In this chapter we deal with the following nonlinear fractional programming problem: 

$$P:\mathop{{\max }}\limits_{{x \in s}} q(x) = (f(x) + \alpha )/((x) + \beta )$$

where f, g: R n → R, α, β ∈ R, S ⊆ R n . To simplify things, and without restricting the generality of the problem, it is usually assumed that, g(x) + β + 0 for all x ∈ S,S is non-empty and that the objective function has a finite optimal value.

Nonlinear Fractional Programming

Distributed and collaborative beamforming (DCBF) scheme in wireless sensor networks (WSNs) is receiving new-found interest in recent times due to the rapid advancements in wireless technology and embedded systems. Although studies on distributed and collaborative beamforming have been carried out for more than ten years, the DCBF was initially considered impractical due to high complexity and hardly achievable requirements. It gained prominence only in the past few years as small wireless communication electronic sensors with high processing capability became easily available. Recent works showcasing distributed and collaborative beamforming as a suitable solution for 5G communication systems such as mm-wave communication and machine to machine communications has further ignited the interest in this research field. Motivated by these factors, this paper presents a survey on the research trends of distributed and collaborative beamforming in WSNs. We provide classifications of the DCBF research areas and conduct an extensive review of the various proposals which have appeared in the literature for each classification. This survey uncovered that majority of existing research can be broadly divided into four major research trends: beampattern analysis, power and lifetime optimization, synchronization, and finally, prototype design. The inherent features, constraints and challenges of each research category in the distributed and collaborative beamforming are presented and the lessons learned from the shortcomings of previous research are summarized. Finally, this paper has unveiled open research directions in the field of distributed and collaborative beamforming in WSNs.

Distributed and Collaborative Beamforming in Wireless Sensor Networks: Classifications, Trends, and Research Directions

We study a multiple-input multiple-output (MIMO) full-duplex (FD) radio system, aiming to increase the feasibility of this technology in bi-directional communications. In particular, we consider that the FD radios are equipped with the State-of-the-Art (SotA) hybrid SI cancellation (SIC) capabilities, but must cope with hardware (HW) and channel state information (CSI) imperfections, contributing four new MIMO beamforming (BF) schemes for such systems. The first is a transmit (TX) beamforming scheme designed via a Fractional Programming (FP) approach, matched with a minimum mean square error (MMSE) beamformer at the receiver. In this benchmark, the FP-based method, the signal to interference-plus-noise ratio (SINR) constraints are relaxed via the quadratic transform (QT), which allows for the SINR-constrained TX-power minimization problem to be solved using interior point methods. Motivated by the high complexity of the latter, three low-complexity alternatives are then derived, in which power minimization is performed via the Perron–Frobenius (PF) approach, while the TX-BF vectors are obtained, respectively, via direct Gradient Projection (GP), QT-relaxation, and via a Double Rayleigh Quotient (DRQ) reformulation of the original optimization problem. The simulation results confirm the significant gains achieved by all four schemes over the SotA, revealing the GP and DRQ as the overall best alternatives depending on power limitation, and HW/CSI qualities.

MIMO Beamforming Schemes for Hybrid SIC FD Radios With Imperfect Hardware and CSI

In this paper, we address the linear precoding and decoding design problem for a bidirectional orthogonal frequency-division multiplexing communication system, between two multiple-input multiple-output (MIMO) full-duplex (FD) nodes. The effects of hardware distortion as well as the channel state information error are taken into account. In the first step, we transform the available time-domain characterization of the hardware distortions for FD MIMO transceivers to the frequency domain, via a linear Fourier transformation. As a result, the explicit impact of hardware inaccuracies on the residual self-interference and inter-carrier leakage is formulated in relation to the intended transmit/received signals. Afterwards, linear precoding and decoding designs are proposed to enhance the system performance following the minimum-mean-squared-error and sum rate maximization strategies, assuming the availability of perfect or erroneous channel state information. The proposed designs are based on the application of alternating optimization over the system parameters, leading to a necessary convergence. Numerical results indicate that the application of a distortion-aware design is essential for a system with a high hardware distortion, or for a system with a low thermal noise variance.

Hardware Impairments Aware Transceiver Design for Bidirectional Full-Duplex MIMO OFDM Systems

In this paper, we address the joint design of the wireless backhauling network topology, as well as the frequency/power allocation on the wireless links, where nodes are capable of full-duplex (FD) operation. The proposed joint design enables the coexistence of multiple wireless links at the same channel, resulting in an enhanced spectral efficiency. Moreover, it enables the usage of FD capability when/where it is gainful. In this regard, a mixed-integer linear program is proposed, aiming at a minimum-cost design for the wireless backhaul network, considering the required rate demand at each base station. Moreover, a retuning algorithm is proposed, which reacts to the slight changes in the network condition, e.g., channel attenuation or rate demand, by adjusting the transmit power at the wireless links. In this regard, a successive-inner-approximation-based design is proposed, where, in each step, a convex subproblem is solved. Numerical simulations show a reduction in the overall network cost via the utilization of the proposed designs, thanks to the coexistence of multiple wireless links on the same channel due to the FD capability.

Environment-Aware Minimum-Cost Wireless Backhaul Network Planning With Full-Duplex Links

In this paper we address the linear precoding and decoding design problem for a bidirectional orthogonal frequencydivision multiplexing (OFDM) communication system, between two multiple-input multiple-output (MIMO) full-duplex (FD) nodes. The effects of hardware distortion as well as the channel state information error are taken into account. In the first step, we transform the available time-domain characterization of the hardware distortions for FD MIMO transceivers to the frequency domain, via a linear Fourier transformation. As a result, the explicit impact of hardware inaccuracies on the residual selfinterference (RSI) and inter-carrier leakage (ICL) is formulated in relation to the intended transmit/received signals. Afterwards, linear precoding and decoding designs are proposed to enhance the system performance following the minimum-mean-squarederror (MMSE) and sum rate maximization strategies, assuming the availability of perfect or erroneous CSI. The proposed designs are based on the application of alternating optimization over the system parameters, leading to a necessary convergence. Numerical results indicate that the application of a distortionaware design is essential for a system with a high hardware distortion, or for a system with a low thermal noise variance.

In this work, we study the linear precoding and decoding design problem for a full-duplex (FD) multi-carrier (MC) decode and forward (DF) relaying system, under multiple sources of impairments. In particular, the impact of non-linear hardware distortions at the transmit and receiver chains, leading to residual self-interference (SI) and inter-carrier leakage (ICL), as well as the imperfect channel state information (CSI) are taken into account. In the first step, the known time-domain characterization of hardware impairments is transformed over a general orthonormal MC basis. As a result, the problem of linear precoding and decoding design is formulated to maximize the MC system sum-rate, however, leading to a non-convex mathematical structure. An alternating quadratic convex program (AQCP) is consequently proposed, with a monotonic improvement at each iteration, leading to a guaranteed convergence. The proposed AQCP framework is then extended, employing the Dinkelbach algorithm, in order to maximize the system energy efficiency in terms of bits-per-Joule. The proposed design strategies are considered both for per-subcarrier as well as the joint-subcarrier coding strategies, wherein the latter case the coding is performed jointly over all subcarriers. Numerical simulations show a significant gain in the performance of the proposed algorithms compared to the half-duplex (HD) counterparts or to the solutions where the impact of impairments are not considered, particularly when the hardware accuracy is not very high.

Hardware Impairments-Aware Transceiver Design for Multi-Carrier Full-Duplex MIMO Relaying

In this paper we address the linear precoding and decoding design problem for a bidirectional orthogonal-frequency-division-multiplexing (OFDM) communication system, between two multiple-input-multiple-output (MIMO) full-duplex (FD) nodes The effects of hardware distortions, leading to residual self-interference and inter-carrier leakage, are taken into account In the first step, the operation of a FD MIMO OFDM transceiver is modeled under the impact of known hardware impairments An alternating quadratic convex program (AltQCP) is then provided to obtain a minimum-mean-squared-error (MMSE) design for the defined system The proposed design is then extended to maximize the system sum rate, applying the weighted-MMSE (WMMSE) method The proposed AltQCP methods result in a monotonic improvement, leading to a necessary convergence to a stationary point Finally, the performance of the defined system is evaluated under various system conditions, and in comparison to the other approaches in the literature A significant gain is observed via the application of the proposed method as the hardware inaccuracy, and consequently inter-carrier leakage, increases

Linear precoder and decoder design for bidirectional full-duplex MIMO OFDM systems

In this paper, we investigate the resource allocation problem for a full-duplex (FD) massive multiple-input-multiple-output (mMIMO) multi-carrier (MC) decode and forward (DF) relay system which serves multiple MC single-antenna half-duplex (HD) nodes In addition to the prior studies focusing on maximizing the sum-rate and energy efficiency, we focus on minimizing the overall delivery time for a given set of communication tasks to the user terminals As our system is an FD MC system, we consider the impact of hardware distortions resulting in residual self-interference and inter-carrier leakage We also consider that only limited channel state information is available A joint power and sub-carrier allocation problem to maximize the sum-rate of the system is then formulated Due to the intractable nature of the underlying problem, an iterative solution is proposed, employing the successive inner approximation (SIA) framework, with guaranteed convergence to the point that satisfies the Karush-Kuhn-Tucker (KKT) conditions For the energy efficiency maximization problem, a two-stage iterative algorithm which follows the SIA and Dinkelbach algorithm is proposed The operation of an FD mMIMO MC DF relay system is evaluated for different system parameters using numerical simulations We also show the importance of considering delivery time minimization rather than sum-rate maximization, ie, maximizing the sum-rate of the system does not necessarily minimize the overall delivery time Numerical results show the significance of distortion-aware design for such systems and also the significant gain in terms of different objectives such as sum-rate, energy efficiency, and delivery time compared to its HD counterpart

Vimal Radhakrishnan

Papers

Hardware Impairments Aware Transceiver Design for Bidirectional Full-Duplex MIMO OFDM Systems

Hardware Impairments Aware Transceiver Design for Bidirectional Full-Duplex MIMO OFDM Systems

Hardware Impairments-Aware Transceiver Design for Multi-Carrier Full-Duplex MIMO Relaying

Linear precoder and decoder design for bidirectional full-duplex MIMO OFDM systems

Impairments-Aware Resource Allocation for FD Massive MIMO Relay Networks: Sum Rate and Delivery-Time Optimization Perspectives