Sum Mean Square Error Research Articles

Pilot Optimization, Channel Estimation, and Optimal Detection for Full-Duplex OFDM Systems With IQ Imbalances

In full-duplex orthogonal frequency-division multiplexing systems with IQ imbalances, a frequency-domain least-squares (FD-LS) channel estimator is proposed to estimate both source-to-destination (intended) and destination-to-destination (self-interference) channels. Subsequently, an optimal closed-form pilot matrix is derived to minimize the sum of mean square errors (sum-MSE) of the proposed FD-LS channel estimator. Then, an improved FD-LS estimator is presented and proved to further improve the performance of the FD-LS by exploiting the time-domain property of the channel. In the presence of channel estimation error, an optimal low-complexity maximum likelihood (ML) detector is developed by using eigenvalue and singular value decompositions and whitening the residual self-interference plus noise. Simulation results show that given the proposed FD-LS estimator, the optimal pilot matrix performs much better than those nonsingular pilot matrices with larger conditional numbers (CN). To be specific, the former achieves about 10-dB signal-to-noise ratio (SNR) gain over the latter with CN = 10, the improved FD-LS channel estimator provides about 6-dB SNR gain over the FD-LS estimator at a fixed bit error rate (BER), and the proposed whitening-filter ML detector performs at least 0.6 dB better than the conventional ML detector at a given BER of $10^{-3}$ in the medium-and high-SNR regions.

Tax declaration rates via audits: a prediction using Markov model

Purpose- This article predicts tax declaration rates by Markov chain model. Methodology- Four Markov models are constructed for the declaration rates of three tax revenues. Declaration probabilities for the year 2017 are estimated by constructing probability matrices of transitions between classes described for every model. Declaration rates are predicted by the product of the initial probability matrix and transition probability matrix. Limiting matrices of predictions are found. The best Markov model was found by estimating the sum of mean square errors for every model. Findings- Main results of this study are i) transitions of tax declarations are declining in higher states and improving in lower states, ii) in its best model corporate tax declaration rate is predicted to be between 47% and 64.5% in 2017 with a probability of 78% and would be stable in the same interval at a probability of 60% in 2038, iii) in the long run income tax would decrease ₺20,3 billion with a probability of 42% and Value Added Tax would decrease ₺26,2 billion with a probability of 40% and iv) expected declaration rates of income tax, corporate tax and value added tax in 2017 are 52.3%, 61.6% and 62.8%, respectively. Conclusion- Income tax and Value Added Tax payoffs may substantially decrease from 2015 to 2038 and 2023 respectively. This may cause a revenue deficiency to Turkish Revenue Administration. Therefore Income tax and Value Added Tax audits should be increased. Even though tax revenues increase over time, the declaration rates show a decreasing to stationary or increasing to stationary behavior.

Pilot Optimization and Power Allocation for OFDM-Based Full-Duplex Relay Networks With IQ-Imbalances

In OFDM relay networks with IQ imbalances and full-duplex relay station (RS), how to optimize pilot pattern and power allocation using the criterion of minimizing the sum of mean square errors (Sum-MSE) for the frequency-domain least-squares channel estimator has a heavy impact on self-interference cancellation. Firstly, the design problem of pilot pattern is casted as a convex optimization. From the KKT conditions, the optimal analytical expression is derived given the fixed source power and RS power. Subsequently, an optimal power allocation (OPA) strategy is proposed and presented to further alleviate the effect of Sum-MSE under the total transmit power sum constraint of source node and RS. Simulation results show that the proposed OPA performs better than equal power allocation (EPA) in terms of Sum-MSE, and the Sum-MSE performance gain grows with deviating $\rho$ from the value of $\rho^o$ minimizing the Sum-MSE, where $\rho$ is defined as the average ratio of the residual SI channel at RS to the intended channel from source to RS. For example, the OPA achieves about 5dB SNR gain over EPA by shrinking or stretching $\rho$ with a factor $4$. More importantly, as $\rho$ decreases or increases more, the performance gain becomes more significant.

Low complexity robust linear transceiver design for MIMO interference channel

This paper focuses on the linear transceiver design for multiple input multiple output (MIMO) interference channel (IC), in which a bounded channel error model is assumed. Two optimization problems are formulated as minimizing maximum per-user mean square error (MSE) and sum MSE with the per-transmitter power constraint. Since these optimization problems are not jointly convex on their variable matrices, the transmitter and receiver can be optimized alternately respectively. For each matrix, an approximated approach is presented where the upper bound of constraint is derived so that it has less semidefinite, thus the problem can be viewed as second-order-cone programming (SOCP) and gets less computational complexity. Compared with the conventional S-procedure method, the proposed approach achieves similar performance, but reduces the complexity significantly, especially for the system with large scale number of antennas.

Integer Forcing-and-Forward Transceiver Design for MIMO Multipair Two-Way Relaying

In this paper, we propose a new transmission scheme, named as Integer Forcing-and-Forward (IFF), for communications among multi-pair multiple-antenna users in which each pair exchanges their messages with the help of a single multi antennas relay in the multiple-access and broadcast phases. The proposed scheme utilizes Integer Forcing Linear Receiver (IFLR) at relay, which uses equations, i.e., linear integer-combinations of messages, to harness the intra-pair interference. Accordingly, we propose the design of mean squared error (MSE) based transceiver, including precoder and projection matrices for the relay and users, assuming that the perfect channel state information (CSI) is available. In this regards, in the multiple-access phase, we introduce two new MSE criteria for the related precoding and filter designs, i.e., the sum of the equations MSE (Sum-Equation MSE) and the maximum of the equations MSE (Max-Equation MSE), to exploit the equations in the relay. In addition, the convergence of the proposed criteria is proven as well. Moreover, in the broadcast phase, we use the two traditional MSE criteria, i.e. the sum of the users' mean squred errors (Sum MSE) and the maximum of the users' mean squared errors (Max MSE), to design the related precoding and filters for recovering relay's equations by the users. Then, we consider a more practical scenario with imperfect CSI. For this case, IFLR receiver is modified, and another transceiver design is proposed, which take into account the effect of channels estimation error. We evaluate the performance of our proposed strategy and compare the results with the conventional amplify-and-forward (AF) and denoise-and-forward (DF) strategies for the same scenario. The results indicate the substantial superiority of the proposed strategy in terms of the outage probability and the sum rate.

Robust Transceiver Design for SC-FDE Multi-hop Full-Duplex Decode-and-Forward Relaying Systems

In this paper, we consider the robust transceiver design for a multi-hop full-duplex decode-and-forward (DF) relay system employing single-carrier transmission with frequency-domain equalization (SC-FDE). We take into account the effect of imperfect channel state information (CSI) where the CSI errors are modeled as Gaussian random variables with known statistics. The design of the precoding at the transmitter and the equalization at the receiver is formulated as an optimization problem with the objective to minimize two relevant performance metrics, namely, the sum mean-square error (MSE) and the maximum MSE across the different hops, subject to separate transmit power constraints for the nodes. We show that the equalization filters can be optimized individually at the receiving nodes and take the form of robust Wiener filters. However, due to the loopback/backward interference, the transmit signals in the different hops are coupled and the transmit precoding problem leads to a nonconvex power allocation problem in the frequency domain. To find the optimal power allocation, we first employ a sequential geometric programming (sGP) approach, which uses the condensation technique to transform the objective function into a posynomial and then solves a sequence of standard GP problems. The sGP approach requires global channel knowledge at a central node and the involved subproblems admit only numerical solutions. To gain further insight into the structure of the problem, we also consider an alternating optimization (AO) approach for power allocation where convex programming problems and difference of convex programming problems are solved in an alternating manner. The resulting AO algorithm admits closed-form solutions in each iteration step and requires less signaling overhead compared to the centralized sGP scheme. Numerical results for the MSEs and achievable rates of the proposed robust schemes are provided, showing that the proposed sGP and AO algorithms yield significant performance gains compared to conventional half-duplex relay systems and nonrobust full-duplex designs.

Simplified MMSE Precoding Design in Interference Two-Way MIMO Relay Systems

We investigate the transceiver design for interference two-way amplify-and-forward multiple-input multiple-output relay communication systems. A novel algorithm with a closed-form solution is developed to optimize the relay precoding matrix based on its optimal structure and a modified transmission power constraint at the relay node. An iterative algorithm is proposed to minimize the sum mean-squared error of the signal waveform estimation. Simulation results demonstrate that the proposed algorithm achieves a better performance-complexity tradeoff compared with existing techniques.

Relay Precoder Designs for Two-Way Amplify-and-Forward MIMO Relay Systems: An Eigenmode-Selection Approach

In this paper, we present new relay precoder designs for two-way amplify-and-forward multiple-input multiple-output (MIMO) relay systems. We first derive the mean-squared error (MSE) matrices of the received signals at two terminals, and show that their behavior strongly depends on the singular values of the effective MIMO channels of the corresponding relay system. Motivated by this property, a set of relay precoders are constructed based on the singular vector subspaces of the MIMO channels, and one of them is selected for meeting a specific design criterion. Four design criteria are investigated, including the minimum sum of MSEs, the maximum sum of capacities, and the minimum or maximum sum of condition numbers, where the condition number is defined as the ratio of the largest to the smallest singular value of a MIMO channel. Compared to the conventional iterative methods, the proposed relay precoders based on minimizing the sum of MSEs or maximizing the sum of capacities achieve close performance while requiring much lower computational complexity. In contrast, the proposed designs based on minimizing or maximizing the sum of condition numbers provide further complexity reduction, with similar performance at high signal-to-noise ratios (SNRs) but a performance loss at low SNRs.

Transceiver Design for Interference MIMO Relay Systems with Direct Links

In this paper, we consider interference multiple-input multiple-output (MIMO) relay systems where multiple pairs of transmitters–receivers simultaneously communicate through a single relay node and where all nodes are equipped with multiple antennas. We propose a new iterative algorithm to jointly optimize the relay precoding matrix and the receiver matrices of such a system based on the minimum sum mean-squared error (MSE) criterion. The optimal structure of the relay precoding matrix is developed to decrease the computational complexity of transceiver optimization. Simulation results demonstrate that the proposed transceiver optimization algorithm has a better MSE and bit-error-rate (BER) performance and a faster convergence rate than existing works.

Robust Interference Management via Linear Precoding and Linear/Non-Linear Equalization

This work studies the robust design of linear precoding and linear/ non-linear equalization for multi-cell MIMO systems in the presence of imperfect channel state information (CSI). A worst-case design approach is adopted whereby the CSI error is assumed to lie within spherical sets of known radius. First, the optimal robust design of linear precoders is tackled for a MIMO interference broadcast channel (MIMO-IBC) with general unicast/multicast messages in each cell and operating over multiple time-frequency resources. This problem is formulated as the maximization of the worst-case sum-rate assuming optimal detection at the mobile stations (MSs). Then, symbol-by-symbol non-linear equalization at the MSs is considered. In this case, the problem of jointly optimizing linear precoding and decision-feedback (DF) equalization is investigated for a MIMO interference channel (MIMO-IC) with the goal of minimizing the worst-case sum-mean squared error (MSE). Both problems are addressed by proposing iterative algorithms with descent properties. The algorithms are also shown to be implementable in a distributed fashion on processors that have only local and partial CSI by means of the Alternating Direction Method of Multipliers (ADMM). From numerical results, it is shown that the proposed robust solutions significantly improve over conventional non-robust schemes in terms of sum-rate or symbol error rate. Moreover, it is seen that the proposed joint design of linear precoding and DF equalization outperforms existing separate solutions.

Joint spectrum sensing for detection of primary users using cognitive relays with evolutionary computing

The spectrum sensing is one of the most challenging research fields in cognitive radio networks (CRN). Joint spectrum sensing not only improves the detection performance of the system, but also increases overall agility of the CRN. This study presents a centralised relay-based spectrum sensing technique using hybrid nature based algorithm that detects the number of active primary users and jointly estimates (amplitude, carrier frequency and direction of arrival of far-field sources impinging on uniform linear arrays (ULA) mounted on each relay. The fitness function is a sum of mean square error and the correlation error. All the individual decisions from each relay are passed on to the fusion centre that provides the final decision on the values of the aforementioned parameters. The validity of the proposed scheme is investigated for various SNR levels along with different sizes of ULAs on each relay.

Robust THP Transceiver Design for MIMO Interference Channel

This letter focuses on robust Tomlinson-Harashima precoding (THP) transceiver optimization for multiple-input multiple-output (MIMO) interference channel, where a bounded channel error model is assumed. Two optimization problems are formulated as minimizing the maximum per-user mean square error (MSE) and sum MSE with per-transmitter power constraint, respectively. Since both optimization problems are not convex, a sub-optimal alternating optimization method is proposed to iteratively update the transmit feedback matrix, precoding matrix and receive equalization matrix of THP transceiver until convergence. We show that the two problems of three matrix variables can be formulated as semidefinite program (SDP) when any two of three matrices are fixed, thus making the problems computationally tractable. Simulation results demonstrate that the proposed THP transceivers can improve the performance over the linear transceivers and are robust to the imperfect channel state information (CSI).

Coordinated beamforming design for multicell systems with transceiver impairments: from perspective of spectral efficiency to energy efficiency

Physical transceiver implementations for wireless communication systems usually suffer from transmit-radio frequency (Tx-RF) and receiver-RF (Rx-RF) impairments. In this paper, we aim to design efficient coordinated beamforming for multicell multiuser multi-antenna systems by fully taking into account the residual transceiver impairments. Our design objectives include both spectral efficiency and energy efficiency. In particular, we first derive the closed-form expression of the mean square error (MSE) which includes the impact of transceiver impairments. Based on that, we propose an alternating optimization algorithm to solve the coordinated multicell beamforming problems with the goal of minimizing the worst user MSE, and the sum MSE. Then, by exploiting the relationship between the minimum mean square error (MMSE) and the achievable rate, we develop a new algorithm to address the sum rate maximization problem. This approach is further generalized to solve the more intractable energy efficiency optimization problem. We prove that all the proposed iterative algorithms guarantee to converge to a stationary point. Numerical results show that our proposed schemes achieve a better performance than conventional coordinated beamforming algorithms that were designed ignoring the transceiver impairments.

Distributed Synchronization and Beamforming in Uplink Relay Asynchronous OFDMA CoMP Networks

In this paper, we use delay-amplify-and-forward relays in the uplink direction of a coordinated multi-point network based on orthogonal frequency division multiplexing. The key novelty is that we assume delay from users to different base stations (BSs), in general, may exceed cyclic prefix (CP) length as might be the case in large cells and cannot be completely compensated by traditional timing advance strategies. Consequently, interchannel interference and intersymbol interference may arise under such assumptions. We first optimize the adjustable delays added at users, relays and BS nodes in order to reduce the effective delay spread at the receive sites, then we optimize relays' weights and post-processing matrices at BS nodes to reduce the residual interference. For this purpose, we propose an iterative method that at each step first fixes either the relay weights or the post-processing matrices and then optimizes the signal-to-interference-plus-noise-ratio (SINR) over the other variable. Furthermore, we investigate the optimization problem of minimizing sum mean square error (SMSE) at the receive side under total relay power constraint. Simulation results show significant improvement in terms of SINR and SMSE in comparison with traditional systems in which no relay is deployed and the limited CP length is not addressed properly.

Robust Transceiver Design for Downlink Multiuser MIMO AF Relay Systems

In this paper, we investigate the robust transceiver design for a downlink multiuser multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay system with imperfect channel state information (CSI). We consider that the actual channel is within the neighborhood of a nominal channel and formulate two optimization problems following the philosophy of worst-case robustness, i.e., minimizing the sum mean-square-error (SMSE) and minimizing the total transmit power for any channel realization in the uncertainty region. In order to efficiently find the solutions, we transform the original problems into suitable forms using the sign-definiteness lemma and then propose an alternating iterative algorithm with guaranteed convergence. To further reduce the computational complexity, the cutting-set method is developed, which alternates between transceiver design and channel determination steps. Moreover, some interesting extensions of the proposed methods are discussed, including various types of uncertainty models and transmit power constraints, nonlinear transceiver structure, and uncertain noise covariance. Simulation results are presented to demonstrate the effectiveness of the proposed robust designs.

Pilot Reuse for Massive MIMO Transmission over Spatially Correlated Rayleigh Fading Channels

We propose pilot reuse (PR) in single cell for massive multiuser multiple-input multiple-output (MIMO) transmission to reduce the pilot overhead. For spatially correlated Rayleigh fading channels, we establish a relationship between channel spatial correlations and channel power angle spectrum when the base station antenna number tends to infinity. With this channel model, we show that sum mean square error (MSE) of channel estimation can be minimized provided that channel angle of arrival intervals of the user terminals reusing the pilots are non-overlapping, which shows feasibility of PR over spatially correlated massive MIMO channels with constrained channel angular spreads. Regarding that channel estimation performance might degrade due to PR, we also develop the closed-form robust multiuser uplink receiver and downlink precoder that minimize sum MSE of signal detection, and reveal a duality between them. Subsequently, we investigate pilot scheduling, which determines the PR pattern, under two minimum MSE related criteria, and propose a low complexity pilot scheduling algorithm which relies on the channel statistics only. Simulation results show that the proposed PR scheme provides significant performance gains over the conventional orthogonal training scheme in terms of net spectral efficiency.

Sum-MSE Optimization for Joint Transmission With Limited Backhaul

In this letter, we study beamformer design to minimize the sum mean square error (SMSE) in a multiple-input–multiple-output (MIMO) joint transmission system. By assuming that the backhaul capacity is non-ideal, the original problem is mixed with a $l_{0}$ norm, which is non-convex and NP hard. Therefore, we introduce a weighted $l_{1}$ norm to relax it and propose a suboptimal iterative scheme to derive the transmit and receive beamformers. This algorithm is proved to be convergent and can be implemented in a distributed way. Simulation shows that our method can achieve an SMSE performance that is similar to the ideal backhaul-based SMSE minimization, whereas the former can decrease 20% backhaul consumption at the same time.

Sum MSE Minimization for Downlink Multi-Relay Multi-User MIMO Network

We propose methods of linear transceiver design for two different power constraints, sum relay power constraint and per relay power constraint, which determine signal processing matrices such as base station (BS) transmitter, relay precoders and user receivers to minimize sum mean square error (SMSE) for multi-relay multi-user (MRMU) networks. However, since the formulated problem is non-convex one which is hard to be solved, we suboptimally solve the problems by defining convex subproblems with some fixed variables. We adopt iterative sequential designs of which each iteration stage corresponds to each subproblem. Karush-Kuhn-Tucker (KKT) theorem and SMSE duality are employed as specific methods to solve subproblems. The numerical results verify that the proposed methods provide comparable performance to that of a full relay cooperation bound (FRCB) method while outperforming the simple amplify-and-forward (SAF) and minimum mean square error (MMSE) relaying in terms of not only SMSE, but also the sum rate.

Filter-And-Forward Relay Design for MIMO-OFDM Systems

In this paper, the filter-and-forward (FF) relay design for multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems is investigated. Due to the considered MIMO structure, the FF relay design is investigated in the framework of joint design together with the linear MIMO transceiver. As the design criterion, first, the minimization of weighted sum mean square error (MSE) is considered. The joint design in this case is approached based on alternating optimization that iterates between the optimal design of the FF relay for given MIMO precoding and decoding matrices and the optimal design of MIMO precoding and decoding matrices for a given FF relay filter. Second, a more advanced problem of joint design for rate maximization is considered. The second problem is approached based on the obtained result regarding the first problem of weighted sum MSE minimization and the existing result regarding the relationship between weighted MSE minimization and rate maximization. Numerical results show the effectiveness of the proposed FF relay design method and significant performance improvement by the proposed FF relay over widely considered simple AF relays for MIMO-OFDM systems.

시계열 분석을 이용한 가스사고 발생 예측 연구

In this study, the number of gas accidents prediction model was suggested by analyzing the gas accidents occurred in Korea. In order to predict the number of gas accidents, simple moving average method (3, 4, 5 period), weighted average method and exponential smoothing method were applied. Study results of the sum of mean-square error acquired by the models of moving average method for 4 periods and weighted moving average method showed the highest value of 44.4 and 43 respectively. By developing the number of gas accidents prediction model, it could be actively utilized for gas accident prevention activities.