transformation $\vm{y}=\vm{D} \vm{x}$ of $M(< N)$ dimension. Minimizing the $l_{1}$-norm of $\vm{x}$ under the constraint $\vm{y} = \vm{D} \vm{x}$ is a standard approach for the recovery problem, and earlier studies report that the critical condition for typically successful $l_1$-recovery is universal over a variety of randomly constructed matrices $\vm{D}$. For examining the extent of the universality, we focus on the case in which $\vm{D}$ is provided by concatenating $\nb=N/M$ matrices $\vm{O}_{1}, \vm{O}_{2},..., \vm{O}_\nb$ drawn uniformly according to the Haar measure on the $M \times M$ orthogonal matrices. By using the replica method in conjunction with the development of an integral formula for handling the random orthogonal matrices, we show that the concatenated matrices can result in better recovery performance than what the universality predicts when the density of non-zero signals is not uniform among the $\nb$ matrix modules. The universal condition is reproduced for the special case of uniform non-zero signal densities. Extensive numerical experiments support the theoretical predictions.

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