Two-Way Filter-and-Forward Beamforming for Frequency-Selective Channels

• Published in: IEEE transactions on wireless communications Vol. 10; no. 12; pp. 4172 - 4183
• Main Authors: Liang, Yang-wen, Ikhlef, Aissa, Gerstacker, Wolfgang, Schober, Robert
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; beamforming; Channels; Cooperative network; Decision feedback equalizers; Detection, estimation, filtering, equalization, prediction; Economic models; Equalization; Equalizers; Exact sciences and technology; Finite impulse response filter; frequency-selective channels; Impulse response; Information, signal and communications theory; Interference (signal); Minimization; Operation, maintenance, reliability; Optimization; Radiocommunications; Relay; Relays; Signal and communications theory; Signal to noise ratio; Signal, noise; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transceivers; Transmission and modulation (techniques and equipments); Transmitters. Receivers; two-way relaying; Infinite impulse response filter; Second order; Cooperative network; Relay; Relay network; Decision feedback equalizers; Beam forming; Optimization; Transceiver; Mean square error; Digital filter; Frequency selection; two-way relaying; Design for environment; Fading channels; frequency-selective channels; Maximin problem; Single carrier; Equalization; Carrier frequency; One way; Minimax method; Finite impulse response filter; Signal to interference plus noise ratio; beamforming; Service quality
• DOI: 10.1109/TWC.2011.101511.101952
• ISSN: 1536-1276

In this paper, we consider filter-and-forward beamforming (FF-BF) for two-way relay networks employing single-carrier transmission over frequency-selective channels. In FF-BF, the relay nodes filter the received signal using finite impulse response (FIR) or infinite impulse response (IIR) filters. For the processing at the transceivers, we investigate two different cases: (1) simple slicing without equalization and (2) linear equalization (LE) or decision-feedback equalization (DFE). For the first case, we optimize FIR FF-BF filters, respectively, for maximization of the minimum transceiver signal-to-interference-plus-noise ratio (SINR) subject to a relay transmit power constraint and for minimization of the total relay transmit power subject to two quality of service (QoS) constraints. We show that both problems can be transformed into a convex second-order cone programming (SOCP) problem, which can be efficiently solved using standard tools. For the second case, we optimize IIR and FIR FF-BF filters for max-min optimization of the SINR, and for transceivers with zero-forcing LE, also for minimization of the sum mean-squared error (MSE) at the equalizer outputs of both transceivers. Leveraging results from FF-BF for one-way relaying, we establish an upper and an achievable lower bound for the max-min problem and an exact solution for the sum MSE problem. Since the gap between the upper and the lower bound for the max-min problem is small, a close-to-optimal solution is obtained. Our simulation results reveal that the performance of FF-BF without equalization at the transceivers crucially depends on the slicer decision delay and transceivers with slicers can closely approach the performance of transceivers with equalizers provided that the FF-BF filters are sufficiently long and a sufficient number of relays is deployed.