This review of array antennas highlights those elements of theory and hardware that are a part of the present rapid technological growth. The growth and change in array antennas include increased emphasis on "special-purpose" array techniques such as conformal and printed circuit arrays, wide angle scanning arrays, techniques for limited sector coverage, and antennas with dramatically increased pattern control features such as low sidelobe, adaptively controlled patterns. These new topics have substantially replaced large radar arrays in the literature and constitute a major change in the technology. The paper presents a tutorial review of theoretical developments emphasizing techniques appropriate to finite arrays, but indicating parallel developments in infinite array theory, which has become the useful tool for analysis of large arrays. A brief review of the theory of ideal arrays is followed by a generalized formulation of array theory including mutual coupling effects, and is appropriate to finite or infinite arrays of arbitrary wire elements or apertures in the presence of a conducting ground screen. Some results of array tolerance theory are summarized from the literature and retained as reference throughout discussions of array component requirements and device tolerance for low sidelobe arrays. Examples from present technology include conformal and hemispherical coverage arrays, lightweight printed circuit arrays, systems for use with reflectors and lenses in limited sector coverage applications, and wide-band array techniques.

Phased array theory and technology

Every new generation of mobile systems should provide higher capacity, serve more users, be more energy efficient, and have lower cost. Radio-access hardware constitutes a major bottleneck for reaching these goals, which is a particularly noticeable issue now that 5G communication systems are being developed. A combination of breakthroughs in communication theory-as in massive multiple input/multiple output (MIMO) [1], highly integrated semiconductor and packaging technologies, and extended spectrum allocations- has enabled a paradigm shift in the way radio hardware will be realized. Today's high-power, fewantenna, sectorized systems will soon be replaced with highly integrated active antenna systems having up to hundreds of individually driven low-power radios operating with very wideband signals.

Linearity and Efficiency in 5G Transmitters: New Techniques for Analyzing Efficiency, Linearity, and Linearization in a 5G Active Antenna Transmitter Context

In this paper, a full-angle digital predistortion (DPD) technique is proposed to linearize fifth-generation (5G) millimeter-wave (mmWave) massive multiple-input-multiple-output (mMIMO) transmitters with low implementation complexity. It is achieved by compensating the differences of power amplifiers (PAs) in different transmitter chains first and then adopting a common digital block to linearize the whole subarray. Based on this operation, all the transmitter chains can be efficiently linearized simultaneously, providing the merits of full-angle linearization including the main beam and sidelobes. To validate the proposed idea, an mmWave full-digital beam-forming transmitter has been developed, which is operated at the center frequency of 24.75–28.5 GHz to meet the 5G candidate frequency bands. Experimental results show that the proposed method can effectively linearize the mmWave mMIMO transmitter in all directions, which provides a promising linearization solution for 5G mMIMO beam-forming systems.

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Full-Angle Digital Predistortion of 5G Millimeter-Wave Massive MIMO Transmitters

Massive multiple-input multiple-output (MIMO) is playing a crucial role in the fifth generation (5G) and beyond 5G (B5G) communication systems. Unfortunately, the complexity of massive MIMO systems is tremendously increased when a large number of antennas and radio frequency chains (RF) are utilized. Therefore, a plethora of research efforts has been conducted to find the optimal precoding algorithm with lowest complexity. The main aim of this paper is to provide insights on such precoding algorithms to a generalist of wireless communications. The added value of this paper is that the classification of massive MIMO precoding algorithms is provided with easily distinguishable classes of precoding solutions. This paper covers linear precoding algorithms starting with precoders based on approximate matrix inversion methods such as the truncated polynomial expansion (TPE), the Neumann series approximation (NSA), the Newton iteration (NI), and the Chebyshev iteration (CI) algorithms. The paper also presents the fixed-point iteration-based linear precoding algorithms such as the Gauss-Seidel (GS) algorithm, the successive over relaxation (SOR) algorithm, the conjugate gradient (CG) algorithm, and the Jacobi iteration (JI) algorithm. In addition, the paper reviews the direct matrix decomposition based linear precoding algorithms such as the QR decomposition and Cholesky decomposition (CD). The non-linear precoders are also presented which include the dirty-paper coding (DPC), Tomlinson-Harashima (TH), vector perturbation (VP), and lattice reduction aided (LR) algorithms. Due to the necessity to deal with a high consuming power by the base station (BS) with a large number of antennas in massive MIMO systems, a special subsection is included to describe the characteristics of the peak-to-average power ratio precoding (PAPR) algorithms such as the constant envelope (CE) algorithm, approximate message passing (AMP), and quantized precoding (QP) algorithms. This paper also reviews the machine learning role in precoding techniques. Although many precoding techniques are essentially proposed for a small-scale MIMO, they have been exploited in massive MIMO networks. Therefore, this paper presents the application of small-scale MIMO precoding techniques for massive MIMO. This paper demonstrates the precoding schemes in promising multiple antenna technologies such as the cell-free massive MIMO (CF-M-MIMO), beamspace massive MIMO, and intelligent reflecting surfaces (IRSs). In-depth discussion on the pros and cons, performance-complexity profile, and implementation solidity is provided. This paper also provides a discussion on the channel estimation and energy efficiency. This paper also presents potential future directions in massive MIMO precoding algorithms.

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Overview of Precoding Techniques for Massive MIMO

Joint communication and sensing (JCAS) is an emerging technology for managing efficiently the scarce radio frequency (RF) spectrum, and is expected to be a key ingredient in beyond fifth-generation (5G) networks. We consider a JCAS system, where the full-duplex radar transceiver and the communication transmitter are the same device, and pursue orthogonal frequency-division multiplexing (OFDM) waveform optimization by jointly minimizing the lower bounds of delay and Doppler estimation. This is attained by filling the empty subcarriers within the OFDM frame with optimized samples while reallocating a proportion of the communication subcarriers’ power, which essentially controls the fairness between the two functionalities. Both communication and filled radar subcarriers are used for radar processing. The optimized sample values are found analytically, and a computationally feasible algorithm is presented for this task. We also address how the peak-to-average power ratio of the waveform can be controlled and minimized along the optimization process. The results are then numerically evaluated in 5G New Radio (NR) network context, which indicate a trade-off between the minimization of the lower bounds. The main-lobe width and the peak side-lobe level (PSL) of the range and velocity profiles of the radar image are also analyzed. An inverse relation between the lower bounds and the PSLs is observed, while the main-lobe width can be minimized simultaneously. The trade-off between communication and sensing is investigated, which indicates that the lower bounds can be improved at the cost of the communication capacity. Moreover, over-the-air RF measurements are carried out with unoptimized and optimized 5G NR waveforms at the 28GHz mm-wave band, to validate the range profile’s PSL improvement in an outdoor mapping scenario, depicting considerable performance gain.

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Optimized Waveforms for 5G–6G Communication with Sensing: Theory, Simulations and Experiments

This paper investigates digital predistortion (DPD) linearization of hybrid beamforming large-scale antenna transmitters. We propose a novel DPD processing and learning technique for an antenna subarray, which utilizes a combined signal of the individual power amplifier (PA) outputs in conjunction with a decorrelation-based learning rule. In effect, the proposed approach results in minimizing the nonlinear distortions in the direction of the intended receiver. This feature is highly desirable, since emissions in other directions are naturally weak due to beamforming. The proposed parameter learning technique requires only a single observation receiver, and therefore supports simple hardware implementation. It is also shown to clearly outperform the current state-of-the-art technique that utilizes only a single PA for learning. Analysis of the feedback network amplitude and phase imbalances reveals that the technique is robust even to high levels of such imbalances. Finally, we also show that the array system out-of-band emissions are well-behaving in all spatial directions, and essentially below those of the corresponding single-antenna transmitter, due to the combined effects of the DPD and beamforming.

Digital Predistortion for Hybrid MIMO Transmitters

In this paper, we describe a novel framework for digital predistortion (DPD) based linearization of strongly nonlinear millimeter-wave active antenna arrays. Specifically, we formulate a piecewise (PW) closed-loop (CL) DPD solution and low-complexity gradient-adaptive parameter learning algorithms, together with a region partitioning method, that can efficiently handle deep compression of the PA units. The impact of beamsteering on the DPD performance is studied, showing strong beam-dependence, thus necessitating frequent updating of the DPD. In order to facilitate fast adaptation, an inexpensive, non-iterative, pruning algorithm is introduced, which allows to significantly reduce the amount of model coefficients. The proposed methods are validated with extensive over-the-air RF measurements on a 64-element active antenna array transmitter operating at 28 GHz carrier frequency and transmitting a 400 MHz 5G New Radio (NR) standard-compliant orthogonal frequency division multiplexing waveform. The obtained results demonstrate the excellent linearization capabilities of the proposed solution, conforming to the new 5G NR requirements for frequency range 2 (FR2) in terms of both inband waveform quality and out-of-band emissions. The proposed PW-CL DPD is shown to outperform the state-of-the-art PW DPD based on the indirect learning architecture, as well as the classical single-polynomial based DPD solutions in terms of linearization performance and computational complexity by a clear margin.

Piecewise Digital Predistortion fo mmWave Active Antenna Arrays: Algorithms and Measurements

Efficient mitigation of power amplifier (PA) nonlinear distortion in multi-user hybrid precoding based broadband mmWave systems is an open research problem. In this article, we carry out detailed signal and distortion modeling in broadband multi-user hybrid MIMO systems, with a bank of nonlinear PAs in each subarray, while also take the inevitable crosstalk between the antenna/PA branches into account. Building on the derived models, we adopt and describe an efficient closed-loop (CL) digital predistortion (DPD) solution that utilizes only a single-input DPD unit per transmit chain or subarray, despite crosstalk, providing thus substantial complexity-benefit compared to the state-of-the art multi-dimensional DPD solutions. We show that under spatially correlated multipath propagation, each single-input DPD unit can provide linearization towards every intended user, or more generally, towards all spatial directions where coherent propagation is taking place, and that the adopted CL DPD system is robust against crosstalk. Extensive numerical results building on practical measurement-based mmWave PA models are provided, demonstrating and verifying the excellent linearization performance of the overall DPD system in different evaluation scenarios.

Digital Predistortion for Multiuser Hybrid MIMO at mmWaves

In this paper, new digital predistortion (DPD) solutions for power amplifier (PA) linearization are proposed, with particular emphasis on reduced processing complexity in future 5G and beyond wideband radio systems. The first proposed method, referred to as the spline-based Hammerstein (SPH) approach, builds on complex spline-interpolated lookup table (LUT) followed by a linear finite impulse response (FIR) filter. The second proposed method, the spline-based memory polynomial (SMP) approach, contains multiple parallel complex spline-interpolated LUTs together with an input delay line such that more versatile memory modeling can be achieved. For both structures, gradient-based learning algorithms are derived to efficiently estimate the LUT control points and other related DPD parameters. Large set of experimental results are provided, with specific focus on 5G New Radio (NR) systems, showing successful linearization of multiple PA samples as well as a 28 GHz active antenna array, incorporating channel bandwidths up to 200 MHz. Explicit performance-complexity comparisons are also reported between the SPH and SMP DPD systems and the widely-applied ordinary memory-polynomial (MP) DPD solution. The results show that the linearization capabilities of the proposed methods are very close to that of the ordinary MP DPD, particularly with the proposed SMP approach, while having substantially lower processing complexity.

Gradient-Adaptive Spline-Interpolated LUT Methods for Low-Complexity Digital Predistortion

In this letter, we propose an efficient solution to linearize mmWave active antenna array transmitters that suffer from beam-dependent load modulation. We consider a dense neural network that is capable of modeling the correlation between the nonlinear distortion characteristics among different beams. This allows providing consistently good linearization regardless of the beamforming direction, thus avoiding the necessity of executing continuous digital predistortion parameter learning. The proposed solution is validated, conforming to 5G new radio transmit signal quality requirements, with extensive over-the-air RF measurements utilizing a state-of-the-art 64-element active antenna array operating at 28-GHz carrier frequency.

Alberto Brihuega

Papers

Digital Predistortion for Hybrid MIMO Transmitters

Piecewise Digital Predistortion fo mmWave Active Antenna Arrays: Algorithms and Measurements

Digital Predistortion for Multiuser Hybrid MIMO at mmWaves

Gradient-Adaptive Spline-Interpolated LUT Methods for Low-Complexity Digital Predistortion

Neural-Network-Based Digital Predistortion for Active Antenna Arrays Under Load Modulation