Massive Multiple-input Single-output Research Articles

Fast Antenna Array Calibration Using One External Receiver.

In multiple array communication or radar systems, waveform diversity can be utilized for beampattern design. However, one of the critical issues for such systems is the presence of mutual coupling, which degrades the beampattern design's quality. We address the calibration of the mutual coupling of transmit arrays by developing a new matrix-inversion-free algorithm that requires only a single antenna receiver. It has a very low computational complexity for accelerating the mutual coupling calibration compared to previous methods; therefore, it can be utilized for large array systems such as massive multiple-input-single-output (MISO) systems. The key idea here revolves around utilizing fast Fourier transform (FFT). This approach simplifies matrix calculations and reduces the number of multiplications required to compute the inverse of FFT. Moreover, the algorithm is applicable for high-power active radar calibration, since it incorporates a constant modulus training sequence. The application of the algorithm in MISO systems, including massive MISO, offers the potential for calibrating mutual coupling. It enables the precise measurement and compensation of mutual coupling effects, improving the signal quality and system performance in areas such as radars, mobile communications and more. We evaluated the proposed algorithm under various scenarios, compared it with the ground truth and showed that it achieves excellent performance with few computations.

Design of Multi-User Noncoherent Massive SIMO Systems for Scalable URLLC.

This paper develops and optimizes a non-orthogonal and noncoherent multi-user massive single-input multiple-output (SIMO) framework, with the objective of enabling scalable ultra-reliable low-latency communications (sURLLC) in Beyond-5G (B5G)/6G wireless communication systems. In this framework, the huge diversity gain associated with the large-scale antenna array in the massive SIMO system is leveraged to ensure ultra-high reliability. To reduce the overhead and latency induced by the channel estimation process, we advocate for the noncoherent communication technique, which does not need the knowledge of instantaneous channel state information (CSI) but only relies on large-scale fading coefficients for message decoding. To boost the scalability of noncoherent massive SIMO systems, we enable the non-orthogonal channel access of multiple users by devising a new differential modulation scheme to ensure that each transmitted signal matrix can be uniquely determined in the noise-free case and be reliably estimated in noisy cases when the antenna array size is scaled up. The key idea is to make the transmitted signals from multiple geographically separated users be superimposed properly over the air, such that when the sum signal is correctly detected, the signal sent by each individual user can be uniquely determined. To further enhance the average error performance when the array antenna number is large, we propose a max-min Kullback-Leibler (KL) divergence-based design by jointly optimizing the transmitted powers of all users and the sub-constellation assignments among them. The simulation results show that the proposed design significantly outperforms the existing max-min Euclidean distance-based counterpart in terms of error performance. Moreover, our proposed approach also has a better error performance compared to the conventional coherent zero-forcing (ZF) receiver with orthogonal channel training, particularly for cell-edge users.

Analysis and Optimization of Spectral and Energy Efficiency in Underlaid D2D Multi-Cell Massive MISO Over Rician Fading

This paper investigates the uplink spectral efficiency (SE) characterization and energy efficiency (EE) optimization of device-to-device (D2D) communications underlying a multi-cell massive multiple-input single-output (m-MISO) network, assuming that the channels are modeled with Rician fading. First, an analytical expression for the lower-bound of the ergodic capacity of a typical cellular user (CU) is derived with imperfect channel state information in the presence of D2D links’ interference. Then, a closed-form approximate achievable SE expression for a typical D2D pair is derived considering Rician fading between D2D pairs. The asymptotic SE behavior is analyzed in strong line-of-sight (LOS) conditions for CU and D2D pairs. Also, simplified expressions are obtained for the special case of Rayleigh fading. Next, to optimize the total EE, a transmit data power allocation based on the derived rate expressions is formulated. Since the optimization problem has a non-linear and non-convex objective function, it is intractable to be solved straightforwardly. Therefore, we resort to utilizing an iterative algorithm relying on fractional programming. The numerical results show that a stronger LOS component (i.e., larger Rician K-factor) between a typical CU and its serving BS leads to a significant improvement in the system performance, while it has less effect on the D2D network.

Approximative Threshold Optimization From Single Antenna to Massive SIMO Authentication

In a wireless sensor network, data from various sensors are gathered to estimate the system-state of a process system. However, adversaries aim at distorting the estimation, for which they may infiltrate sensors or position additional devices in the environment. For authentication, the receiver can evaluate the integrity of measurements from different sensors jointly with the temporal integrity of channel measurements from each sensor. Therefore, we design a security protocol, in which Kalman filters predict the system-state and the channel-state values. Then, the received data is authenticated by a hypothesis test. We theoretically analyze the adversarial success probability and the reliability in two ways, based on chi-square and Gaussian approximations. The two approximations are exact for small and large data vectors, respectively. Hence, the Gaussian approximation is suitable for analyzing massive single-input multiple-output (SIMO) setups. This approximation is adapted to channel hardening, which occurs in massive SIMO fading channels. As adversaries always look for the weakest point, a time-independent security level is required. Hence, the approximations are used to propose time-varying thresholds for the hypothesis test, which approximately attain a constant security level. Numerical results show that either the security level or the threshold value can be time-independent, but not both.

Enhanced Signal Detection and Constellation Design for Massive SIMO Communications With 1-Bit ADCs

In this paper, we investigate a transmitter and receiver design for a single-user massive SIMO (single-input multiple-output) system with 1-bit analog-to-digital converters (ADCs) at the base station (BS), where the user adopts higher-order modulation, e.g., 16-quadrature amplitude modulation (16-QAM), for the data transmission. For the channel estimation and the signal detection, linear least-squares (LS) estimation and maximum ratio combining (MRC) are respectively employed. In this context, we first introduce closed-form formulas for the mean of the estimated symbols and for the correlation matrix between their real and imaginary parts considering the effect of 1-bit quantization. The study of the distribution of the estimated symbols indicates that, in presence of 1-bit ADCs, the conventional 16-QAM detector and the typical square 16-QAM modulation are not adequate. In light of this, we propose three novel symbol detectors and re-design the 16-QAM modulation in order to improve the symbol error rate (SER). Furthermore, the upper bound on the SER is analyzed based on the pair-wise error probability and the boundary equation between two regions is also studied. Through numerical results, the proposed framework, i.e., the symbol detector and the transmit constellation design, shows a significant enhancement in the SER performance against the conventional detector and the typical square 16-QAM modulation.

Constellation Design for Energy-Based Noncoherent Massive SIMO Systems Over Correlated Channels

This letter concerns the constellation design problem in energy-based noncoherent massive single-input multiple-output (SIMO) systems over correlated channels. Thanks to the large number of receiving antennas, we approximate the detection error minimization problem by the maximization of the minimum Kullback-Leibler (KL) divergence of the received signal vectors corresponding to different transmitted symbols. However, the max-min KL divergence problem is still difficult to solve. This is because the KL divergence expression involves summations of nonlinear functions of the transmitted signal powers induced by the channel correlation. We then resort to the Szegö’s theorem on large Hermitian Toeplitz matrices to simplify the formulated problem, which subsequently can be optimally solved by a one-dimensional bisection search. Simulation results demonstrate that the constellation designed by our approach outperforms its counterpart without considering the channel correlation, and the performance gain enlarges as the degree of correlation increases.

Semi-Blind Channel Estimation for RIS-Assisted MISO Systems Using Expectation Maximization

<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Reconfigurable intelligent surface (RIS) is a passive antenna array composed of a large number of reflecting elements. In a RIS-assisted communication system, it is a challenging task to acquire accurate channel state information (CSI). In this paper, we propose a semi-blind channel estimation method for a RIS-assisted massive multiple-input single-output (MISO) system. Assuming a Gaussian</b> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <b>priori</b> </i> <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on the data symbols, an iterative expectation maximization (EM)-based algorithm is developed to obtain the maximum likelihood (ML) estimate of the cascaded RIS channel. Different from existing pilot-based methods, the proposed semi-blind channel estimation method exploits the data symbols for channel estimation enhancement and only a fraction of full-pilot signaling overhead is required. Simulation results verify that the proposed method achieves significant improvement in the accuracy of the channel estimation while it noticeably reduces the training pilot overhead.</b>

Spectral efficiency for IRS-assisted uplink mmWave massive MISO systems with low-resolution ADCs

In this paper, we investigate the uplink achievable spectral efficiency (SE) for an intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) multiple-input single-output (MISO) system, where all antennas at the BS are equipped with cheaper low-resolution analog-to-digital converters (ADCs) and an IRS adjusts its reflecting phase shifts to facilitate information transfer. To maximize the uplink achievable SE, we design the phase shift of each reflecting element and obtained the optimal phase shift matrix in the terms of the statistical channel state information (CSI). An theoretical expression of the uplink achievable SE of massive MISO system is obtained with the zero forcing (ZF) detector is derived. Based on this derived theoretical result, the behaviors of the achievable SE with respect to several physical parameters are revealed that includes the number of antennas, the transmit power, the number of reflecting elements, and the quantization bits of the low-resolution ADCs. Finally, we provide the numerical results by Monte Carlo simulation to verify that our theoretical analysis is accurate. Results show that the achievable SE increases with the number of antennas, the number of quantization bits of the ADC and the reflecting elements of the IRS, but tends to a saturation rate. In addition, we find that the SE inevitably suffers a certain loss due to the phase shift noise is unavoidable and the quantization accuracy of IRS, which can be compensated by increasing the transmit power and the number of reflecting elements.

Min-SINR Maximization for mmWave Massive MISO-NOMA System With Randomly Directional Beamforming

Based on the high-direction characteristic of millimeter wave (mmWave) transmission, randomly directional beamforming (RDB) can be used for the mmWave massive multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) system to reduce the number of radio frequency (RF) chains. However, the impact of RDB on the signal-to-interference-plus-noise ratio (SINR) of each user is related to the corresponding beamforming gain and interference from other users. Thus, in this paper, we investigate the max-min SINR among all users to evaluate user fairness. In particular, we focus on the single-cell downlink mmWave MISO-NOMA system with RDB, where single-antenna users are divided into multiple NOMA clusters according to their azimuth angles. We formulate the minimum achievable SINR maximization problem associated with power allocation and propose the sum of power allocation coefficients based iterative algorithm (SPACIA) to find the max-min SINR. We also prove that the max-min SINR monotonically decreases as the number of paired users in an NOMA cluster increases as well as the number of beams in the cell with large-scale base station (BS) antenna array increases. Moreover, we derive the upper bound of the max-min SINR. Simulation results verify our theoretical analyses and demonstrate that the proposed algorithm guarantees user fairness, thus outperforming existing schemes.

Optimal Joint Channel Estimation and Data Detection for Massive SIMO Wireless Systems: A Polynomial Complexity Solution

By exploiting large antenna arrays, massive MIMO (multiple input multiple output) systems can greatly increase spectral and energy efficiency over traditional MIMO systems. However, increasing the number of antennas at the base station (BS) makes the uplink joint channel estimation and data detection (JED) challenging in massive MIMO systems. In this paper, we consider the JED problem for massive SIMO (single input multiple output) wireless systems, which is a special case of wireless systems with large antenna arrays. We propose exact Generalized Likelihood Ratio Test (GLRT) optimal JED algorithms with low expected complexity, for both constant-modulus and nonconstant-modulus constellations. We show that, despite the large number of unknown channel coefficients, the expected computational complexity of these algorithms is polynomial in channel coherence time (T) and the number of receive antennas (N), even when the number of receive antennas grows polynomially in the channel coherence time (N=O(T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> ) suffices to guarantee an expected computational complexity cubic in T and linear in N). Simulation results show that the GLRT-optimal JED algorithms achieve significant performance gains (up to 5 dB improvement in energy efficiency) with low computational complexity.

Capacity Scaling in a Non-Coherent Wideband Massive SIMO Block Fading Channel

The scaling of coherent and non-coherent channel capacity is studied in a single-input multiple-output (SIMO) block Rayleigh fading channel as both the bandwidth and the number of receiver antennas go to infinity jointly with the transmit power fixed. The transmitter has no channel state information (CSI), while the receiver may have genie-provided CSI (coherent receiver), or the channel statistics only (non-coherent receiver). Our results show that if the available bandwidth is smaller than a threshold bandwidth which is proportional (up to leading order terms) to the square root of the number of antennas, there is no gap between the coherent capacity and the non-coherent capacity in terms of capacity scaling behavior. On the other hand, when the bandwidth is larger than this threshold, there is a capacity scaling gap. Since achievable rates using pilot symbols for channel estimation are subject to the non-coherent capacity bound, this work reveals that pilot-assisted coherent receivers in systems with a large number of receive antennas are unable to exploit excess spectrum above a given threshold for capacity gain.

On 3D Cluster-Based Channel Modeling for Large-Scale Array Communications

With the rapid development of wireless communications, the understanding of three-dimensional (3D) propagation channels becomes essential for design and testing of some new wireless technologies, e.g., massive multiple-input multiple-output (MIMO) and full dimensional beamforming. To not only fully exploit the 3D multiplexing but also circumvent the size limitation of base station (BS), antenna elements in massive MIMO are usually arranged both horizontally and vertically. Based on an elaborate channel measurement campaign conducted at 11 GHz in a lobby environment, a 3D extended cluster-based channel model is proposed in this paper for massive multiple-input single-output (MISO) multi-user communications. In the model, the channel characteristics in both azimuth and elevation dimensions, and the visibility regions which are parametrized by observed cluster lengths across the large-scale array in both horizontal and vertical directions, are taken into consideration. Moreover, the spherical wavefront phenomenon observed from the measurements is also incorporated in the model. Model parametrization, implementation, and validation are presented in detail. Validations show that the proposed model can accurately reflect the realistic channel, and the spatial non-stationarity and the spherical wavefront should be carefully considered in the channel models for large-scale array communications.

Detection of Jamming Attack in Non-Coherent Massive SIMO Systems

In recent studies, a simple non-coherent communication scheme based on energy detection is proposed in massive single-input multiple-output (SIMO) systems. Before data transmission, the transmitter sends pilots to the receiver for the purpose of estimating the channel statistics. However, this training phase unintentionally provides opportunity for a malicious jammer to attack legitimate communication. In order to secure the legitimate communication, this paper proposes a jamming detection method in non-coherent SIMO systems, in which the information of channel statistics is not required. First, the transmitter sends pilots to the receiver, then the receiver sends the conjugate of its received signal (which may contain jammer signal) back to the transmitter, where the final decision on jamming detection is made. According to the likelihood ratio test principle, two detectors based on variance and standard variance normalization are proposed. The performance analysis indicates that these two detectors are of similar detection performance but of different complexity. Furthermore, it is revealed that the probability of detection initially grows with the number of receive antennas but converges quickly then, whereas the channel statistics from the jammer to the receiver always greatly influences the performance. Finally, the numerical simulations are carried out to validate the proposed detection method.

Analysis of residual CFO impact on downlink massive MISO systems

Massive antenna technologies provide a good power focusing gain for emerging communication systems. They can easily be integrated into an orthogonal frequency-division multiplexing (OFDM) system. However, OFDM is known to be prone to carrier frequency offset (CFO) due to the loss of the orthogonality among OFDM subcarriers. In this Letter, the authors investigate the impact of residual CFO (RCFO) on the downlink performance of massive multiple-input single-output (MISO) OFDM systems using matched-filter (MF) and maximum-ratio-transmission (MRT) precoders. Particularly, the exact mean-square-error (MSE) expressions of the equalised received signal of both MF and MRT systems are derived. Numerical simulations with Rayleigh fading channels are carried out to validate the analysis. The results show that the RCFO causes a MSE plateau compared to the ideal case of no CFO.

Energy-Efficient and Low-Latency Massive SIMO Using Noncoherent ML Detection for Industrial IoT Communications

To enable ultrareliable low-latency wireless communications required in the Industrial Internet of Things, in this paper we develop an energy-based modulation [i.e., non-negative pulse amplitude modulation (PAM)] constellation design framework for noncoherent detection in massive single-input multiple-output (SIMO) systems. We consider that one single-antenna transmitter communicates to a receiver with a large number of antennas over a Rayleigh fading channel, and the receiver decodes the transmitted information at the end of every symbol. For such an SIMO system with non-negative PAM modulation, we first propose a fast noncoherent maximum-likelihood decoding algorithm and derive a closed-form expression of its symbol error probability (SEP). We then enhance the system energy efficiency by finding the optimal PAM constellation that minimizes the exact SEP subject to a total signal power constraint for such a system with an arbitrary number of receiver antennas, signal-to-noise ratio (SNR), and constellation size. Furthermore, the closed-form upper and lower bounds on the optimal SEP are derived. Based on these bounds, the exact expression for coding gain of the dominant term of the SEP is presented for such an optimal massive SIMO system. We also present an asymptotic SEP expression at a high SNR regime and the approximate diversity gain of the system. Simulation results for the proposed optimal PAM constellation validate the theoretical analysis, and show that our presented optimal constellation attains significant performance gains over the currently available minimum-distance-based constellation systems.

Design of Optimal Noncoherent Constellations for SIMO Systems

In this paper, we consider a single-input multiple-output (SIMO) system, in which a single-antenna transmitter communicates with a receiver having multiple antennas. It is assumed that the channel coefficients keep constant during two consecutive time slots, after which they become new independent values. For such a system, we focus on the concept of uniquely factorable constellations (UFCs) in the design of noncoherent coding schemes under two communication scenarios. The first scenario is the massive SIMO system, in which only the first and second order channel statistical information is available. The second is the traditional Rayleigh fading SIMO system. First, parameterized massive UFC (MUFC) and unitary UFC (UUFC) are designed for each scenario. It is proved that these designs ensure the unique identification of the transmitted signals when there is no additive Gaussian white noise. Second, using the Riemannian distance (RD) metric for the RD-based detector and coding gain criterion for generalized likelihood ratio test receiver, the optimal MUFCs and UUFCs of various sizes are constructed, respectively. Finally, we exploit the structures of our proposed designs to reduce the decoding complexities compared to the exhaustive search methods. Comprehensive computer simulations show that our proposed schemes outperform the current designs in literature.

Non-Coherent Massive SIMO System Based on M-DPSK for Rician Channels

In this paper, we propose a new constellation design for a non-coherent massive single input multiple output (m-SIMO) uplink system based on M-DPSK suitable for Rician channels. Under Rician propagation, the non-coherent systems proposed until now cannot completely remove the interference. This new design takes into account the inter user and inter symbol interferences in order to convert them into useful terms that help us in the non-coherent detection. We propose an algorithm to non coherently detect the joint symbol with the information from all users leveraging the characteristics of the new constellation. In addition, the signal-to-interference-plus-noise ratio is derived and is used to present analytical bounds for the symbol error rate. It is shown that the analytical results tightly match the numerical simulation. We show that with the proposed constellation and detection algorithm we are able to leverage the line-of-sight component of the Rician propagation, obtaining a better performance than with Rayleigh channels.

Massive MIMO 1-Bit DAC Transmission: A Low-Complexity Symbol Scaling Approach

We study multi-user massive multiple-input single-output systems and focus on downlink transmission for PSK modulation, where the base station employs a large antenna array with low-cost 1-bit digital-to-analog converters (DACs). The direct combination of existing beamforming schemes with 1-bit DACs is shown to lead to an error floor at medium-to-high SNR regime, due to the coarse quantization of the DACs with limited precision. In this paper, based on the constructive interference, we consider both a quantized linear beamforming scheme where we analytically obtain the optimal beamforming matrix and a non-linear mapping scheme where we directly design the transmit signal vector. Due to the 1-bit quantization, the formulated optimization for the non-linear mapping scheme is shown to be non-convex. The non-convex constraints of the 1-bit DACs are first relaxed into convex, followed by an element-wise normalization to satisfy the 1-bit DAC transmission. We further propose a low-complexity symbol scaling scheme that consists of three stages, in which the quantized transmit signal on each antenna element is selected sequentially. Numerical results show that the proposed symbol scaling scheme achieves a comparable performance to the optimization-based non-linear mapping approach, while the corresponding performance-complexity tradeoff is more favorable for the proposed symbol scaling method.

Non-Coherent Massive SIMO Systems in ISI Channels: Constellation Design and Performance Analysis

A massive single-input multiple-output (SIMO) system with a single transmit antenna and a large number of receive antennas in intersymbol interference (ISI) channels is considered. Contrast to existing energy detection (ED)-based non-coherent receiver where conventional pulse amplitude modulation (PAM) is employed, we propose a constellation design which minimizes the symbol-error rate (SER) with the knowledge of channel statistics. To make a comparison, we derive the SERs of the ED-based receiver with both the proposed constellation and PAM, namely $P_{e\_opt}$ and $P_{e\_pam}$. Specifically, asymptotic behaviors of the SER in regimes of a large number of receive antennas and high signal-to-noise ratio (SNR) are investigated. Analytical results demonstrate that the logarithms of both $P_{e\_opt}$ and $P_{e\_pam}$ decrease approximately linearly with the number of receive antennas, while $P_{e\_opt}$ degrades faster. It is also shown that the proposed design is of less cost, because compared with PAM, less antennas are required to achieve the same error rate.

Rate-Splitting to Mitigate Residual Transceiver Hardware Impairments in Massive MIMO Systems

Rate-splitting (RS) has recently been shown to provide significant performance benefits in various multiuser transmission scenarios. In parallel, the huge degrees-of-freedom provided by the appealing massive multiple-input multiple-output (MIMO) necessitate the employment of inexpensive hardware, being more prone to hardware imperfections, in order to be a cost-efficient technology. Hence, in this paper, we focus on a realistic massive multiple-input single-output broadcast channel hampered by the inevitable hardware impairments. We consider a general experimentally validated model of hardware impairments, accounting for the presence of multiplicative distortion due to phase noise, additive distortion noise and thermal noise amplification. Under both scenarios with perfect and imperfect channel state information at the transmitter (CSIT), we analyze the potential robustness of RS to each separate hardware imperfection. We analytically assess the sum-rate degradation due to hardware imperfections. Interestingly, in the case of imperfect CSIT, we demonstrate that RS is a robust strategy for multiuser MIMO in the presence of phase and amplified thermal noise, since its sum-rate does not saturate at high signal-to-noise ratio (SNR), contrary to conventional techniques. On the other hand, the additive impairments always lead to a sum-rate saturation at high SNR, even after the application of RS. However, RS still enhances the performance. Furthermore, as the number of users increases, the gains provided by RS decrease not only in ideal conditions, but in practical conditions with residual transceiver hardware impairments as well. Notably, although a deterministic equivalent analysis is employed, the analytical and simulation results coincide even for finite system dimensions. As a consequence, the applicability of these results also holds for current “small scale” multiantenna systems.