Minimum Mean Square Error Estimator Research Articles

Minimum Mean Squared Error Estimation and Mutual Information Gain

Information theoretic quantities such as entropy, entropy rate, information gain, and relative entropy are often used to understand the performance of intelligent agents in learning applications. Mean squared error has not played a role in these analyses, primarily because it is not felt to be a viable performance indicator in these scenarios. We build on a new quantity, the log ratio of entropy powers, to establish that minimum mean squared error (MMSE) estimation, prediction, and smoothing are directly connected to mutual information gain or loss in an agent learning system modeled by a Markov chain for many probability distributions of interest. Expressions for mutual information gain or loss are developed for MMSE estimation, prediction, and smoothing, and an example for fixed lag smoothing is presented.

Enhancing spectral efficiency in uplink/downlink channels of multi-cell massive MIMO for 5G networks

Massive multiple-input multiple-output (MIMO) systems are at the forefront of 5G technology, significantly improving energy efficiency compared to earlier wireless communication systems. This study develops an optimal model for energy-efficient massive MIMO systems, aiming to increase spectral efficiency (SE) within a multi-cell framework. Base stations (BSs) use various techniques for channel estimations during uplink (UL) transmission, including minimum mean-squared error (MMSE), Least Squares, and Element-wise MMSE (EW-MMSE) estimators. The research evaluates the SE achievable through MMSE channel estimation by applying different receive combining schemes. Additionally, it explores downlink (DL) transmission using various precoding schemes, utilizing vectors similar to those in combining schemes. Simulations show a significant improvement in SE by advancing UL and DL transmission models. The study highlights that optimized MMSE channel estimation, along with an increased number of BS antennas and the ability to serve multiple user equipment (UEs) per cell, can enhance the average SE per cell. The findings indicate that optimizing channel estimation is crucial for the development of massive MIMO systems, especially for improving SE in both UL and DL transmissions.

Event-Based Remote State Estimation for Nonlinear Systems: A Box Particle Filtering Method.

This article is concerned with the problem of event-based remote state estimation for nonlinear/non-Gaussian systems on a wireless network with limited bandwidth. To reduce unnecessary data transmissions, a novel event-triggering mechanism is developed by using the least-square technique. Based on this, an event-triggered box particle filtering scheme is designed to realize the minimum mean-squared error estimation at the remote estimator end, in which the posterior probability density functions are calculated separately according to the information of the event-triggered indicator to avoid the problem of excessive estimation error. Different from the existing approaches, the proposed algorithm does not depend on any Gaussian assumptions and reduces the computational complexity under the premise of ensuring the estimation performance. Finally, two simulation examples are performed to demonstrate the validity of the proposed algorithm.

An Integrated Orthogonal Frequency-Division Multiplexing Chirp Waveform Processing Method for Joint Radar and Communication Based on Low-Density Parity-Check Coding and Channel Estimation

With the advancement of information technology construction, the integration of radar and communication represents a crucial technological evolution. Driven by the research boom of integrated sensing and communications (ISACs), some scholars have proposed utilizing orthogonal frequency-division multiplexing (OFDM) to separately modulate radar and communication signals. However, the OFDM symbols in this paper incorporate a cyclic prefix (CP) and a virtual carrier (VC) instead of zero padding (ZP). This approach mitigates out-of-band power caused by ZP, in addition to reducing adjacent channel interference (ACI). In addition, we introduce low-density parity-check (LDPC) and use an improved normalized min-sum algorithm (NMSA) in decoding. The enhanced decoding efficiency and minimized system errors render the proposed waveform more suitable for complex environments. In terms of signal processing methods, this paper continues to use radar signals as a priori information to participate in channel estimation. Further, we consider the symbol timing offset (STO) and carrier frequency offset (CFO) issues. In order to obtain more reliable data, we use the minimum mean-square error (MMSE) estimation based on the discrete Fourier transform (DFT) to evaluate the channel. Simulation experiments verify that the system we propose not only realizes the transmission and detection functions but also improves the performance index of the integrated signal, such as the bit error rate (BER) of 7 × 10−5, the peak side lobe ratio (PSLR) of −13.81 dB, and the integrated side lobe ratio (ISLR) of −8.98 dB at a signal-to-noise ratio (SNR) of 10 dB.

Evaluating Performance: A Study of Encrypted vs. Unencoded Signals in SISO-OFDM with LS and MMSE Estimations

The continuous progress in digital communication has played a crucial role in meeting the increasing need for faster data rates. Orthogonal Frequency Division Multiplexing (OFDM), a pivotal methodology in this progression, attains improved data rates through the efficient utilisation of densely packed carriers within a specified channel bandwidth. This article focuses on the investigation of channel estimation in OFDM systems. the study of search lies in its examination of the performance consequences associated with the incorporation or lack thereof of a convolutional encoder in OFDM systems and looks at how well two well-known channel estimation algorithms, Least Square (LS) and Minimum Mean Square Error (MMSE), work in 4-Quadrature amplitude modulation (4-QAM) OFDM systems with and without a convolutional encoder with a comprehensive evaluation of the efficacy of the OFDM system across various channel conditions. It uses MATLAB implementations as its main tool. The findings of the study indicate that the MMSE algorithm, despite its higher complexity, exhibits superior performance in comparison to the LS algorithm when combined with a convolutional encoder. The gain in terms of bit error rate (BER) improvement approximately 12 dB. This represents the logarithmic scale improvement in BER from BER1(uncoded) to BER2(coded) at the same the energy per bit to noise power spectral density ratio (Eb/N0) of 40 dB.

Unified ISAC Pareto Boundary Based on Mutual Information and Minimum Mean-Square Error Estimation

Unified ISAC Pareto Boundary Based on Mutual Information and Minimum Mean-Square Error Estimation

Channel Estimation for LEO Satellite Massive MIMO OFDM Communications

In this paper, we investigate the massive multiple-input multiple-output orthogonal frequency division multiplexing channel estimation for low-earth-orbit satellite communication systems. First, we use the angle-delay domain channel to characterize the space-frequency domain channel. Then, we show that the asymptotic minimum mean square error (MMSE) of the channel estimation can be minimized if the array response vectors of the user terminals (UTs) that use the same pilot are orthogonal. Inspired by this, we design an efficient graph-based pilot allocation strategy to enhance the channel estimation performance. In addition, we devise a novel two-stage channel estimation (TSCE) approach, in which the received signals at the satellite are manipulated with per-subcarrier space domain processing followed by per-user frequency domain processing. Moreover, the space domain processing of each UT is shown to be identical for all the subcarriers, and an asymptotically optimal vector for the per-subcarrier space domain linear processing is derived. The frequency domain processing can be efficiently implemented by means of the fast Toeplitz system solver. Simulation results show that the proposed TSCE approach can achieve a near performance to the MMSE estimation with much lower complexity.

Information theoretic waveform design with applications to adaptive‐on‐transmit radar

AbstractThe marginal Fisher information (MFI) metric is used to design waveforms for the sake of informationally optimal adaptive‐on‐transmit radar operation. A framework for MFI waveform design is developed and the Polyphase‐Coded FM (PCFM) waveform model is utilised to produce a constant‐modulus, spectrally contained signal amenable to transmission with high‐power amplifiers. The efficacy of the MFI waveform design and minimum mean square error (MMSE) estimation is experimentally demonstrated and extended into an adaptive and dynamic sensing paradigm. The radar transmit waveform is optimised to maximise the Fisher information with respect to the range profile. Upon observing new information from radar echoes, the iterative MMSE (iMMSE) estimator then minimises the estimation error variance according to prior observations. Sequential information maximisation (via waveform design) and error minimisation (via iMMSE) tends towards the Cramér–Rao lower bound (CRLB) with additional measurements improving radar resolution and accuracy. These concepts maximise the information extracted by a radar operating in a congested spectrum where the available bandwidth is limited.

End-to-end DVB-S2X system design with DL-based channel estimation over satellite fading channels at Ka-band

Satellite channels suffer from heavy fading due to the atmospheric impairments at high frequencies. Therefore, channel estimation is essential for coherent detection and demodulation in satellite-coded systems. The conventional minimum mean square error (MMSE) estimator (the theoretical upper bound) requires a priori knowledge about the channel statistics which is not feasible to obtain in a real transmission. Also, it suffers from high complexity. However, deep learning (DL) estimators do not require any information about the channel statistics. Therefore, in this paper, two DL-based channel estimators are proposed for digital and video broadcasting second generation extension (DVB-S2X) system with less complexity than the MMSE estimator. In particular, the bidirectional long-short term memory (BLSTM) and the gated recurrent unit (GRU) are adopted in our proposed estimators which are termed as DLBLSTM and DLGRU, respectively. The proposed estimators evaluated over two satellite fading channels; one with heavy fading and the other with low fading. Moreover, these estimators are compared with the conventional estimators, the least square (LS) and the MMSE, in terms of the normalized mean square error (NMSE) and the bit error rate (BER). Simulation results show that the proposed DL-based estimators have better performance than the LS estimator and the DLBLSTM has better performance than the DLGRU estimator in terms of NMSE and BER with both satellite channels.

Decentralized Linear Quadratic Systems With Major and Minor Agents and Non-Gaussian Noise

A decentralized linear quadratic system with a major agent and a collection of minor agents is considered. The major agent affects the minor agents, but not vice versa. The state of the major agent is observed by all agents. In addition, the minor agents have a noisy observation of their local state. The noise processes is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">not</i> assumed to be Gaussian. The structures of the optimal strategy and the best linear strategy are characterized. It is shown that major agent's optimal control action is a linear function of the major agent's MMSE (minimum mean squared error) estimate of the system state while the minor agent's optimal control action is a linear function of the major agent's MMSE estimate of the system state and a “correction term” which depends on the difference of the minor agent's MMSE estimate of its local state and the major agent's MMSE estimate of the minor agent's local state. Since the noise is non-Gaussian, the minor agent's MMSE estimate is a non-linear function of its observation. It is shown that replacing the minor agent's MMSE estimate by its LLMS (linear least mean square) estimate gives the best linear control strategy. The results are proved using a direct method based on conditional independence, common-information-based splitting of state and control actions, and simplifying the per-step cost based on conditional independence, orthogonality principle, and completion of squares.

Joint Receiver Design for Integrated Sensing and Communications

In this letter, we investigate the joint receiver design for integrated sensing and communication (ISAC) systems, where the communication signal and the target echo signal are simultaneously received and processed to achieve a balanced performance between both functionalities. In particular, we proposed two design schemes to solve the joint sensing and communication problem of receive signal processing. The first is based on maximum likelihood (ML) detection, minimum mean squared error (MMSE) estimation and interference cancellation (IC), and the other formulates a tailored MMSE estimator for target estimation that is independent to the detector, which form a Non-IC design. We show that with the structural information of the communication signal taken into account, the Non-IC approach outperforms the IC method and achieves optimal performance. Numerical results are provided to validate the effectiveness of the proposed optimal designs.

Super-resolution Direction of Arrival Estimation Using a Minimum Mean-Square Error Framework

This paper develops a novel sparse direction-of-arrival (DOA) estimation technique that avoids the common requirement of hyperparameters, which are typically difficult to set suitably in practice. Using the presented minimum mean-square error (MMSE) estimation framework, we propose a computationally efficient super-resolution DOA estimator that is implemented using an alternate updating of the spatial power distribution of the signals and of the dictionary matrix using a ridge regression algorithm. The regularization parameter determining the sparsity of the solution is formed from the previous spatial power distribution estimates using a SPICE-based criteria. The method employs an adaptive gridding strategy to avoid the grid mismatch problem. The computational complexity is further reduced by the use of an integrated wideband dictionary, determing the active dictionary in an iterative manner. The method offers high resolution estimates of closely spaced sources even for very low sample support (single snapshot) without assuming prior knowledge of the number of sources. Our evaluations illustrate the preferable performance of the proposed estimator as compared to various state-of-the art estimators, also indicating that the method’s performance approaches the Cramér-Rao lower bound (CRB) for the examined problem as the signal-to-noise ratio (SNR) increases.

Joint Activity Detection and Channel Estimation for Intelligent-Reflecting-Surface-Assisted Wireless IoT Networks

Intelligent reflecting surfaces (IRSs) provide the ability to tune the wireless environments by introducing passive scattering elements between the base station (BS) or access points (APs) and users, and it is a promising technology for next generation wireless networks. In this paper, we consider joint activity detection and channel estimation in both centralized and distributed IRS assisted IoT networks. We determine the explicit distribution for the equivalent channel coefficients from the BS or APs to the users. It is shown that this distribution can be equivalently represented with a Gaussian scale mixture (GSM) model. With generalized approximate message passing (GAMP) algorithm, the received pilot signals at the BS or APs are decoupled into scalar Gaussian noise corrupted versions of the effective channel coefficients. Subsequently, minimum mean square error (MMSE) estimate of the effective channel coefficients and threshold detection rules are acquired. Finally, the optimal fusion rule is used to obtain the activity detection results of each user. As an additional low-complexity approach, we approximate the equivalent channel coefficients with a Gaussian approximation (GA) model. We derive the theoretical mean square error for the MMSE estimate of the effective channel coefficients using the GA model and the state evolution equations of the GAMP algorithm, under the assumption that the direct links from the BS to the users can be neglected due to unfavorable propagation conditions. Numerical results show that the Gaussian approximation for the distribution of the equivalent channel coefficients is accurate even for moderate number of elements at the IRS. And the theoretical mean square error for the MMSE estimate of the effective channel coefficients under the assumption that direct link is negligible is shown to overlap with the corresponding numerical simulations.

Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density

The penalized least squares regression (PLSR) is usually used for solving linear inverse problems in signal processing, such as the denoising (noise reduction) and deconvolution problems. The performance of this method is based on the penalty function (regularization). Therefore, we propose the novel regularization based on the Pareto distribution. Here, famous regularizations, such as the logarithm and ratio regularizations, are included in the mathematical form of this proposed regularization. Moreover, mathematical models of the Bayesian estimator, such as the maximum a posteriori (MAP) and minimum mean square error (MMSE) estimations, in additive white Gaussian noise (AWGN) are similar to the PLSR. Therefore, we propose denoising methods via PLSRs using the proposed regularization which are equivalent to the MAP and MMSE estimations. In numerical results, proposed methods give good denoising results.

Indexed-channel estimation under frequency and time-selective fading channels in high-mobility systems

&lt;p&gt;&lt;span lang="EN-US"&gt;Index modulation (IM) techniques have been employed in different communication systems to improve bandwidth efficiency by carrying additional information bits. In high-mobility communication systems and under both time-selective and frequency-selective fading channels with Doppler spread, channel variations can be tracked by employing pilot-aided channel estimation with minimum mean-squared error estimation. However, inserting pilot symbols among information symbols reduces the system's spectral efficiency in pilot-aided channel estimation schemes. We propose pilot-aided channel estimation with zero-pilot symbols and an energy detection scheme to tackle this issue. Part of the information bit-stream is conveyed by the indices of zero-pilot symbols leading to an increase in the system's spectral efficiency. We used an energy detector at the receiver to detect the transmitted zero-pilot symbols. This paper examines the impacts of diversity order on the zero-pilot symbol detection error probability and the mean-squared of error estimation. The impacts of pilot symbols number and the zero-pilot symbol number on the mean-squared error of the minimum mean-squared error (MMSE) estimator and the system error performance are also investigated in this paper.&lt;/span&gt;&lt;/p&gt;

Information Rates for Channels with Fading, Side Information and Adaptive Codewords.

Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel models with additive white Gaussian noise (AWGN) and circularly-symmetric complex Gaussian inputs. One variation uses reverse channel models with minimum mean square error (MMSE) estimates that give the largest rates but are challenging to optimize. A second variation uses forward channel models with linear MMSE estimates that are easier to optimize. Both model classes are applied to channels where the receiver is unaware of the CSIT and for which adaptive codewords achieve capacity. The forward model inputs are chosen as linear functions of the adaptive codeword's entries to simplify the analysis. For scalar channels, the maximum GMI is then achieved by a conventional codebook, where the amplitude and phase of each channel symbol are modified based on the CSIT. The GMI increases by partitioning the channel output alphabet and using a different auxiliary model for each partition subset. The partitioning also helps to determine the capacity scaling at high and low signal-to-noise ratios. A class of power control policies is described for partial CSIR, including a MMSE policy for full CSIT. Several examples of fading channels with AWGN illustrate the theory, focusing on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions in terms of mutual and directed information.

Massive MIMO Communication With Intelligent Reflecting Surface

This paper studies the feasibility of deploying intelligent reflecting surfaces (IRSs) in massive multiple input multiple-output (MIMO) systems to improve the performance of users in the service dead zone. One question of paramount importance is as follows: if the overhead of channel training and the computational complexity of algorithm design arising from the huge number of IRS reflecting elements and base station (BS) antennas have to be controlled, can we provide reasonable performance to the users with weak direct channels? This paper provides an affirm answer to this question. Specifically, to reduce the channel training overhead, we consider an appealing protocol for the uplink communication in the IRS-assisted massive MIMO systems. Under this protocol, the IRS reflection coefficients are optimized based on the channel covariance matrices, which are generally fixed for many coherence blocks, to boost the long-term performance. Then, given the IRS reflecting coefficients, the BS beamforming vectors are designed in each coherence block based on the effective channel of each user, which is the superposition of its direct and reflected user-IRS-BS channels, to improve the instantaneous performance. Since merely the user effective channels are estimated in each coherence block, the training overhead of this protocol is the same as that in the legacy wireless systems without IRSs. Moreover, in the asymptotic regime that the numbers of IRS elements and BS antennas both go to infinity with a fixed ratio, we manage to first characterize the minimum mean-squared error (MMSE) estimators of the user effective channels and then quantify the closed-form user achievable rates as functions of channel covariance matrices with channel training overhead and estimation error taken into account. Interestingly, it is shown that the properties of channel hardening and favorable propagation still hold for the user effective channels, and satisfactory user rates are thus achievable even if simple BS beamforming solutions, e.g., maximal-ratio combining, are employed. Finally, thanks to the rate characterization, we design a low-complexity algorithm to optimize the IRS reflection coefficients based on channel covariance matrices.

A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation

Covariance matrix estimation plays a significant role in both in the theory and practice of portfolio analysis and risk management. This paper deals with the available data prior to developing a factor model to enhance covariance matrix estimation. Our work has two main outcomes. First, for a general linear model with unknown prior parameters, a class of best linear empirical Bayes estimators is established through two kinds of architectures to improve the estimation accuracy by utilizing additional data prior. The theoretical results indicate two key points: the proposed estimators are equivalent to the linear minimum mean-square error estimator when complete or sufficient partial data prior are provided; and the proposed estimators perform better than the optimal weighted least squares method, which ignores the data prior in each situation. Second, the proposed estimators are used for calculating a high-dimensional covariance matrix through factor models. The numerical example and the simulation results verify the effectiveness of our methods.

Innovation-based stealthy attack against distributed state estimation over sensor networks

This paper presents a new design of an innovation-based stealthy attack strategy against distributed state estimation over a sensor network. In the absence of network attack, an optimal distributed minimum mean-square error (MMSE) estimator is developed by fusing the interaction measurements from neighboring nodes in the sensor network. Also, the boundedness of distributed estimation covariance is discussed over a regionally observable sensor network, which weakens the requirement for local observability of each sensor. Then, a stealthy attack framework embedded with an adjustable parameter is proposed, under which the attack strategy is to maximize the distributed estimation covariance. Sufficient conditions on the boundedness of the compromised covariance are derived, and the tradeoff between attack stealthiness and attack effects is determined. Finally, numerical examples are shown to verify the developed techniques.

Self-interference cancellation in underwater acoustic communications systems using orthogonal pilots in IBFD

This paper proposes a Self-interference (SI) cancellation system model of Underwater acoustic (UWA) communication for in-band full-duplex (IBFD) technology. The SI channel is separated from the Far channel by exploiting a concurrently orthogonal pilot channel estimation technique using two orthogonal frequency-division multiplexing (OFDM) blocks to establish orthogonality between them based on a unitary matrix. Compared to the half-duplex channel estimator, the mean squared error (MSE) and the bit error rate (BER) provided strong evidence for the efficiency of the proposed SI cancellation. Since full-duplex systems are more efficient than half-duplex ones, the proposed approach might be seen as a viable option for them. The proposed method proved effective when used with a fixed full-duplex (FD) position and FD shifting of up to 4°. Different channel lengths and distances are adopted to evaluate the proposed method. Initial findings indicate that MSE for the SI channel minimum mean-square error (MMSE) estimator at 20 dB is 0.118 · 10−3, for fixed FD. In addition, this paper presents a geometry channel model for the Far channel in the IBFD underwater communication system that describes the propagation delay of the multipath reflection. The simulation results for the multipath propagation delay spread are similar to the traditional results, with the delay spread of the suggested model reaching (79 ms), which is close to the Bellhop simulator result (78 ms).