Optimal Linear Minimum Mean Square Error Research Articles

Deep Learning at the Edge for Channel Estimation in Beyond-5G Massive MIMO

Massive multiple-input multiple-output (mMIMO) is a critical component in upcoming 5G wireless deployment as an enabler for high data rate communications. mMIMO is effective when each corresponding antenna pair of the respective transmitter-receiver arrays experiences an independent channel. While increasing the number of antenna elements increases the achievable data rate, at the same time computing the channel state information (CSI) becomes prohibitively expensive. In this article, we propose to use deep learning via a multi-layer perceptron architecture that exceeds the performance of traditional CSI processing methods like least square (LS) and linear minimum mean square error (LMMSE) estimation, thus leading to a beyond fifth generation (B5G) networking paradigm wherein machine learning fully drives networking optimization. By computing the CSI of all pairwise channels simultaneously via our deep learning approach, our method scales with large antenna arrays as opposed to traditional estimation methods. The key insight here is to design the learning architecture such that it is implementable on massively parallel architectures, such as GPU or FPGA. We validate our approach by simulating a 32-element array base station and a user equipment with a 4-element array operating on millimeter-wave frequency band. Results reveal an improvement up to five and two orders of magnitude in BER with respect to fastest LS estimation and optimal LMMSE, respectively, substantially improving the end-to-end system performance and providing higher spatial diversity for lower SNR regions, achieving up to 4 dB gain in received power signal compared to performance obtained through LMMSE estimation.

A Novel LMMSE-EM Channel Estimator for High Mobility STBC-OFDM System

In time-selective fading channel, the Alamouti orthogonality principle is lost due to the variation of channel from symbol-to-symbol in space–time block-coded orthogonal frequency division multiplexing (STBC-OFDM) system and causes co-channel interference (CCI) effects. To combat the CCI effects, various signal detection schemes have been proposed earlier by assuming that a priori channel state information (CSI) is known to the receiver. However, in practice, the CSI is unknown and therefore accurate estimation of channel is required for efficient signal detection. In this paper, by exploiting circulant properties of the channel frequency response (CFR) autocorrelation matrix [Formula: see text], we propose an efficient low complexity linear-minimum-mean-square-error (LMMSE) estimator. This estimator applies an expectation–maximization (EM) iterative process to reduce the computational complexity significantly. Finally, we compare the proposed LMMSE-EM estimator with conventional least square (LS) and LMMSE estimator in terms of performance and computational complexity. The simulation results show that the proposed LMMSE-EM estimator achieves exactly the same performance as the optimal LMMSE estimator with much lower computational complexity.

On the Capacity of Iteratively Estimated Channels Using LMMSE Estimators

This paper investigates the capacity of radio channels when iterative channel estimation, data detection, and decoding are employed. Knowing the capacity gain from iterative detection versus purely pilot-based channel estimation helps a designer compare the performance of an iterative receiver against a noniterative receiver and select the best balance between performance and cost. A bound is put on the linear minimum mean square error (LMMSE) channel estimation error, based on which a bound on the capacity is obtained. The attainable capacity is related to the channel estimation error of the receiver. The bounds take into account the uncertainty in symbol detection on channel estimation and incorporate the effect of channel estimation error on channel capacity. The interaction between the symbol detector and the decoder is analytically characterized and depicted in an extrinsic information transfer (EXIT) chart, where a bound on the detector curve is found. With optimal LMMSE pilot-based channel estimation, the results of this paper demonstrate that iterative channel estimation provides insignificant capacity advantage at fading rates below 1% of the symbol rate, although a computational-cost gain is still available. Iterative channel estimation provides a capacity benefit if suboptimal pilot signaling is used to provide initial channel estimates.

Distributed Adaptive Node-Specific Signal Estimation in Fully Connected Sensor Networks—Part I: Sequential Node Updating

We introduce a distributed adaptive algorithm for linear minimum mean squared error (MMSE) estimation of node-specific signals in a fully connected broadcasting sensor network where the nodes collect multichannel sensor signal observations. We assume that the node-specific signals to be estimated share a common latent signal subspace with a dimension that is small compared to the number of available sensor channels at each node. In this case, the algorithm can significantly reduce the required communication bandwidth and still provide the same optimal linear MMSE estimators as the centralized case. Furthermore, the computational load at each node is smaller than in a centralized architecture in which all computations are performed in a single fusion center. We consider the case where nodes update their parameters in a sequential round robin fashion. Numerical simulations support the theoretical results. Because of its adaptive nature, the algorithm is suited for real-time signal estimation in dynamic environments, such as speech enhancement with acoustic sensor networks.

Suboptimal Linear MMSE Equalizers With Minimum Redundancy

Recent works have proposed practical zero-forcing (ZF) and linear minimum mean squared-error (LMMSE) solutions for fixed and memoryless block-based transceivers with minimum redundancy, using only half the amount of redundancy employed in standard systems. Their equalization processes require only O(M log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> M) operations. However, it may be difficult to apply LMMSE equalizers with minimum redundancy in some practical systems, given their higher number of operations. This letter proposes novel suboptimal LMMSE equalizers with minimum redundancy that require the same amount of computations of ZF equalizers, with a mild decrease in the throughput performance when compared to the optimal LMMSE solution.

Receiver design for multicarrier CDMA using frequency-domain oversampling

Based on the frequency-domain oversampling and minimum mean-square error (MMSE) principles, we propose three linear single-user detectors for downlink multicarrier codedivision multiple-access (MC-CDMA) systems. We begin with an optimal linear MMSE detector, which is computationally demanding. To reduce the complexity, a two-stage MMSE detector and a diagonal one-stage MMSE detector are developed subsequently. Simulation results show that the proposed detectors can efficiently suppress the multiple access interference (MAI) caused by frequency-selective fading, near-far effect, frequency offset, and nonlinear power amplification.

Decision-directed channel estimation based on iterative linear minimum mean square error for orthogonal frequency division multiplexing systems

A decision-directed (DD) channel estimation based on iterative linear minimum mean square error (LMMSE) is proposed for orthogonal frequency division multiplexing systems. Existing DD channel estimation is well known to have the problem of error propagation because of symbol-by-symbol detection. The proposed algorithm can estimate the correction term of current channel state information (CSI) according to the error vector of previous CSI by applying the orthogonality principle, and corrects the current CSI with this correction term. Analysis and simulation results have shown that this method has no error propagation problem. The performance of the proposed algorithm is much better than the conventional DD channel estimation, and close to the optimal LMMSE estimator, but with much less computational complexity compared with the optimal LMMSE estimator.

Feature-specific structured imaging

We present a feature-specific imaging system based on the use of structured light. Feature measurements are obtained by projecting spatially structured illumination onto an object and collecting all the reflected light onto a single photodetector. Principal component features are used to define the illumination patterns. The optimal linear minimum mean-square error (LMMSE) operator is used to generate object estimates from the measured features. We study the optimal allocation of illumination energy into each feature measurement in the presence of additive white Gaussian detector noise and optical blur. We demonstrate that this new imaging approach reduces imager complexity and provides improved image quality in high noise environments. Compared to the optimal LMMSE postprocessing of a conventional image, feature-specific structured imaging provides a 38% rms error reduction and requires 400 times fewer measurements for a noise standard deviation of sigma = 2 x 10(-3). Experimental results validate these theoretical predictions.

The Kalman filter as the optimal linear minimum mean-squared error multiuser CDMA detector

It is shown that a first-order linear state-space model applies to the asynchronous code-division multiple-access (CDMA) channel, and thus the Kalman filter produces symbol estimates with the minimum mean-squared error (MMSE) among all linear filters, in long- or short-code systems for a given detection delay. This result may be used as a benchmark against which to compare the performance of other linear detectors in asynchronous channels. It also reveals that a time-varying recursive filter with a fixed and finite complexity implements the fixed-lag linear MMSE (LMMSE) detector, which hitherto has been assumed to require a processing window (and hence complexity) that grows with time.