Equal Gain Transmission Research Articles

Finite-Resolution Digital Beamforming for Multi-User Millimeter-Wave Networks

Recent studies have shown that low-resolution analog-to-digital-converters and digital-to-analog-converters (ADCs and DACs) can make fully-digital beamforming more power efficient than its analog or hybrid beamforming counterpart over wide-band millimeter-wave (mmWave) channels. Inspired by this, we propose a computationally efficient fully-digital beamformer relying on low-resolution ADCs/DACs for multi-user mmWave communication networks. Both a generalized (unstructured) beamformer (GB) and a structured zero-forcing beamformer (ZFB) are proposed. For maintaining fairness among all users in the network, specifically tailored objective functions are considered under sum-power constraints, namely that of maximizing the geometric mean (GM) of users’ rate and their max-min rate. These computationally challenging beamforming design problems are tackled by developing computationally efficient steep ascent algorithms, which have the radical benefit of relying on a closed-form solution at each iteration. Moreover, to facilitate the employment of low-cost amplifiers at each antenna, the GB design problem subject to the equal-gain transmission constraint is considered, which assigns equal transmit power to each transmit antenna. The proposed algorithms promise a user-rate distribution having a reduced deviation among the user-rates, i.e., improved rate-fairness. Our extensive simulation results show an approximately upto 45% reduction for the GM-rate of a 2-bit ADC (4-bin quantization) compared to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\infty$</tex-math></inline-formula> -resolution ADC.

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.

Joint Power Allocation and Hybrid Beamforming for Downlink mmWave-NOMA Systems

This paper investigates the application of nonorthogonal multiple access (NOMA) in millimeter-Wave (mmWave) communications to address resource allocation issues for multiuser downlink transmission. Inspired by the K-means clustering algorithm, a NOMA user grouping policy is first employed in accordance with the channel correlation between users. The first-stage decoding order for each NOMA group is then determined by merely utilizing the users’ channel gain to formulate a joint power allocation and hybrid beamforming optimization problem. Specifically, we use signal-to-leakage-plus-noise ratio (SLNR) as the performance index of the optimization problem to reduce the computational complexity, because it can decouple the design of the beamforming and power allocation issues so they can be executed iteratively. Under given beamforming matrix, the power allocation issue is expressed as a quadratic programming (QP) problem, and then transformed into a convex problem by introducing an auxiliary-positive real variable to solve through the Lagrange multiplier method. On the contrary, the beamforming optimization problem is non-convex and very difficult to solve due to the constant modulus constraints in the hybrid architecture. However, the optimum solution of the ideal full-digital beamforming can be acquired primarily by generalized eigenvalue decomposition (GED). In this condition, two hybrid beamforming algorithms are proposed, in which normalized phase matching and equal gain transmission are performed respectively in the analog domain. On this basis, a second-stage decoding order can be employed according to the effective channel gain of users to perform successive interference cancellation (SIC) successfully. Numerical results show that the proposed joint power allocation and hybrid beamforming algorithms are superior to the classical mmWave-NOMA and orthogonal multiple access (OMA) schemes not only in lower implementation complexity, but also in better spectrum efficiency and energy efficiency performance.

Applying Nakagami distribution for BER analysis of equal gain transmission in MU-MIMO systems

In this paper, the bit-error rate (BER) performance of equal gain transmission (EGT) has been analyzed in multiuser multiple-input multiple-output (MU-MIMO) systems. The multiuser interference (MUI), conditioned by the EGT precoding, is found highly correlated with the desired signal when the number of transmit antennas M is in moderate-scale (M⩽64). For such case, the common independent Gaussian assumption for MUI loses precision. In this paper, a translated Nakagami approximation is proposed to characterize the equivalent channel effect, including the channel fading of the desired user and the correlated MUI. The resulted analytical BER equation shows a satisfactory accuracy for both moderate-scale and large-scale MU-MIMO systems.

Hybrid Precoding in Cooperative Millimeter Wave Networks

In this paper, we study the performance of cooperative millimeter wave (mmWave) networks with hybrid precoding architectures. Considering joint transmissions and BS silence strategy, we propose hybrid precoding algorithms which minimize the sum power consumption of the base stations (BSs), for both fully- and partially-connected hybrid precoding (FHP and PHP, respectively) schemes, for single-carrier and orthogonal frequency-division multiplexing systems. We reformulate the analog precoding part as an equal-gain transmission problem, which only depends on the channel information, and the digital precoding part as a relaxed convex semidefinite program subject to per-user quality-of-service constraints that gives the optimal sum power consumption in terms of the BS silence strategy. In order to reduce the complexity of the hybrid precoding algorithm with optimal BS silence strategy, we propose a sub-optimal hybrid precoding algorithm that iteratively put BSs with small power into the silent mode. The simulation results show that, depending on the parameter settings, the power consumption of the PHP may be dominated by the RF transmit power and it may result in a larger power consumption than the FHP. For the cases with 2 BSs and 4 users, implementation of the FHP and the PHP in cooperative networks reduces the required RF transmit power, compared to the case in a non-cooperative network, by 71% and 56%, respectively.

Precoding Design and Power Control for SINR Maximization of MISO System With Nonlinear Power Amplifiers

In practical multi-antenna systems, the design of precoding and power control is not straightforward even for multi-input single-output (MISO) systems because of the distortion caused by nonlinear power amplifiers. Through analysis of the signal-to-interference-plus-noise ratio (SINR), we found that the equal gain transmission scheme can achieve the maximum SINR of a nonlinear MISO system only at the point of local optimal transmit power. Then we derived an approximated optimal transmit power for the nonlinear MISO system. To maximize the SINR in all transmit power region, we propose a precoding and power control algorithm for a MISO system with nonlinear power amplifiers under power constraint. By simulation, we show that the proposed scheme can achieve the local optimum SINR, and outperform other baseline precoding techniques.

On the Achievable Rate of MISO Fading Channels With Instantaneous CSI Only at the Transmitter

We investigate Multiple-Input Single-Output (MISO) fading channels with perfect instantaneous Channel State Information (CSI) at the transmitter and with statistical average CSI at the receiver. We outline achievable rates for maximum ratio transmission and show that the rate loss of not having instantaneous CSI at the receiver behaves like an additional noise term whose variance is equal to one fourth of the transmit power. Similar results are obtained for equal gain transmission. The simulation results are in agreement with the theoretical bounds and indicate that requirement of instantaneous CSI at the receiver becomes obsolete up to a certain transmit power.

Downlink Transmission of Multicell Distributed Massive MIMO With Pilot Contamination Under Rician Fading

In this paper, we investigate the spectral efficiency (SE) of a multicell downlink (DL) distributed massive MIMO (DM-MIMO) system with pilot contamination operating over Rician fading channels in which each remote access unit (RAU) is equipped with a large number of distributed massive antenna arrays, while each user has a single antenna. In contrast to many previous works about DM-MIMO systems, the channel between users and the RAUs antennas in the same cell is modeled to be Rician fading, which is general for the 5G scenarios like Internet of Things. We explore maximum-ratio transmission (MRT) and line-of-sight (LOS) component-based equal-gain transmission (EGT) under imperfect channel state information. The tractable, but accurate closed-form expressions for the lower bounds of the achievable rate are derived for the MRT and the LOS component-based EGT over Rician fading channels in the DM-MIMO systems. Based on the obtained closed-form expressions, various power scaling laws concerning DL data transmit power and pilot transmit power are analyzed in detail. Numerical results are used to corroborate that these approximations are asymptotically tight, but accurate for systems. They also show that employing the LOS component-based EGT processing is more preferable than the MRT processing for DM-MIMO systems in conditions having a large number of RAU antennas and stronger LOS scenarios. Finally, the simulation results further show that when the number of all antennas for RAUs is fixed, the better SE performance can be obtained with more RAUs.

Pricing user scheduling and precoding in relay‐assisted massive MIMO systems

A downlink user scheduling algorithm based on the pricing scheduling factor is proposed for the established relay-assisted massive multiple input multiple output (MIMO) model, which represents the typical remote cell with multiple relays and a massive MIMO base station. Different from the traditional scheduling algorithms, the authors' proposed scheduling algorithm simultaneously takes account of the strength of the desired signal and interference, in which the proposed scheduling factor takes interference strength as the price to select appropriate users. An analysis on the optimal precoding vector is given by assuming each relay adopts equal gain transmission (EGT). According to the analysis, a non-cooperative solution based on the phase difference of EGT is proposed to search the optimal transmission direction of EGT with low complexity. An analytical upper bound of system sum rate is also obtained. Simulation results indicate that the proposed scheduling algorithm has excellent sum rate performance and slight rate degradation compared with the brute-force search algorithm.

LOS-Based Equal Gain Transmission and Combining in General Frequency-Selective Ricean Massive MIMO Channels

In general frequency-selective Ricean fading environments with doubly-ended spatial correlation, this paper investigates the spectral efficiency of a broadband massive multiple-input multiple-output (MIMO) system. In particular, in order to reduce overhead of channel estimation effectively, it proposes a scheme of equal gain transmission and combining, which is only based on line- of-sight (LOS) component and has low hardware complexity. With the scheme, several interesting transmit power scaling properties without and with spatial correlation are derived when the number of antennas at the transmitter or the number of antennas at the receiver grows in an unlimited way. Furthermore, the asymptotical rate analysis is extended to the cooperative relaying scenarios with decode-and-forward and amplify-and-forward protocols, respectively, and then two novel power scaling laws are given.

Hybrid Ray-Tracing/FDTD Method for Human Exposure Evaluation of a Massive MIMO Technology in an Industrial Indoor Environment

This paper presents a numerical approach for massive multiple-input multiple-output (MIMO) human exposure assessment. It combines ray-tracing for the estimation of the wireless channel and the finite-difference time-domain method to simulate the exposure of a realistic human phantom. We apply it to estimate the exposure in a model of an industrial indoor environment with a single massive MIMO base station (BS). The exposure scenarios include line-of-sight and non-line-of-sight propagation with the BS using equal gain transmission precoding at 3.5 GHz. Calculated channel parameters are discussed in comparison with the data available in the literature. The exposure in the phantom's head is evaluated in terms of the peak-spatial specific absorption rate averaged over a 10-g cube and referenced to the free-space time-averaged Poynting vector magnitude at the same location.

Reducing the Codeword Search Complexity of FDD Moderately Large MIMO Beamforming Systems

It is of great interest to develop larger scale multiple-input multiple-output (MIMO) technology based on frequency division duplexing (FDD) for backward compatibility with existing standards and already deployed cellular networks. One hindrance to the FDD approach is the complexity of the codeword search performed by the receiver, which is known to scale with the number of transmit antennas $N_{t}$ in a system. The codeword search complexity does not scale linearly and soon becomes infeasible even for the not-so-massive MIMO systems expected in the very near future. We address this problem by proposing a natural sequence-based orthogonal codebook and an intra-array interference magnitude (IIM) framework for MIMO beamforming based on quantized equal gain transmission that altogether tremendously simplifies the codeword search problem. We also present an assessment on the quality of the codeword selected by the proposed framework that explains it’s near optimal performance, and, provide detailed codeword search complexity quantification. Finally, we provide simulation analyses of beamforming gain under time selective fading channels and an FDD MIMO system transmit delay model. Our analyses indicate that despite significantly reducing complexity, the proposed IIM framework executed by already commercialized processors is capable of approaching the ideal performance of an static system even in the presence of time-selectivity inherent to high-speed mobile communications. Our analyses also quantify the impact of feedback delay on average beamforming gain of moderately large transmit arrays.

Equal-Gain Transmission in Massive MIMO Systems Under Ricean Fading

This paper considers a multicell downlink (DL) massive MIMO system operating over Ricean fading channels in which each base station (BS) is equipped with a massive antenna array, while each user has a single antenna. We explore equal-gain transmission (EGT), line-of-sight (LOS) component-based EGT (LOS-EGT) and maximum-ratio transmission (MRT) under imperfect channel state information. Closed-form expressions for lower bounds of the achievable rates are derived for EGT over Ricean and Rayleigh fading channels, and for LOS-EGT and MRT over Ricean fading channels. With the obtained closed-form expressions, various power scaling laws concerning DL data transmit power and uplink (UL) pilot transmit power are established and discussed. In particular, it is found that, as the number of BS antennas $M$ grows unlimited, the lower bounds on the rates achieved with EGT, LOS-EGT and MRT schemes approach infinity and are not affected by pilot contamination, while the DL data transmit power and UL pilot transmit power can be scaled down proportionally to ${M^{ -a}}$ and ${M^{ - b}}$ (where $0 \leq a and $b > 0$ ), respectively. Numerical results corroborate the tightness and accuracy of these closed-form expressions and they also show that, when the number of antennas and intercell interference level are large, compared to the MRT, EGT and LOS-EGT are more resistant to intercell interference and pilot contamination.

Intrinsic Secrecy of EGT and MRT Precoders for Proper and Improper Modulations

This paper makes an information theoretical analysis of the intrinsic secrecy level of M-QAM and M-PSK modulation schemes considering the use of equal gain transmission and maximum ratio transmission precoding techniques. In addition to the analysis of the conventional proper M-QAM and M-PSK constellations, a recently proposed family of improper versions of the M-QAM and M-PSK modulation schemes is also evaluated. With the exception of proper M-PSK, which verifies always full secrecy for the considered precoders, the main results show that for low order constellations, the amount of intrinsic secrecy provided by the combination of the precoder and modulation scheme is significant and, therefore, can be exploited in the design of a full secrecy solution. The theoretical derivations provided in this paper can be directly applied to quantify the minimal entropy that a secret key must have to fully secure the exchange of information for these transmission schemes.

A New Transmit Beamforming Scheme for Bidirectional Relaying

In this paper, we study the bidirectional/two-way relaying while considering dual antennas at the relay. With detect-and-forward relaying, we propose a transmit beamforming scheme using equal gain transmission (EGT) principle in the bidirectional relaying. Analytical outage probability and symbol error probability for the proposed scheme are presented and a close match with the numerical results is observed. Through numerical results, we show that EGT based transmit beamforming performs slightly worse than the optimum transmit beamforming scheme, while EGT is simpler to implement and requires partial channel state information (CSI). We also show that EGT based transmit beamforming outperforms existing transmission schemes in the presence of CSI error .

Low‐complexity hybrid precoding for multi‐user massive MIMO systems: a hybrid EGT/ZF approach

Massive multiple-input multiple-output (MIMO) systems bring manifold improvements in the system spectral efficiency but result in high hardware and processing complexity at the base station. Employing hybrid precoding at the base station can reduce such complexity. In this study, unlike most existing work on hybrid precoding design, the authors consider a sub-connected analogue combining structure to reduce the complexity. Starting from an important observation on the effect of sequentially designed analogue phased arrays on users' sum rate, the authors develop three low-complexity hybrid precoding schemes for a multi-user massive MIMO system. The proposed schemes apply equal gain transmission (EGT) based analogue beamforming to reap the diversity benefit of an analogue phased array and employ zero-forcing (ZF) beamforming for nullifying inter-user interference. The authors carry out an extensive computational complexity analysis and simulation study on the proposed schemes. The proposed singular-value decomposition based EGT scheme outperforms all others but incurs the highest computational burden. On the other hand, the sequential-EGT scheme is the least computationally intensive scheme but shows the worse performance amongst them.

The Capacity of Gaussian MIMO Channels Under Total and Per-Antenna Power Constraints

The capacity of a fixed Gaussian multiple-input multiple-output (MIMO) channel and the optimal transmission strategy under the total power (TP) constraint and full channel state information are well known. This problem remains open in the general case under individual per-antenna (PA) power constraints, while some special cases have been solved. These include a full-rank solution for the MIMO channel and a general solution for the multiple-input single-output (MISO) channel. In this paper, the fixed Gaussian MISO channel is considered and its capacity and optimal transmission strategies are determined in a closed form under the joint total and PA power constraints in the general case. In particular, the optimal strategy is hybrid and includes two parts: first is equal-gain transmission and second is maximum-ratio transmission, which are responsible for the PA and TP constraints, respectively. The optimal beamforming vector is given in a closed form and an accurate yet simple approximation to the capacity is proposed. Finally, the above results are extended to the MIMO case by establishing the ergodic capacity of fading MIMO channels under the joint power constraints when the fading distribution is right unitary-invariant (of which i.i.d. and semi-correlated Rayleigh fading are special cases). Unlike the fixed MISO case, the optimal signaling is shown to be isotropic in this case.

BER Analysis for Equal Gain Transmission in Downlink Multiuser MIMO Systems

In this letter, we derive the bit error rate (BER) performance of a multiuser multiple-input multiple-output (MU-MIMO) system using equal gain transmission (EGT) precoding. Considering binary phase shift keying (BPSK) modulation, we analyze and propose a statistical model based on the Nakagami distribution for the interference terms involved in the received signals. The precision of our model is compared with the common Gaussian approximation and validated through simulation results. A closed-form BER expression is derived as a function of the number of transmit antennas for arbitrary $E_b/N_0$ .

PAPR Analysis and Mitigation Algorithms for Beamforming MIMO OFDM Systems

Beamforming (or precoding) techniques have been widely adopted in modern MIMO OFDM systems. Using beamforming can significantly improve the receive SNR of OFDM systems. However, the combination of transmit signals after beamforming deteriorates the peak-to-average power ratio (PAPR), which has long been considered a major issue of OFDM systems. High PAPR not only complicates the design of the power amplifier, but also increases power consumption. In this paper, we theoretically analyze the PAPR performance of MIMO OFDM systems that adopt either one of the two popular beamforming schemes, i.e. MRT (maximum ratio transmission) and EGT (equal gain transmission). The analysis considers different numbers of channel taps after sampling. The results may provide important reference for practical designs when evaluating the required power amplifiers and power consumption. Moreover, the theoretical results show that MRT OFDM systems generally perform much worse than EGT OFDM systems in terms of PAPR. Furthermore, motivated from the derived results, PAPR reduction algorithms are proposed for both MRT OFDM and EGT OFDM systems. It is worth to mention that for MRT OFDM systems, the proposed algorithm can improve both PAPR and bit error rate; for EGT OFDM systems, the proposed algorithm improves PAPR while it only slightly degrades bit error rate.

Performance of time reversal precoding technique for MISO-OFDM systems

Time reversal (TR) is considered as a promising technique for green and multi-user communications thanks to its time and space focusing properties. TR can be viewed as a precoding scheme which can be combined with orthogonal frequency division multiplexing (OFDM) and easily carried out in a multiple transmit antenna context. This paper analyzes the performance of TR for a multiple-input single-output (MISO) OFDM system and provides a comparison with maximum ratio transmission (MRT) and equal gain transmission (EGT) precoding techniques. The analytical performance of the three precoding techniques is derived by computing the capacity and the bit error rate (BER) as a function of the transmit signal-to-noise ratio (SNR). First, the capacity analysis highlights the ability of the TR system to provide higher bit rates than the MRT system at low SNRs, while the capacity of the MRT system is the highest at high SNRs. From the obtained BER analytical expressions, the diversity exploitation of each system is discussed. In particular, it is shown that the TR system only exploits half the available diversity, while the systems using EGT or MRT exploit the full diversity. Hence, contrary to what is expected from the theoretical capacity analysis, the TR system is shown to underperform the other precoding schemes in terms of BER. To overcome such a drawback, the combination of TR with classical adaptive modulation techniques is studied, allowing the achievable throughput to be increased without destroying the focusing properties of TR. It is then observed that TR takes advantage of adaptive modulations and outperforms the other schemes at low SNRs. In this study, analytical results and closed-form expressions of capacity and BER performance are provided and confirmed through Monte Carlo simulations.