Transmitted Symbol Vector Research Articles

Low Complexity Detection of Spatial Modulation Aided OTFS in Doubly-Selective Channels

A spatial modulation-aided orthogonal time frequency space (SM-OTFS) scheme is proposed for high-Doppler scenarios, which relies on a low-complexity distance-based detection algorithm. We first derive the delay-Doppler (DD) domain input-output relationship of our SM-OTFS system by exploiting an SM mapper, followed by characterizing the doubly-selective channels considered. Then we propose a distance-based ordering subspace check detector (DOSCD) exploiting the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information of the transmit symbol vector. Moreover, we derive the discrete-input continuous-output memoryless channel (DCMC) capacity of the system. Finally, our simulation results demonstrate that the proposed SM-OTFS system outperforms the conventional single-input-multiple-output (SIMO)-OTFS system, and that the DOSCD conceived is capable of striking an attractive bit error ratio (BER) vs. complexity trade-off.

Soft-Input Soft-Output Detection via Expectation Propagation for Massive Spatial Modulation MIMO Systems

In this letter, we propose to utilize the expectation propagation (EP) framework for soft-input soft-output (SISO) signal detection in massive spatial modulation (SM) multiple-input multiple-output (MIMO) systems. By using a multivariate complex Gaussian approximation approach, the symbol beliefs of the transmitted symbol vectors are constructed based on the propagation of the mean vectors and covariance matrixes. The log-likelihood ratios (LLRs) of the antenna index bits and the modulation index bits are computed by partitioning the symbol beliefs into different regions. Simulation results illustrate that the proposed SISO EP detector outperforms the state-of-the-art soft-decision algorithms and strikes a desirable performance-complexity tradeoff.

Joint beamforming for intelligent reflecting surface aided wireless communication using statistical CSI

A joint beamforming algorithm is proposed for intelligent reflecting surface (IRS) aided wireless multiple-input multiple-output (MIMO) communication using statistical channel state information (CSI). The beamforming is done by alternatively optimizing the IRS reflecting coefficients and the covariance matrix of the transmit symbol vector, such that the ergodic rate of the system is maximized. The algorithm utilizes only the second order momentum of the random channel matrices and does assume any specific channel distribution, leading to a general framework for ergodic rate evaluation. A practical channel correlation model is configured to validate the performance gain. It is found that the rate can be enlarged by the joint optimization algorithm, however, the gain over that of randomly deployed reflecting coefficients depends highly on the relative correlation distance of the IRS elements and the spatial position of the IRS. In particular, the results suggest that IRS should be placed in the vicinity of either the transmitter or the receiver. Placing IRS far away from those positions is non-beneficial.

Robust transceiver design based on switched preprocessing for K ‐pair MIMO interference channels

In this work, the authors propose a transceiver design strategy based on switched preprocessing (SP) for interference management in K-pair MIMO interference channels. Each transmitter performs SP by using a small number of permutation matrices to allocate the entries of its precoder output vector on different transmit antennas. Each arrangement of permutation matrices among the K transmitters gives rise to a set of K parallel point-to-point transceivers, referred to as MIMO latent transceiver set (MLTS). Based on the given channel state information (CSI), the optimum MLTS among the available ones is chosen by minimising the squared Euclidean distance between the pre-estimated noiseless received vector and the true transmit symbol vector. In addition, they consider two CSI error models, i.e. the stochastic error model and the norm-bounded error model, and for each type they propose robust algorithms for the design of the MLTS associated to the different choices of permutation matrices, which are based on minimising various types of mean square error criteria. A detailed study of computational complexity for the proposed SP-based MIMO transceiver design algorithms is carried out. Simulation results verify the effectiveness of the new SP-based designs for MIMO interference channels.

A Two-Dimensional Vectorized Secure Transmission Scheme for Wireless Communications

Wireless communication security can be enhanced by leveraging the characteristics of the physical (PHY) layer, where discriminatory scrambling can be employed at the symbol level to either improve the signal quality of the legitimate receiver or degrade that of the eavesdroppers. However, in the presence of multiple passive eavesdroppers with more antennas than the transmitter, the transmitted signals can still be reliably separated from random disturbances. To mitigate this challenge, we propose a two-dimensional vectorized secure transmission scheme. Unlike existing transmission schemes (where the same data symbol is sent over each antenna with a predesigned complex weight at a time), in the proposed scheme, a sequence of data symbols in a predefined order (named symbol vector) is first pre-superposed through pre-coding with a random complex matrix prior to been sent as a vector in parallel over each transmitting antenna at a time. As a result, physical randomness of the legitimate channel is introduced into the received signals at passive eavesdroppers in the pre-coding procedure. Moreover, to ensure that transmitted data symbols can be recovered in the right order, each symbol vector is sent repeatedly, according to the principle of maximum entropy. To ensure the intended receiver can recover the transmitted symbol vector, the random pre-coding matrices are selected such that a linear constraint imposed by the CSI of the legitimate channel is satisfied. In addition, an extended maximum likelihood (ML) detection method is developed for the desired receiver while the random pre-coding matrices are not required to be transmitted. We then analyze its security based on the signal detection theory to demonstrate that the intended receiver can recover the transmitted symbol vectors while the eavesdroppers are not capable of doing so. We also evaluate the performance of the proposed scheme to demonstrate its effectiveness.

Computationally Efficient Channel Estimation in 5G Massive Multiple-Input Multiple-output Systems

Traditional channel estimation algorithms such as minimum mean square error (MMSE) are widely used in massive multiple-input multiple-output (MIMO) systems, but require a matrix inversion operation and an enormous amount of computations, which result in high computational complexity and make them impractical to implement. To overcome the matrix inversion problem, we propose a computationally efficient hybrid steepest descent Gauss–Seidel (SDGS) joint detection, which directly estimates the user’s transmitted symbol vector, and can quickly converge to obtain an ideal estimation value with a few simple iterations. Moreover, signal detection performance was further improved by utilizing the bit log-likelihood ratio (LLR) for soft channel decoding. Simulation results showed that the proposed algorithm had better channel estimation performance, which improved the signal detection by 31.68% while the complexity was reduced by 45.72%, compared with the existing algorithms.

Modified Spatial Modulation: An Alternate to Spatial Multiplexing for 5G-Based Compact Wireless Devices

Spatial modulation (SM) is a spectrum and energy-efficient simple digital modulation scheme, which uses the transmitter antenna indices to convey the additional bits. The conventional SM variants have high complex receivers and offer poor performance under spatially correlated and line-of-sight (LOS) channel conditions. In this work, a new variant, modified spatial modulation (MSM) for $$8 \times 8$$ multiple input multiple output (MIMO) configuration is proposed, which uses one or two transmitter antennas based on the incoming bit patterns. The adaptive mapping used at the transmitter side for antenna selection and modified maximum likelihood (ML) detection used at the receiver side reduces the computational complexity. Every possible bit per channel use (bpcu) is mapped to a unique transmit symbol vector, which minimizes the receiver complexity, while combating the effect of spatial correlation. Through simulation results, it is observed that the average bit error rate (ABER) performance of the MSM-ML scheme is much better than that of the conventional SM-ML, generalized spatial modulation (GSM)-ML and redesigned spatial modulation (ReSM)-ML schemes under spatially correlated and LOS channel conditions. The promising results prove that the proposed scheme can be a better alternative to spatial multiplexing (SMX) in battery-driven compact handheld devices, which can be used for international mobile telecommunication-2020 (IMT-2020).

One-Bit Sphere Decoding for Uplink Massive MIMO Systems With One-Bit ADCs

This paper presents a low-complexity near-maximum-likelihood-detection (near-MLD) algorithm called one-bit-sphere-decoding for an uplink massive multiple-input multiple-output (MIMO) system with one-bit analog-to-digital converters (ADCs). The idea of the proposed algorithm is to estimate the transmitted symbol vector sent by uplink users (a codeword vector) by searching over a sphere, which contains a collection of codeword vectors close to the received signal vector at the base station in terms of a weighted Hamming distance. To reduce the computational complexity for the construction of the sphere, the proposed algorithm divides the received signal vector into multiple sub-vectors each with reduced dimension. Then, it generates multiple spheres in parallel, where each sphere is centered at the sub-vector and contains a list of sub-codeword vectors. The detection performance of the proposed algorithm is also analyzed by characterizing the probability that the proposed algorithm performs worse than the MLD. The analysis shows how the dimension of each sphere and the size of the sub-codeword list are related to the performance-complexity tradeoff achieved by the proposed algorithm. Simulation results demonstrate that the proposed algorithm achieves near-MLD performance, while reducing the computational complexity compared to the existing MLD method.

Error Recovery Based Low-Complexity Detection for Uplink Massive MIMO Systems

In this letter, we introduce a new approach based on error recovery for detection in uplink massive multiple-input multiple-output (MIMO) systems. In the proposed work, first, the non-sparse massive MIMO system is converted into a quasi-sparse error (i.e., error vector consists of a small fraction of significant elements) system by using a rough initial estimate of the transmitted symbol vector. Next, the error is estimated by a low-complexity error recovery technique which detects the error elements in an ordered pattern. Finally, to obtain the output symbol vector, the estimated error vector is combined with the initial solution vector. Furthermore, in order to enhance performance of the algorithm, multiple iterations of error recovery technique are performed. Simulation results reveal that the proposed algorithm outperforms the recently reported methods with approximately equal complexity.

Expanded Constellation Mapping for Enhanced Far-End-Cross-Talk Cancellation in G.fast

We propose the novel concept of expanded constellation mapping (ECM) for maximising the received signal power, while cancelling the far-end-cross-talk in copper-based wireline communications. The goal of ECM is to beneficially map the transmitted symbol vector to its expanded constellation set by carefully exploiting the copper channels’ specific characteristics. To elaborate, ECM is comprised of the control entity and of the match entity, where the former determines how the ECM would be applied, while the latter searches for the best mapping of the transmitted symbol vector to the expanded constellation set. Our numerical results demonstrate that with the aid of the ECM, more than 25-dB power efficiency gain may be achieved over linear vectoring. Similarly, about 20-dB gain may be achieved over non-linear vectoring. From an implementation point of view, the ECM imposes minimal structural changes on G.fast, whilst exhibiting beneficial reconfigurability and compatibility.

Robust MMSE Precoding Based on Switched Relaying and Side Information for Multiuser MIMO Relay Systems

This paper proposes a novel precoding scheme for multiuser multiple-input–multiple-output (MIMO) relay systems in the presence of imperfect channel state information (CSI). The base station (BS) and the MIMO relay station (RS) are both equipped with the same codebook of unitary matrices. According to each element of the codebook, we create a latent precoding matrix pair, namely, a BS precoding matrix and an RS precoding matrix. The RS precoding matrix is formed by multiplying the appropriate unitary matrix from the codebook by a power scaling factor. Based on the given CSI and a block of transmit symbols, the optimum precoding matrix pair, within the class of all possible latent precoding matrix pairs derived from the various unitary matrices, is selected by a suitable selection mechanism for transmission, which is designed to minimize the squared Euclidean distance between the pre-estimated received vector and the true transmit symbol vector. We develop a minimum mean-square-error (MMSE) design algorithm to construct the latent precoding matrix pairs. In the proposed scheme, rather than sending the complete processing matrix, only the index of the unitary matrix and its power scaling factor are sent by the BS to the RS. This significantly reduces the overhead. Simulation results show that, compared with other recently reported precoding algorithms, the proposed precoding scheme is capable of providing improved robustness against the effects of CSI estimation errors and multiuser interference.

Performance Analysis of Layer Pruning on Sphere Decoding in MIMO Systems

Sphere decoding (SD) for multiple-input and multiple-output systems is a well-recognized approach for achieving near-maximum likelihood performance with reduced complexity. SD is a tree search process, whereby a large number of nodes can be searched in an effort to find an estimation of a transmitted symbol vector. In this paper, a simple and generalized approach called layer pruning is proposed to achieve complexity reduction in SD. Pruning a layer from a search process reduces the total number of nodes in a sphere search. The symbols corresponding to the pruned layer are obtained by adopting a QRM-MLD receiver. Simulation results show that the proposed method reduces the number of nodes to be searched for decoding the transmitted symbols by maintaining negligible performance loss. The proposed technique reduces the complexity by 35% to 42% in the low and medium signal-to-noise ratio regime. To demonstrate the potential of our method, we compare the results with another well-known method — namely, probabilistic tree pruning SD.

Analysis of MIMO Receiver Using Generalized Least Squares Method in Colored Environments

The classical detection techniques for multiple-input multiple-output (MIMO) systems are usually designed with the assumption that the additive complex Gaussian noise is uncorrelated. However, for closely spaced antennas, the additive noise is correlated due to the mutual antenna coupling. This letter analyzes an improved zero-forcing (ZF) technique for MIMO channels in colored environments. The additive noise is assumed to be correlated and the Rayleigh MIMO channel is considered doubly correlated. The improved ZF detector, based on the generalized least squares estimator (GLS), takes into account the noise covariance matrix and provides an unbiased estimator of the transmitted symbol vectors. We introduce some novel bounds on the achievable sum rate, on the normalized mean square error at the receiver output, and on the outage probability. The derived expressions are compared to Monte Carlo simulations.

Linear detection for the nonorthogonal amplify and forward protocol

In this paper, we present three new detection schemes for the nonorthogonal amplify and forward (NAF) protocol in a cooperative diversity system based on a multiuser detection approach, namely, a channel inversion type detector, a maximal-ratio combining (MRC) type detector, and a biased maximum likelihood (ML) detector. The decision variables in these schemes are linear functionals of the transmitted symbol vector and therefore they are termed as ldquolinearrdquo detectors. A cooperative relay network using the NAF protocol with N - 1 relays is considered where the source transmits symbols in N - 1 blocks of two time slots in a Rayleigh fading environment. For the case of a general linear space-time block coding scheme using K symbols, we present the performance of this protocol in terms of the code symbol error probability when the symbols come from an M-ary phase-shift keying constellation. The approach is further extended to the transmission in N - 1 blocks of L time slots. Numerical results show that the performance of the MRC type detector is superior to that of the channel inversion type detector, while the biased ML detector has the best performance. However, the MRC type detector has the lowest complexity while the biased ML detector the highest.

Iterative Reconfigurable Tree Search Detection of MIMO Systems

This paper is concerned with reduced-complexity detection, referred to as iterative reconfigurable tree search (IRTS) detection, with application in iterative receivers for multiple-input multiple-output (MIMO) systems. Instead of the optimum maximum a posteriori probability detector, which performs brute force search over all possible transmitted symbol vectors, the new scheme evaluates only the symbol vectors that contribute significantly to the soft output of the detector. The IRTS algorithm is facilitated by carrying out the search on a reconfigurable tree, constructed by computing the reliabilities of symbols based on minimum mean-square error (MMSE) criterion and reordering the symbols according to their reliabilities. Results from computer simulations are presented, which proves the good performance of IRTS algorithm over a quasistatic Rayleigh channel even for relatively small list sizes.

Metric Selection for Reduced-Complexity MAP Detectors in MIMO Systems

Reduced-complexity maximum a posteriori probability (MAP) signal detection is a promising technique for multiple-input multiple-output space division multiplexing (MIMO-SDM) transmission. These detectors avoid exhaustive searches for all possible transmitted symbol vectors by generating a set of candidate symbol vectors. One problem with the reduced-complexity MAP detectors when used in conjunction with soft input decoders is the inaccuracy of log likelihood ratio (LLR) values since they are computed from a handful of candidate symbol vectors, which degrades the subsequent decoding process. To rectify this weakness, this paper proposes an LLR computation scheme for reduced complexity MAP detectors. The unique feature of the proposed scheme is that it utilizes the statistical property of the MIMO channel metric to narrow down further the number of candidate symbol vectors. Toward this goal, metric selection is performed to select only a statistically good portion of the candidate symbol vectors. Computer simulation results show that the proposed LLR computation scheme is more effective than the existing schemes especially when the number of candidate symbol vectors becomes smaller in reduced-complexity MAP detection.

A Semidefinite Relaxation Approach to MIMO Detection for High-Order QAM Constellations

A new and conceptually simple semidefinite relaxation approach is proposed for MIMO detection in communication systems employing high-order QAM constellations. The new approach affords improved detection performance compared to existing solutions of comparable worst-case complexity order, which is nearly cubic in the dimension of the transmitted symbol vector and independent of the constellation order for uniform QAM, or affine in the constellation order for nonuniform QAM

A Simplified Maximum Likelihood Detector for OFDM-SDM Systems in Wireless LAN

This paper presents a reduced-complexity maximum likelihood detection (MLD) scheme for orthogonal frequency division multiplexing with space division multiplexing (OFDM-SDM) systems. Original MLD is known to be an optimal scheme for detecting the spatially multiplexed signals. However, MLD suffers from an exponentially computational complexity because it involves an exhaustive search for the optimal result. In this paper, we propose a novel detection scheme, which drastically reduce the complexity of MLD while keeping performance losses small. The proposed scheme decouples the spatially multiplexed signals in two stages. In stage one, the estimated symbols obtained from zero-forcing (ZF) are used to limit the candidate symbol vectors. In stage two, to form a final estimate of the transmitted symbol vector, the Euclidean or original defined likelihood metric is examined over all symbol vectors obtained from stage 1. Both the bit error rate (BER) and packet error rate (PER) performances are evaluated over a temporally and spatially uncorrelated frequency selective channel through the computer simulations. For a four-transmit and four-receive OFDM-SDM system transmitting data at 144 Mbit/s and 216 Mbit/ss i.e., employing 16 Quadrature Amplitude Modulation (16QAM) and 64QAM subcarrier modulation over 16.6 MHz bandwidth channel, the degradation in required SNR from MLD for PER = 1% are about 0.6 dB and 1.5 dB, respectively. However, the complexity of MLD is reduced to 0.51000% and 0.01562%.

Space division multiplexing scheme using grouped quasi-amicable orthogonal designs

A new space division multiplexing scheme is proposed. With grouped quasi-amicable orthogonal designs (GQOD), the joint detection of the transmitted symbol vector is transferred to the detection of the separate symbols. Compared with V-BLAST architecture, the GQOD scheme can achieve dramatic performance improvement with fewer transmit antennas and lower computational complexity.