Robust Training Sequence Design for Correlated MIMO Channel Estimation

A novel training-based channel estimation scheme is presented for an uncoded layered space-time system that operates in a wideband frequency selective fading environment of a time-varying multiple-input multiple-output (MIMO) channel. The method uses a pilot matrix consisting of pilot symbols derived from the Paley-Hadamard matrix to estimate the MIMO channel impulse response. The orthogonality of the pilot matrix resolves both the intersymbol interference and the cochannel interference of the wideband MIMO channel. The Toeplitz-like structure of the Paley-Hadamard matrix is exploited to minimise the length of the pilot sequence, reducing pilot symbol overhead. A decision feedback algorithm is used to track the time-varying MIMO channel. Results are presented which demonstrate the performance of the proposed MIMO channel estimator in a layered space-time system for different mobile velocities and system configurations.

Recent advances in multiple-input multiple-output (MIMO) systems have renewed the interests of researchers to further explore this area for addressing various dynamic challenges of emerging radio communication networks. Various measurement campaigns reported recently in the literature show that physical multipath MIMO channels exhibit sparse impulse response structure in various outdoor radio propagation environments. Therefore, a comprehensive physical description of sparse multipath MIMO channels is presented in first part of this paper. Superimposing a training sequence (low power, periodic) over the information sequence offers an improvement in the spectral efficiency by avoiding the use of dedicated time/frequency slots for the training sequence, which is unlike the traditional schemes. The main contribution of this paper includes three superimposed training (SiT) sequence based channel estimation techniques for sparse multipath MIMO channels. The proposed techniques exploit the compressed sensing theory and prior available knowledge of channel's sparsity. The proposed sparse MIMO channel estimation techniques are named as, SiT based compressed channel sensing (SiT-CCS), SiT based hardlimit thresholding with CCS (SiT-ThCCS), and SiT training based match pursuit (SiT-MP). Bit error rate (BER) and normalized channel mean square error are used as metrics for the simulation analysis to gauge the performance of proposed techniques. A comparison of the proposed schemes with a notable first order statistics based SiT least squares (SiT-LS) estimation technique is presented to establish the improvements achieved by the proposed schemes. For sparse multipath time-invariant MIMO communication channels, it is observed that SiT-CCS, SiT-MP, and SiT-ThCCS can provide an improvement up to 2, 3.5, and 5.2 dB in the MSE at signal to noise ratio (SNR) of 12 dB when compared to SiT-LS, respectively. Moreover, for $$\mathrm {BER}=10^{-1.9}$$BER=10-1.9, the proposed SiT-CCS, SiT-MP, and SiT-ThCCS, compared to SiT-LS, can offer a gain of about 1, 2.5, and 3.5 dB in the SNR, respectively. The performance gain in MSE and BER is observed to improve with an increase in the channel sparsity.

In the emerging high mobility vehicle-to-everything (V2X) communications using millimeter wave (mmWave) and sub-THz, multiple-input multiple-output (MIMO) channel estimation is an extremely challenging task. At mmWaves/sub-THz frequencies, MIMO channels exhibit few leading paths in the space-time (ST) domain (i.e., directions or arrival/departure and delays). Algebraic low-rank (LR) channel estimation exploits ST channel sparsity through the computation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">position-dependent</i> MIMO channel eigenmodes leveraging recurrent training vehicle passages in the coverage cell. LR requires vehicles’ geographical positions and tens to hundreds of training vehicles’ passages for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">each</i> position, leading to significant complexity and control signaling overhead. Here, we design a deep-learning (DL)-based LR channel estimation method to infer MIMO channel eigenmodes in V2X urban settings, starting from a single least squares (LS) channel estimate and without needing vehicle’s position information. Numerical results show that the proposed method attains comparable mean squared error (mse) performance as the position-based LR. Moreover, we show that the proposed model can be trained on a reference scenario and be effectively transferred to urban contexts with different ST channel features, providing comparable mse performance without an explicit transfer learning procedure. This result eases the deployment in arbitrary dense urban scenarios.

Conventional correlation models fail to accurately represent the correlation properties of ultrawideband (UWB) multiple-input multiple-output (MIMO) channels. In our previous work, a framework for constructing correlated UWB MIMO channel models was proposed, where spatial correlation was introduced into both the multipath amplitude and time-of-arrival (ToA) in the channel impulse response. Based on this framework, in this paper we first present a simplified UWB MIMO channel model that represents a reasonable compromise between analytical tractability and model accuracy. We show that this model yields a structured space-frequency (SF) channel covariance matrix, making it suitable for theoretical system performance analysis. To illustrate the merit of this model, we apply it to evaluate the maximum diversity order in SF coded UWB MIMO systems. In contrast to previous work based on conventional wideband MIMO correlated channel models, we show that the maximum diversity order of a UWB MIMO system is not limited by the sum of the ranks of multipath amplitude correlation matrices.

This paper deals with optimized Multiple-Input Multiple Output (MIMO) channel estimation and ensuing information throughput conveyed by pilot-based multi-antenna systems affected by both spatially colored Multiple Access Interference (MUI) and errors in the available channel estimates. The architecture of the Minimum Mean Square Error (MMSE) MIMO channel estimator is derived and the related analytical conditions for the optimal design of space-time training sequences are provided. Afterwards, closed form expressions for the maximum information throughput sustained by the considered systems for Gaussian distributed input signals are given and, then, a novel powers’ allocation algorithm for the asymptotical achievement of the system capacity is developed. Considerations about optimized space-division MAC strategies are also provided.

Space-time techniques for multiple-input multiple-output (MIMO) systems potentially provide vast increases in capacity. In order to achieve the quoted capacity gains the MIMO channel impulse response (CIR) must be known or estimated. Thus far, existing MIMO channel estimation techniques have been limited to the narrowband case or cater specifically for coded space-time systems. In this paper, we present a novel training-based MIMO channel estimation scheme for an uncoded layered space-time system that operates in the wideband frequency-selective fading environment. The method uses a pilot matrix consisting of pilot symbols derived from the Paley-Hadamard matrix in order to jointly estimate the individual CIR of the MIMO channel. The orthogonal property of the pilot matrix is utilized to resolve both intersymbol interference and intercarrier interference of the multiple transmit and received signals. The Paley Toeplitz structure is also exploited in order to minimise the length of the pilot sequence for a given length of CIR and thus maximise the effective data throughput. Results are presented which demonstrate the accuracy of the proposed channel estimation scheme and its performance in a layered space-time system.

After a few decades’ evolution of wireless communication systems, to ensure reliable highspeed communication over unreliable wireless channels is still one of the major challenges facing researchers and engineers. The use of multiple antennas at transmitter and receiver, known as multiple-input multiple-output (MIMO) communications, is one promising technology delivering desired wireless services. The main goal of this thesis is to study two important issues in wireless MIMO communication systems: receiver design for coded MIMO systems, and diversity-multiplexing tradeoff analysis in general fading channels. In the first part of this thesis, we decompose the receiver design problem into two subproblems: MIMO channel estimation and MIMO detection. For the MIMO channel estimation, we develop an expectation-maximization (EM) based semi-blind channel and noise covariance matrix estimation algorithm for space-time coding systems under spatially correlated noise. By incorporating the proposed channel estimator into the iterative receiver structure, both the channel estimation and the error-control decoding are improved significantly. We also derive the modified Cramer-Rao bounds (MCRB) for the unknown parameters as the channel estimation performance metric, and demonstrate that the proposed channel estimation algorithm can achieve the MCRB after several iterations. For the MIMO detection, we propose a novel lowcomplexity MIMO detection algorithm, which has only cubic order computational complexity, but with near-optimal performance. For a 4×4 turbo-coded system, we show that the proposed detector had the same performance as the maximum a posteriori (MAP) detector for BPSK modulation, and 0.1 dB advantage over the approximated MAP detector (list sphere decoding algorithm) for 16-QAM modulation at BER = 10−4. In the second part of this thesis, we derive the optimal diversity-multiplexing tradeoff for

This paper presents a novel iterative detection and channel estimation scheme that combines the effort of superimposed training (ST) and pilot-aided training (PAT) for multiple-input multiple-output (MIMO) flat fading channels. The proposed method, hereafter known as joint mean removal ST and PAT (MRST-PAT), implements an iterative detection and channel estimation that achieves the performance of data-dependent ST (DDST) algorithm, with the difference that the data arithmetic cyclic mean is estimated and removed from data at the receiver’s end. It is demonstrated that this iterative and cooperative detection and channel estimator algorithm surpasses the effects of data detection identifiability condition that DDST has shown when higher orders of modulation are used. Theoretical performance of the MRST-PAT scheme is provided and corroborated by numerical simulations. In addition, the performance comparison between the proposed method and different MIMO channel estimation techniques is analyzed. The joint effort between ST and PAT shows that MRST-PAT is a solid candidate in communications systems for multiamplitude constellations in Rayleigh fading channels, while achieving high-throughput data rates with manageable complexity and bit-error rate (BER) as a figure of merit.

This paper describes investigations into the antenna mutual coupling (MC) effect on channel estimation and capacity of a multiple-input multiple-output (MIMO) wireless communication system. The presented investigations close the gap existing in the previous works which assessed the effect of mutual coupling on MIMO capacity under the assumption of availability of perfect channel state information (CSI) at the receiver. The new approach assumes that the perfect CSI is not available due to channel estimation errors. The investigations are carried out for different spacing between array antenna elements producing a varying effect of mutual coupling on the channel estimation and the resulting MIMO channel capacity.

Novel matrix singular value inequalities are established for a sum/product of three matrices. Their application to the uncertain (compound) multiple-input multiple-output (MIMO) channel subject to normed additive uncertainty establishes the saddle-point property for a wide range of performance metrics monotonic in the channel singular values, including, among others, the mutual information, MMSE, error exponent, and pairwise error probability. This, in turn, implies that the transmission on the eigenmodes of the nominal (or worst case) channel is also optimal for the whole set of channels under a general power constraint and hence achieves the compound channel capacity. The worst case channel turns out to be antiparallel of the nominal one for all these performance metrics. An application of these results to beamforming over compound MIMO channels is discussed. An optimal robust precoder for the uncertain MIMO channel is obtained in a closed-form under the sum-MSE criterion and the total power constraint. The saddle-point property is shown to hold and the optimal strategy is to diagonalize the nominal (or worst case) channel.

Based on the knowledge of instantaneous channel state information (CSI), the optimal source and relay pre-coding matrices have been developed recently for multiple-input multiple-output (MIMO) relay communication systems. However, in real communication systems, the instantaneous CSI is unknown and needs to be estimated at the destination node. In this paper, we propose a superimposed channel training method for MIMO relay communication systems. It is shown that to minimize the mean-squared error (MSE) of channel estimation, the optimal training sequence at each node matches the eigenvector matrix of the transmitter correlation matrix of the forward MIMO channel. Then we optimize the power allocation among different streams of the training sequence at the source node and the relay node. Simulation results show that the proposed algorithm leads to a smaller MSE of channel estimation compared with the conventional MIMO relay channel estimation algorithm.

We investigate the capacity loss for using uncorrelated Gaussian input over a multiple-input multiple-output (MIMO) linear additive-noise channel. We upper-bound the capacity loss by a universal constant C* which is independent of the channel matrix and the noise distribution. For a single-user MIMO channel with n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> inputs and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> outputs C* = min [ 1/2, n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> /n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (1+n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> /n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ) ] bit per input dimension (or 2C* bit per transmit antenna per second per hertz), under both total and per-input power constraints. If we restrict attention to (colored) Gaussian noise, then the capacity loss is upper-bounded by a smaller constant C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> = n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> /2n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> /n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ) for n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ges n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> /e, and C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> = 0.265 otherwise, and this bound is tight for certain cases of channel matrix and noise covariance. We also derive similar bounds for the sum-capacity loss in multiuser MIMO channels. This includes in particular uncorrelated Gaussian transmission in a MIMO multiple-access channel (MAC), and "flat" Gaussian dirty-paper coding (DPC) in a MIMO broadcast channel. In the context of wireless communication, our results imply that the benefit of beamforming and spatial water-filling over simple isotropic transmission is limited. Moreover, the excess capacity of a point-to-point MIMO channel over the same MIMO channel in a multiuser configuration is bounded by a universal constant.

The purpose of robust design optimization is to minimize variations in design performances and therefore to make the design insensitive to uncertainties. Current robust design methods fall into two types — probabilistic robust design and worst-case (interval) robust design. The former method is used when random variables are involved. In this method, robustness is measure by standard deviations of design performances. The later method is used when uncertainties are represented by intervals. The widths of design performances are then used to measure robustness. In many engineering application, both random variables and interval variables may exist simultaneously. In this paper, a general approach to robust design optimization is proposed. The generality comes from the ability to handle both random and interval variables. To alleviate the computational burden, we employ a previously developed general robustness assessment method — semi-second-order Taylor expansion method, to evaluate the maximum and minimum standard deviations of a design performance. An efficient integration strategy of the general robustness assessment and optimization is proposed. With the integration strategy, the number of function calls can be reduced while good accuracy is maintained. A robust shaft design problem is given for demonstration.

This paper proposes a low-complexity signal detection algorithm for spatially correlated multiple-input multiple-output (MIMO) channels. The proposed algorithm sets a minimum mean-square error (MMSE) detection result to a starting point, and searches for signal candidates in multi-dimensions of the noise enhancement from which the MMSE detection suffers. The multi-dimensional search is needed because the number of dominant directions of the noise enhancement is likely to be more than one over the correlated MIMO channels. To reduce computational complexity of the multi-dimensional search, the proposed algorithm limits the number of signal candidates to $O(N_T)$ where $N_T$ is the number of transmit antennas. Specifically, the signal candidates, which are unquantized, are obtained as the solution of a minimization problem under a constraint that a stream of the candidates should be equal to a constellation point. Finally, the detected signal is selected from hard decisions of both the MMSE detection result and unquantized signal candidates on the basis of the log likelihood function. For reducing the complexity of this process, the proposed algorithm decreases the number of calculations of the log likelihood functions for the quantized signal candidates. Computer simulations under a correlated MIMO channel condition demonstrate that the proposed scheme provides an excellent trade-off between BER performance and complexity, and that it is superior to conventional one-dimensional search algorithms in BER performance while requiring less complexity than that of the conventional algorithms.

Multiple Input Multiple Output (MIMO) system with orthogonal frequency division multiplexing (OFDM) is a promising physical layer candidate for the current and future wireless standards. MIMO increases system throughput while OFDM maximizes spectrum efficiency. To reduce the impacts of frequency selective fading and increase the capacity, MIMO requires precise channel state information (CSI). The presence of carrier frequency offset (CFO) introduces intercarrier interference (ICI) among the subcarriers which degrades the system performance. MIMO channel estimation is done under the assumption of perfect frequency synchronisation between the transmitter and receiver, or zero CFO. However, such an assumption is incorrect for time-varying and frequency-selective wireless channels, and the presence of CFO has an impact on channel estimation accuracy. In the existing methods, CFO and channel estimations are carried out independently using separate training sequences which reduces the spectral efficiency. As a result, the pilot aided interpolation approach is proposed in this paper for the joint estimate and compensation of CFO and channel effects using the same set of pilot tones. Theresults show that the proposed method offers precise CFO and channel estimation which improves the bit error rate performance and carrier to interference power ratio (CIR) of MIMO-OFDM system.