Optimum Combining Research Articles

An adaptive optimum weighted mean filter and bilateral filter for noise removal in cardiac MRI images

Medical diagnosis greatly benefits from the use of MRI images. There have been many MRI image enhancement algorithms proposed over the years to aid doctors in disease diagnosis. Conventional image enhancing methods, nevertheless, may also boost the noise that was already there in the captured picture, which might cause distortion, which is unfavourable for the disease diagnosis. Therefore, an appropriate technique for noise suppression is necessary. An attempt has been made to incorporate a two-step filtering based algorithm for noise removal in cardiac MRI images while maintaining the images crucial compositional elements, such as their borders and textures. A combination of adaptive optimum weighted mean filter (AOWMF) and bilateral filter (BF) has been implemented to reduce impulsive noise and Gaussian noise that are both present as mixed noise. The fundamental idea of the AOWMF approach includes the detection of noise pixels using Crow Optimization Algorithm (COA), and replacing them with an optimum weighted mean value depending on a criterion of maximization fitness function. Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) have been used to assess the effectiveness of the employed noise reduction technique. The result analysis are experimented in MATLB which reveals that proposed method is able to achieve high PSNR and SSIM and further, this method has the potential to enhance more detail structures of the input cardiac MRI images than existing methods.

Hybrid beamforming for millimeter-wave massive MIMO heterogeneous networks

In this paper, we investigate the hybrid beamforming designs in millimeter wave (mmWave) massive MIMO relaying heterogeneous networks (HetNet), where small cells are overlaid onto the service area of a macrocell. The deployment of HetNet and utilization of the adequate bandwidth in the mmWave band are capable of addressing the explosive growth of data rates in next-generation wireless networks. However, the severe path loss and attenuation in the mmWave band and complex interference in HetNet should be addressed. For the macrocell, we propose a minimum mean squared error (MMSE)-based alternative iterative hybrid analog/digital beamforming algorithm for the downlink multi-user mmWave relaying system. With the constant modulus constraints and the higher-order polynomial function, we reformulate the optimization problem as three convex quadratic subproblems, and the coupling approximate optimal precoders and combiners are jointly obtained by the proposed alternative iterative algorithm. For the picocells, we propose a hybrid beamforming algorithm for downlink mmWave massive MIMO system. An alternative iterative optimization algorithm based on manifold optimization is developed to approximate the optimal beamforming designs. The baseband digital beamforming scheme is investigated by leveraging the mean square error (MSE) criteria for macrocell users and picocell users to manage cross-tier and inter-user interference. Simulation results demonstrate the obvious advantages of the proposed hybrid beamforming algorithms in terms of achievable sum-rate for various setting scenarios.

An affine combination of two augmented CLMS adaptive filters for processing noncircular Gaussian signals

This paper investigates the statistical behavior of an affine combination of two augmented complex least mean-square (ACLMS) adaptive filters for processing noncircular Gaussian signals. First, the optimal affine combiner is studied and its steady state mean behavior is explicitly quantified. This makes it possible to reveal the impact of the input second-order noncircularity coefficient on the combiner. Next, the mean square error analysis of the proposed affine-combined ACLMS filters is provided, proving that the combined scheme performs no less than the best of the individual ACLMS subfilters. Besides, to facilitate physically realization of the combination strategy, an error power based algorithm that can iterate the affine combiner to the optimal one is also proposed. Finally, illustrative numerical simulations are provided to support the theoretical results.

Spectral-efficient hybrid precoding for multi-antenna multi-user mmWave massive MIMO systems with low complexity

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems allow for a data transmission rate of gigabits per second owing to the large bandwidth available in the mmWave spectrum and the antenna gains provided by the massive MIMO system. However, hybrid precoding with high complexity and low spectral efficiency cannot address the challenge of high cost and power consumption of RF chains of multi-user systems. In this paper, we propose a low-complexity hybrid precoding scheme for downlink multi-antenna multi-user mmWave massive MIMO systems, aiming to enhance the sum spectral efficiency (SSE) performance. We first extend the dimension of the analog precoding matrix into a square matrix and find the optimal analog combiner by selecting some of the discrete Fourier transform (DFT) bases, which enhances the equivalent baseband channel matrix gain. Then, we directly aggregate the channel gain through the equal gain transmission (EGT) method to ensure the frequency efficiency performance. Finally, we propose an improved BD scheme to design the digital precoder and combiner to reduce the inter-user interference. We consider both the mmWave channel and the Rayleigh channel to evaluate the performance of the proposed algorithm. The simulation results verify that the proposed scheme enjoys near-optimal achievable sum spectrum efficiency and BER performance in both the mmWave channel and Rayleigh channel and performs even better in Rayleigh channel than in the mmWave channel.

Tree-Coding-Aided Adaptive-Cross-Entropy Algorithm for Hybrid Precoding With Low-Resolution Analog Phase Shifters

This paper considers the hybrid precoder design in millimeter wave (mmWave) multi-input multi-output (MIMO) systems with low-resolution analog phase shifters. Aiming at reducing the complexities of the near-optimal algorithms, we propose a low-complexity multi-user hybrid precoding scheme based on tree-coding-aided adaptive-cross-entroy (TC-ACE) algorithm. By defining some discrete variables for the analog precoders and combiners, the problem of hybrid precoding is transformed into a cross-entroy (CE) optimization problem, which can be solved by iteratively updating the probability distributions of the predefined discrete variables. In order to derive the closed-form expression of the probability distributions, tree-coding is used to encode each entry of the analog precoders and combiners with a binary number. Through iterations, optimal analog precoders and combiners will be obtained when its probabilities are sufficiently high. Simulation results show that when the number of users exceeds a certain value, the proposed scheme outperforms the alternating minimization algorithm and coordinate descent method in terms of both the sum-rate and complexity.

High-Resolution and Low-Complexity Direction of Arrival Estimation for Hybrid Array of Subarrays

In this paper, the problem of direction-of-arrival (DoA) estimation for a hybrid array of subarrays is considered in millimeter-wave communication systems. Unlike much prior work using the outputs from the analog subarrays with symbol-wise processing, the proposed framework jointly exploits multiple outputs in time domain for high-resolution DoA estimation. With block-wise processing, the proposed method designs an optimal hybrid combiner maximizing beamforming gain, while reducing a receiver complexity based on fast Fourier transform filtering for each blocked signal. The performance of the proposed method is analyzed, including estimation performance with a limited training signal, training overhead, and computational complexity. An extension of the proposed method to a uniform planar array case is also discussed. Numerical results show the effectiveness of the proposed algorithm.

Partially-Connected Hybrid Beamforming for Spectral Efficiency Maximization via a Weighted MMSE Equivalence

Hybrid beamforming (HBF) is an attractive technology for practical massive multiple-input and multiple-output (MIMO) millimeter wave (mmWave) systems. Compared with the fully-connected HBF architecture, the partially-connected one can further reduce the hardware cost and power consumption. However, the special block diagonal structure of its analog beamforming matrix brings additional design challenges. In this paper, we develop effective HBF algorithms for spectral efficiency maximization (SEM) in wideband mmWave massive MIMO systems with the partially-connected architecture. One main contribution is that we prove the equivalence of the SEM problem and a weighted mean square error minimization (WMMSE) problem, which leads to a convenient algorithmic approach to directly tackle the SEM problem. Specifically, we decompose the equivalent WMMSE problem into the hybrid precoding and hybrid combining subproblems, for which both the optimal digital precoder and combiner have closed-form solutions. For the more challenging analog precoder and combiner, we propose an element iteration based algorithm and a manifold optimization based algorithm. Finally, the hybrid precoder and combiner are alternatively updated. The overall HBF algorithms are proved to monotonously increase the spectral efficiency and converge. Furthermore, we also propose modified algorithms with reduced computational complexity and finite-resolution phase shifters. Simulation results demonstrate that the proposed HBF algorithms achieve significant performance gains over conventional algorithms.

A new method for ensemble combination based on adaptive decision making

Ensemble classifiers methods are considered as one of the strongest classification approaches in different applications. A key factor in creating a successful ensemble is to design an optimal combiner that minimizes classification errors. Unfortunately, finding the best fusion methodology that maximizes ensemble performance is a challenge. Most popular ensemble classifiers systems use fixed fusion methods such as average and majority voting. For a given application, there is no clear understanding of why a fusion method might work better than other methods. In this work, decision-making based on Adaptive Power Mean Combiner (APMC) is investigated. A mathematical and experimental framework for ensemble classifier systems based on APMC is proposed. The theoretical results explain why a given algebraic combiner such as average, product, maximum, minimum, and others works best for a given dataset while providing poor results on other datasets. It was shown that selecting an optimal fusion method is strongly dependent on the statistics of base learners’ outputs. Theoretical results for a given ensemble condition show that an improvement in classification accuracy of ∼8% compared to the average fusion method is achieved. Guided by theoretical results, we propose an experimental ensemble-learning algorithm based on surrogate optimization method for searching fusion methods for a given ensemble condition. The performance trend predicted by the mathematical model is validated through several datasets and compared against different fusion methods. Experimental results show the proposed algorithm achieves notable classification results compared to several fusion methods.

Generalized Space–Time Line Code With Receive Combining for MIMO Systems

In this article, a generalized space–time line code (GSTLC) is proposed. The proposed GSTLC concurrently transmits multiple data streams obtained by space–time line code encoding and precoding to provide spatial multiplexing and diversity. When full channel state information (CSI) is available to the transmitter and limited CSI is available to the receiver, an optimal precoding matrix is derived for GSTLC with linear combining that is based on the minimum mean square error (MMSE) criterion. Moreover, the detection signal-to-interference-plus-noise ratio (SINR) is derived corresponding to the optimal MMSE precoder. Using the SINR, we propose a receiver combining scheme that selects the best combining matrix, thereby minimizing the bit error rate (BER) from a codebook that includes candidate combining matrices. Through numerical simulations, we demonstrate that the proposed GSTLC with the optimal combiner achieves the theoretical lower bound of BER. In addition, we show that the GSTLC with combiner selection performs better than conventional precoded spatial multiplexing methods in terms of the BER.

A novel committee machine hybrid precoding and combining algorithm for mmWave massive MU-MIMO systems

Millimeter-wave (mmWave) massive multi-user multiple input multiple output (MU-MIMO) systems employ hybrid analog-digital precoding/combining design, to reduce the number of radio-frequency (RF) chains without large sum-rate performance loss. Committee machines combine several expert algorithms to yield better reliable estimates to those of its constituent experts. However, several committee machines approach mainly rely on the ‘quality’ of the joint support-set of expert algorithms combine by committee machine. In this paper, we present hybrid analog-digital precoder and combiner designs for mmWave massive MU-MIMO systems by exploiting the intersection of the estimated support-sets, namely, common support-set of ‘expert’ algorithms in a committee machine methodology. With S denoting the sparsity level, the proposed algorithms perform two essential tasks to identify in which subspace, generated by not more than S columns of the matrix of array response vectors, the optimal hybrid analog-digital precoders or combiners lie: Firstly, the selection of the committee machine common support set, which accepts the section where both the ‘experts’ agree. Secondly, if some column indices of the optimal hybrid analog-digital precoders or combiners do not lie in the current common support-set for the correct spanning space, −the algorithm searches over the matrix of array response vectors and selects column indices that exhibit the highest correlation with the signal residual, to acquire the remaining support. We derive the theoretical analysis for performance enhancement of the proposed algorithm. Simulation results demonstrate that the proposed design allows mmWave massive MU-MIMO systems to approach their unconstrained performance limits, and exhibits substantial sum-rate performance improvement over existing regularized channel diagonalization based schemes and the beam steering solution.

Optimum Combiner for Spatially Correlated Nakagami-m Fading Channels

This paper proposes a novel optimum combiner that raises the time-averaged signal-to-interference-plus-noise ratio (SINR) for maximal-ratio combining (MRC) reception over spatially correlated Nakagami-m fading channels. By exploiting the principal component analysis (PCA) with eigenvalue decomposition (EVD) of the covariance matrix analytically evaluated offline, a complete set of orthonormal basis functions can be obtained. A decorrelation process analyzes and then projects the received signal into the space spanned by the basis functions. In accordance with the theorem of irrelevance, a principal component selection combining (PCSC) method is proposed to remove components in a few dimensions in which SINRs are considered low to raise the resulting time-averaged SINR on the subsequent MRC reception. The proposed technique also avoids noise enhancement occurring with MRC reception in the scenario where noises on different branches are correlated. The SINR distribution, level-crossing rate (LCR) and average fade duration (AFD) are derived. Based on a novel scattering model interpretation, a simulator consisting of spatially correlated Nakagami-m fading channels is developed according to the analytically evaluated covariance matrix. Computer simulations show that the proposed optimum combiner not only decreases interference and noise from the irrelevant subspace to achieve higher time-averaged SINR and lower AFD but also significantly reduces the complexity required for subsequent signal processing.

Airline investments in exclusive airport facilities: Timing decisions under demand ambiguity

In this paper, we study the timing decision of airlines’ investments in exclusive airport facilities in the presence of demand ambiguity and competition. We model the investment decision as a real options problem under ambiguity. An airline's ambiguity-averse preferences are modeled using the multiple prior expected utility form. We obtain the optimal investment timing rule for the airline and find that it requires the airline's expected present value of its future incremental profit from investing to exceed the investment cost by the option value multiplier. We then compare the airline's optimal investment timing rule to the social optimum and discuss two possible subsidy policies, a lump-sum subsidy and a per-unit subsidy, with which the government can align the airline's investment timing rule with the social optimum. We characterize the stepwise structure of both subsidy policies, in which the optimal time to invest in an exclusive terminal depends on three thresholds: the social optimum, the airline's break-even point, and a combination of the social optimum and the airline optimum. We conclude that the two subsidy policies have equivalent effects when the government and the airline have the same ambiguity levels, as they lead to the same investment timing and require the same amount of government funds.

MmWave Amplify-and-Forward MIMO Relay Networks With Hybrid Precoding/Combining Design

In this paper, we consider the amplify-and-forward relay networks in mmWave systems and propose a hybrid precoder/combiner design approach. The phase-only RF precoding/combining matrices are first designed to support multi-stream transmission, where we compensate the phase for the eigenmodes of the channel. Then, the baseband precoders/combiners are performed to achieve the maximum mutual information. Based on the data processing inequality for the mutual information, we first jointly design the baseband source and relay nodes to maximize the mutual information before the destination baseband receiver. The proposed low-complexity iterative algorithm for the source and relay nodes is based on the equivalence between mutual information maximization and the weighted MMSE. After we obtain the optimal precoder and combiner for the source and relay nodes, we implement the MMSE-SIC filter at the baseband receiver to keep the mutual information unchanged, thus obtaining the optimal mutual information for the whole relay system. Simulation results show that our algorithm achieves better performance with lower complexity compared with other algorithms in the literature. In addition, we also propose a robust joint transceiver design for imperfect channel state information.

Optimal Frequency-Flat Precoding for Frequency-Selective Millimeter Wave Channels

The two key features of millimeter wave-(mmWave) based MIMO communication are the use of large antenna arrays at the transceivers and large bandwidth. The former complicates the design of optimal beamformers, while the latter makes the system frequency-selective and, thus, requires equalization. Conventionally, for wideband mmWave channels, choosing the precoders/combiners have involved frequency-selective designs that are based on channel state information. In this paper, we show that under some assumptions, semi-unitary frequency-flat precoding and combining are sufficient for low-scattering millimeter wave channels. To show this, we evaluate the conditions and practical settings under which the dominant subspaces of the frequency-domain channel matrices are similar. We model the frequency-dependence of uniform linear antenna arrays, which leads to what is known as beam-squint, for two different practical setting to analyze the optimality of frequency-flat beamforming designs under practical hardware impairments. For the cases when the optimality conditions hold, we propose novel techniques based on compressive subspace estimation to design the optimal frequency-flat, semi-unitary precoders and combiners. Simulation results show that the system achieves near-digital spectral efficiencies at very small implementation cost of beamformers and channel training overhead.

Selective ensemble of multiple local model learning for nonlinear and nonstationary systems

This paper proposes a selective ensemble of multiple local model learning for modeling and identification of nonlinear and nonstationary systems, in which the set of local linear models are self adapted to capture the newly emerging process characteristics and the prediction of the process output is also self adapted based on an optimally selected ensemble of subset linear local models. Specifically, our selective ensemble of multiple local model learning approach performs the model adaptation at two levels. At the level of local model adaptation, a newly emerging process state in the incoming data is automatically identified and a new local linear model is fitted to this newly emerged process state. At the level of online prediction, a subset of candidate local linear models are optimally selected and the prediction of the process output is computed as an optimal linear combiner of the selected subset local linear models. Two case studies involving chaotic time series prediction and modeling of a real-world industrial microwave heating process are used to demonstrate the effectiveness of our proposed approach, in comparison with other existing methods for modeling and identification of nonlinear and time-varying systems.

General performance of detect-and-forward cooperative relaying in the presence of multiple interferers for optimum combining receivers

Detect-and-Forward (DF) is a cooperative technique based on the retransmission of a detected version of the transmit signal. It improves performance, throughput and cellular coverage. However, in cellular scenarios, it coexists with co-channel interference (CCI), which is the principal factor that affects the performance of cellular networks. On the other hand, Optimum Combining (OC) is a low complexity combining technique that maximizes the signal-to-interference-plus-noise ratio (SINR), achieving in this case diversity gain by eliminating the CCI. In the present paper, the performance of cooperative DF network in the presence of multiple CCI at relay and destination is analysed, where relay and destination are equipped with multiple antennas and OC. Furthermore, scenarios by considering multiple antenna transmission (MAT) and transmit antenna selection (TAS) technique at relay are supposed. For both MAT and TAS techniques, a tight approximation of the end-to-end instantaneous SINR is proposed. Subsequently, its moment-generating function is derived in closed-form in order to evaluate the average bit-error rate of the system. Analytical results are validated using Monte-Carlo simulations for several scenarios, showing that OC eliminates fully the CCI, even in the case of high-power CCI. The diversity gain depends on the number of destination antennas, relay antennas and interferers.

On performance analysis for optimum combining of DF relaying with fast-fading multiple correlated CCIs, correlated source-relay, and thermal noise

This paper analyzes the outage probability (OP) and the average symbol error rate (SER) of decode-and-forward (DF) relaying. The paper derives closed-form expressions for the OP and the average SER with optimum combining (OC) considering fast-fading multiple correlated CCIs, the correlated source-relay, and thermal noise. It is shown that the performance of the large distance between the source and the relay is better than that of the small distance, regardless of interference fading speed at the destination. We also show that given the source-relay distance, the performance of slow-fading interference is basically better than that of fast fading, except in the low signal-to-noise-ratio (SNR) regime for the distance being small. In result, the source-relay distance is generally a more dominating factor for the performance than fading CCIs.

Uplink spectral efficiency for small‐cells with dual‐hop amplify‐and‐forward relaying at 28 GHz

In this study, the performance, cellular coverage and average spectral efficiency are analysed for the uplink of small cells with dual-hop amplify-and-forward relaying. Specifically, a cellular network with an optimum combiner at a destination, multiple-antennas relays and multiple-antennas destination affected by multiple interferers is considered. The techniques of multiple relays transmission (MRT) and relay selection with transmit antenna selection (RS-TAS) are analysed and compared. The moment-generating function of the signal-to-interference-plus-noise ratio is derived in order to obtain the average bit-error rate for both transmission techniques. Then, an adaptive scheme modulation and different transmission power levels are used to obtain the coverage and the average cellular spectral efficiency by considering a path-loss model at 28 GHz. Results show that using a relay is so efficient compared to a non-relay system. Moreover, RS-TAS outperforms MRT in both coverage and efficiency.

Impact of Fast Fading CCI on Performance of Optimum Combining in DF Relaying

We present the effect of fast fading co-channel interference (CCI) on the performance of decode-and-forward (DF) relaying. This paper derives closed-form expressions for the average symbol error rate (SER) with optimum combining (OC) in the presence of fast fading CCI. It is shown that the average SER performance of fast fading CCI is worse than that of slow fading CCI, which is the previous research assumption. In result, DF relaying systems should be designed with consideration of fast fading CCI.

Framework of Channel Estimation for Hybrid Analog-and-Digital Processing Enabled Massive MIMO Communications

We investigate a general channel estimation problem in the massive multiple-input multiple-output system which employs the hybrid analog/digital precoding structure with limited radio-frequency (RF) chains. By properly designing RF combiners and performing multiple trainings, the proposed channel estimation can approach the performance of fully-digital estimations depending on the degree of channel spatial correlation and the number of RF chains. Dealing with the hybrid channel estimation, the optimal combiner is theoretically derived by relaxing the constant-magnitude constraint in a specific single-training scenario, which is then extended to the design of combiners for multiple trainings by sequential and alternating methods. Further, we develop a technique to generate the phase-only RF combiners based on the corresponding unconstrained ones to satisfy the constant-magnitude constraints. The performance of the proposed hybrid channel estimation scheme is examined by simulations under both nonparametric and spatial channel models. The simulation results demonstrate that the estimated channel state information can approach the performance of fully-digital estimations in terms of both mean square error and spectral efficiency. Moreover, a practical spatial channel covariance estimation method is proposed and its effectiveness in hybrid channel estimation is verified by simulations.