Unit Modulus Constraints Research Articles

Phase-Only Robust Minimum Dispersion Beamforming

A phase-only robust minimum dispersion (PO-RMD) beamformer is devised for non-Gaussian signals. Unlike conventional beamformers that adjust the complex-valued weights, including both amplitude and phase, of each antenna to fulfill spatial filtering, the proposed PO-RMD employs a unit-modulus constraint on the weights, which is equivalent to simply phase shifting at each antenna. Instead of the widely used minimum variance criterion, the PO-RMD adopts the minimum dispersion criterion, which minimizes the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm of the array output to utilize the non-Gaussianity of the signals. To achieve robustness against model uncertainty, the magnitude response of any steering vector within an uncertainty region is forced to exceed the threshold. A gradient projection (GP) algorithmic framework is developed to solve the resulting nonconvex optimization problem. In order to find a feasible point in the intersection of the unit-modulus, and robustness constraint sets in each iteration, an alternating projection algorithm is also devised. More importantly, the closed-form expressions of the projection onto the two sets are derived, which only need a low complexity of O(M) with M being the number of antennas. Convergence of the alternating projection is analyzed, and the local linear convergence rate is established. Simulation results demonstrate the fast convergence rate, and accuracy of the GP, as well as the simplicity and robustness of the PO-RMD.

Intelligent Reflecting Surface-Enhanced OFDM: Channel Estimation and Reflection Optimization

In the intelligent reflecting surface (IRS)-enhanced wireless communication system, channel state information (CSI) is of paramount importance for achieving the passive beamforming gain of IRS, which, however, is a practically challenging task due to its massive number of passive elements without transmitting/receiving capabilities. In this letter, we propose a practical transmission protocol to execute channel estimation and reflection optimization successively for an IRS-enhanced orthogonal frequency division multiplexing (OFDM) system. Under the unit-modulus constraint, a novel reflection pattern at the IRS is designed to aid the channel estimation at the access point (AP) based on the received pilot signals from the user, for which the channel estimation error is derived in closed-form. With the estimated CSI, the reflection coefficients are then optimized by a low-complexity algorithm based on the resolved strongest signal path in the time domain. Simulation results corroborate the effectiveness of the proposed channel estimation and reflection optimization methods.

Secrecy Rate Maximization for Intelligent Reflecting Surface Assisted Multi-Antenna Communications

We investigate transmission optimization for intelligent reflecting surface (IRS) assisted multi-antenna systems from the physical-layer security perspective. The design goal is to maximize the system secrecy rate subject to the source transmit power constraint and the unit modulus constraints imposed on phase shifts at the IRS. To solve this complicated non-convex problem, we develop an efficient alternating algorithm where the solutions to the transmit covariance of the source and the phase shift matrix of the IRS are achieved in closed form and semi-closed forms, respectively. The convergence of the proposed algorithm is guaranteed theoretically. Simulations results validate the performance advantage of the proposed optimized design.

Robust Joint Hybrid Transceiver Design for Millimeter Wave Full-Duplex MIMO Relay Systems

The joint design of hybrid beamforming matrices is conceived for multiuser mm-wave full-duplex (FD) multiple-input multiple-output (MIMO) relay-aided systems in the presence of realistic channel state information (CSI) errors. Specifically, considering a probabilistic CSI error model, we maximize the system’s worst-case sum rate by jointly optimizing the base station’s (BS’s) analog and digital beamforming matrices, plus the analog receive and transmit beamforming matrices of the relay station (RS) as well as its digital amplify-and-forward beamforming matrix under practical constraints. Explicitly, the transmit power constraints of the BS and RS, the residual self-interference power constraint of the RS, the per-user quality of service constraints, and the unit-modulus constraints on the analog beamforming matrix elements are all taken into account. Since the resultant optimization problem is very challenging due to its highly nonlinear objective function and nonconvex coupling constraints, we first transform it into a more tractable form. We then develop a novel joint optimization algorithm based on the penalty dual decomposition (PDD) technique to solve the resultant problem. The proposed PDD-based algorithm performs double-loop iterations: the inner loop updates the optimization variables in a block coordinate descent fashion, while the outer loop adjusts the Lagrange multipliers and penalty parameter, hence ensuring convergence to the set of stationary solutions of the original problem. Our simulations show that the mm-wave FD hybrid MIMO relay systems relying on our new algorithm significantly outperform both their non-robust FD and conventional half-duplex counterparts.

Energy Efficiency Beamforming Design for UAV Communications With Broadband Hybrid Polarization Antenna Arrays

Stringent physical resource constraints in unmanned aerial vehicle (UAV) communications bring new challenges to energy efficient transmission. In this paper, we study energy efficient beamforming for UAV communications, where a wideband hybrid polarized antenna array with tapped-delay-lines (TDLs) structure is deployed on the UAV. By exploiting hybrid structured, TDLs, and polarized antenna arrays, the strict requirements of hardware size and cost on UAV can be satisfied. It is shown that the energy efficient beamforming with the adopted array can be formulated as a WMMSE-based parameter optimization problem, which however is still a challenging nonconvex problem due to unit modulus constraints in analog beamformer. To overcome the nonconvex nature, an iterative algorithm is proposed, in which the optimization problem is iteratively solved through three convex quadratic programming problems with convex equality or inequality constraints. Finally, the numerical results demonstrate that the proposed wideband beamforming algorithm can significantly improve the energy efficiency, compared with the gradient projection algorithm.

Analog Precoding Designs for Millimeter Wave Communication Systems

Millimeter wave (mmWave) communication is expected to be a key technology for 5G networks, because it can provide high data rates and large available bandwidth. Large antenna array is necessary to be applied to mmWave system to overcome the high path loss. Restricted by power consumption and system complexity, traditional digital precoding cannot be used for mmWave system. Therefore, analog radio frequency signal processing is introduced to simplify the architecture of precoder. In this paper, we propose dominant vector approaching (DVA) searching method for analog precoder design. Assuming that the channel state information is known at both transmitter and receiver sides, we decompose the analog precoding problem into a series of subproblems. For each subproblem, we just need to optimize one column of analog precoding matrix. Then, we can apply DVA searching method to solve these subproblems under unit modulus constraint. For the fully-connected structure (FS) and the partially-connected structure (PS), we propose DVA-FS and DVA-PS as our precoding designs, respectively. In addition, we prove that DVA searching method finds the near-optimal solutions for the nonconvex subproblems. Through simulation, we show that DVA algorithms achieve near-optimal performance with analog precoder in different scenarios. Besides, we investigate the effect of quantization and the energy efficiency of DVA algorithms, and find that they perform well with rough quantization.

A Framework for One-Bit and Constant-Envelope Precoding Over Multiuser Massive MISO Channels

Consider the following problem: A multi-antenna base station (BS) sends multiple symbol streams to multiple single-antenna users via precoding. However, unlike conventional multiuser precoding, the transmitted signals are subjected to binary, unit-modulus, or even discrete unit-modulus constraints. Such constraints arise in the one-bit and constant-envelope (CE) massive MIMO scenarios, wherein high-resolution digital-to-analog converters (DACs) are replaced by one-bit DACs and phase shifters, respectively, for cutting down hardware cost and energy consumption. Multiuser precoding under one-bit and CE restrictions poses significant design difficulty. In this paper we establish a framework for designing multiuser precoding under the one-bit, continuous CE and discrete CE scenarios---all within one theme. We first formulate a precoding design that focuses on minimizations of symbol-error probabilities (SEPs), assuming quadrature amplitude modulation (QAM) constellations. We then devise an algorithm for our SEP-based design. The algorithm combines i) a novel penalty method for handling binary, unit-modulus and discrete unit-modulus constraints; and ii) a first-order non-convex optimization recipe custom-built for the design. Specifically, the latter is an inexact majorization-minimization method via accelerated projected gradient, which, as shown by simulations, runs very fast and can handle a large number of decision variables. Simulation results indicate that the proposed design offers significantly better bit-error rate performance than the existing designs.

A Framework on Hybrid MIMO Transceiver Design Based on Matrix-Monotonic Optimization

Hybrid transceiver can strike a balance between complexity and performance of multiple-input multiple-output (MIMO) systems. In this paper, we develop a unified framework on hybrid MIMO transceiver design using matrix-monotonic optimization. The proposed framework addresses general hybrid transceiver design, rather than just limiting to certain high frequency bands, such as millimeter wave (mmWave) or terahertz bands or relying on the sparsity of some specific wireless channels. In the proposed framework, analog and digital parts of a transceiver, either linear or nonlinear, are jointly optimized. Based on matrix-monotonic optimization, we demonstrate that the combination of the optimal analog precoders and processors are equivalent to eigenchannel selection for various optimal hybrid MIMO transceivers. From the optimal structure, several effective algorithms are derived to compute the analog transceivers under unit modulus constraints. Furthermore, in order to reduce computation complexity, a simple random algorithm is introduced for analog transceiver optimization. Once the analog part of a transceiver is determined, the closed-form digital part can be obtained. Numerical results verify the advantages of the proposed design.

Joint Beamforming and Jamming Design for mmWave Information Surveillance Systems

This paper addresses the design of joint beamforming and jamming for a millimeter wave (mmWave) information surveillance system where a suspicious transmitter in the network sends messages to a suspicious receiver under the supervision of a surveillant controller (SC), which not only carries out the duty of a base station or other access point, but also legitimately monitor the suspicious link. Specifically, we seek to maximize the effective monitoring rate for information surveillance by jointly optimizing the analog transmit and receive beamforming vectors of the suspicious link, the analog jamming and monitoring beamforming vectors at the SC and the jamming signal’s power level under transmit power, successful monitoring, and self-interference power constraints at the SC, along with unit modulus constraint on the elements of the radio frequency analog beamforming vectors. The resulting optimization problem is quite challenging due to the tight coupling of the design variables in the objective function and constraints. To solve it, we develop a novel algorithm based on the penalty dual decomposition (PDD) technique, where the exacting constraints are penalized and dualized into the objective function as augmented Lagrangian components. The proposed PDD-based algorithm performs double-loop iterations, i.e., the inner loop resorts to the concave-convex procedure to update the optimization variables; while the outer loop adjusts the Lagrange multipliers and penalty parameter of the augmented Lagrangian cost function. We show that the proposed PDD-based joint beamforming and jamming algorithm converges to a stationary solution of the original problem. Based on our simulation results, the proposed algorithm achieves significantly better performance than the conventional beamforming and jamming algorithms.

Cognitive Radar-Based Sequence Design via SINR Maximization

The ambiguity function plays an important role in radar systems. In fact, many radar design problems can be interpreted from the perspective of persuing desired ambiguity functions to adapt to various application scenes. In this paper, we consider designing a radar sequence, subject to a peak-to-average power ratio (PAR) constraint, to maximize the signal-to-interference plus noise ratio, which can also be interpreted as designing a sequence with a desired ambiguity function. From an optimization point of view, this is equivalent to optimizing a complex quartic function with the PAR constraint. An efficient algorithm based on the general majorization–minimization (MM) method is developed to solve this problem with guaranteed convergence to a stationary point under some mild conditions. In addition, the unit-modulus constraint, as a special case, is considered and another algorithm is proposed, which is the combination of the general MM and the coordinate descent method. Numerical experiments show that the proposed algorithms can shape a desired ambiguity function based on the prior information, and the performance is much better compared with the existing methods.

Analog Spatial Cancellation for Tackling the Near-Far Problem in Wirelessly Powered Communications

The implementation of wireless power transfer in wireless communication systems opens up a new research area, known as wirelessly powered communications (WPC). In next-generation heterogeneous networks where ultradense small-cell base stations are deployed, simultaneous-wireless-information-and-power-transfer (SWIPT) is feasible over short ranges. One challenge for designing a WPC system is the severe near-far problem where a user attempts to decode an information-transfer (IT) signal in the presence of extremely strong SWIPT signals. Jointly quantizing the mixed signals causes the IT signal to be completely corrupted by quantization noise, and thus the SWIPT signals have to be suppressed in the analog domain. This motivates the design of a framework in this paper for analog spatial cancellation in a multiantenna WPC system. In the framework, an analog circuit consisting of simple phase shifters and adders is adapted to cancel the SWIPT signals by multiplying it with a cancellation matrix having unit-modulus elements and full rank, where the full rank retains the spatial-multiplexing gain of the IT channel. The unit-modulus constraints render the conventional zero-forcing method unsuitable. Therefore, this paper presents a novel systematic approach for constructing cancellation matrices. For the single-SWIPT-interferer case, the matrices are obtained as truncated Fourier/Hadamard matrices after compensating for propagation phase shifts over the SWIPT channel. For the more challenging multiple-SWIPT-interferer case, it is proposed that each row of the cancellation matrix is constructed as a Kronecker product of component vectors, with each component vectors designed to null the signal from a corresponding SWIPT interferer similarly as in the preceding case.

Waveform Design With Unit Modulus and Spectral Shape Constraints via Lagrange Programming Neural Network

To maximize the transmitted power available in active sensing, the probing waveform should be of constant modulus. On the other hand, in order to adapt to the increasingly crowed radio frequency spectrum and prevent mutual interferences, there are also requirements in the waveform spectral shape. That is to say, the waveform must fulfill constraints in both time and frequency domains. In this work, designing these waveforms is formulated as a nonlinear constrained optimization problem. By introducing auxiliary variable neurons and Lagrange neurons, we solve it using the Lagrange programming neural network. We also analyze the local stability conditions of the dynamic neuron model. Simulation results show that our proposed algorithm is a competitive alternative for waveform design with unit modulus and arbitrary spectral shapes.