Yang-wen Liang

Cooperative Filter-and-Forward Beamforming for Frequency-Selective Channels with Equalization

Most of the existing literature on cooperative relay networks has focused on frequency-nonselective channels or frequency-selective channels with multi-carrier transmission. However, several practical systems employ single-carrier transmission over frequency-selective channels and the design of corresponding relaying schemes is a largely under-explored topic. In this paper, we investigate filter-and-forward beamforming (FF-BF) for relay networks employing single-carrier transmission over frequency-selective channels. In contrast to prior work, we assume that the destination node is equipped with a simple linear or decision feedback equalizer. The FF-BF filters at the relays are optimized for maximization of the signal-to-noise ratio at the equalizer output under a joint relay power constraint. For infinite impulse response (IIR) FF-BF filters, we derive a unified expression for the filter frequency response valid for linear equalization, decision feedback equalization, and an idealized matched filter receiver. A numerical algorithm with guaranteed convergence is developed for optimization of the power allocation factor included in the expression for the IIR FF-BF filter frequency response. We also provide an efficient gradient algorithm for recursive calculation of near-optimal finite impulse response (FIR) FF-BF filters. Simulation results show that, in general, short FIR FF-BF filters are sufficient to closely approach the performance of IIR FF-BF filters even in severely frequency-selective channels and that the proposed FF-BF scheme with equalization at the destination achieves substantial performance gains compared to a previously proposed FF-BF scheme without equalization.

Transmit beamforming for frequency-selective channels with decision-feedback equalization

In this paper, we propose beamforming schemes for frequency-selective channels with decision-feedback equalization (DFE) at the receiver and with, respectively, perfect and quantized channel state information (CSI) at the transmitter. For beamforming with perfect CSI and infinite impulse response (IIR) beamforming Alters (BFFs) we provide a closed-form expression for the optimum BFFs. We also devise two efficient numerical methods for recursive calculation of the optimum finite impulse response (FIR) BFFs with perfect CSI. For beamforming with quantized CSI and finite-rate feedback channel, we propose a global vector quantization (GVQ) algorithm for codebook design. This algorithm is deterministic and independent of initial conditions and does not impose any constraints on the number of transmit and receive antennas, the antenna correlation, or the fading statistics. Our simulation results for typical GSM/EDGE channels show that in general short FIR BFFs are sufficient to closely approach the performance of IIR BFFs even in severely frequency-selective channels. Furthermore, finite-rate feedback beamforming with only a few feedback bits achieves significant performance gains over single-antenna transmission, transmit antenna selection, and optimized delay diversity in frequency-selective fading.

Cooperative Amplify-and-Forward Beamforming for OFDM Systems with Multiple Relays

In this paper, we propose frequency-domain (FD) and time-domain (TD) beamforming (BF) schemes for co-operative orthogonal frequency division multiplexing (OFDM) networks with multiple amplify-and-forward relays. Whereas for FD-BF the BF weights are applied in the FD, for TD-BF cyclic BF filters (C-BFFs) are used on the TD signal avoiding discrete-time Fourier transform operations at the relays and drastically reducing the required amount of feedback from the receiver to the relays. Adopting the average mutual information (AMI) per sub-carrier as optimality criterion, we show that the direction of the optimal FD-BF weights can be obtained in closed-form and that the optimal sub-carrier power allocation (PA) problem is convex. For solution of the PA problem an interior point method and a bisectional search dual method are provide. Furthermore, for solution of the C-BFF optimization problem an efficient gradient algorithm is proposed. Simulation results for IEEE 802.11n channels show that TD-BF with short C-BFFs closely approaches the performance of FD-BF and outperforms direct transmission without relaying.

Time-Domain Transmit Beamforming for MIMO-OFDM Systems

Transmit beamforming (BF) and receive combining are simple and popular methods for performance enhancement in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. In this paper, we propose a novel time-domain BF (TD-BF) scheme for MIMO-OFDM systems which uses cyclic BF filters (C-BFFs). Assuming perfect channel state information (CSI) at the transmitter, the C- BFFs are optimized for maximization of the average mutual information per sub-carrier. Using a global vector quantization approach the C-BFFs are quantized for practical finite-rate feedback channels. Simulation and numerical results for typical IEEE 802.11n channels confirm the excellent performance of the proposed scheme and show that TD-BF has a more favorable performance/feedback rate trade-off than previously proposed frequency-domain BF (FD-BF) schemes.

Amplify-and-Forward Multi-Antenna Beamforming with Joint Source-Relay Power Constraint

In this paper, we consider beamforming (BF) for cooperative networks with one multi- antenna source, multiple multi-antenna amplify-and-forward (AF) relays, and one single- antenna destination. The source BF vector and the AF-BF matrices at the relays are optimized for maximization of the signal-to-noise ratio at the destination under a joint power constraint for the source and the relays. We solve the associated optimization problem in two stages. In the first stage, we find the optimal AF-BF matrices for a given BF vector at the source. In particular, the direction of the AF-BF matrices is derived in closed form and an efficient numerical algorithm for the convex power allocation problem between the source and the relays is provided. In the second stage, the optimal source BF vectors are computed. Thereby, we show that the resulting problem can be transformed into a non-convex polynomial programming problem which allows for an exact solution for small-scale networks. For large-scale networks, we propose efficient suboptimal optimization methods for the source BF vector.

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

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. For both cases, we optimize FF-BF filters for maximization of the minimum transceiver signal-to-interference-plus-noise ratio (SINR) subject to a relay transmit power constraint. For case (1), we show that the optimization problem for FIR filters can be transformed into a convex second-order cone programming problem, which can be efficiently solved using standard tools. For case (2), leveraging results from IIR FF-BF for one-way relaying, we establish an upper and an achievable lower bound for the max-min problem. Since the gap between the upper and the lower bound 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 FIR FF-BF filters are sufficiently long.

FIR Beamforming for Frequency-Selective Channels with Linear Equalization

In this letter, we consider transmit beamforming with finite impulse response (FIR) filters for frequency-selective channels and simple linear equalization at the receiver. Since a closed-form solution for the optimum FIR beamforming filters (BFFs) does not seem to exist, an efficient numerical method for their recursive calculation is developed. Our numerical results show that for typical GSM/EDGE channels short FIR BFFs can closely approach the performance of the optimum infinite impulse response (IIR) BFFs derived in [1] and yield significant gains over single-antenna transmission.

Cooperative Filter-and-Forward Beamforming with Linear Equalization

In this paper, we investigate filter--and--forward beamforming (FF--BF) for relay networks employing single--carrier transmission over frequency--selective channels. In contrast to prior work, we assume that the destination node is equipped with a simple linear equalizer. The FF--BF filters at the relays are optimized for maximization of the signal--to--noise ratio at the equalizer output under a joint relay power constraint. For infinite impulse response (IIR) FF--BF filters, we derive a closed--form expression for the filter frequency response, and a numerical algorithm with guaranteed convergence is developed for optimization of the power allocation factor included in the expression. We also provide an efficient gradient algorithm for recursive calculation of near--optimal finite impulse response (FIR) FF--BF filters. Simulation results show that, in general, short FIR FF--BF filters are sufficient to closely approach the performance of IIR FF--BF filters even in severely frequency--selective channels and that the proposed FF--BF scheme with equalization at the destination achieves substantial performance gains compared to a previously proposed FF--BF scheme without equalization.

Minimum BER Transmit Beamforming for MIMO-OFDM Systems with Finite Rate Feedback

In this paper, we consider minimum bit error rate (BER) beamforming (BF) for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. In particular, assuming perfect channel state information (CSI) at the transmitter we optimize cyclic BF filters (C-BFFs) for minimization of the average BER and the maximum sub-carrier BER, respectively. If the C-BFF length Lg is equal to the number of sub-carriers Nc, closed-form solutions to both optimization problems exist. For the practically relevant case Lg < Nc we present numerical methods for calculation of the optimum C-BFFs. For finite-rate feedback channels we provide a global vector quantization (GVQ) scheme for codebook design. Simulation results for typical IEEE 802.11n channels confirm the excellent performance of the proposed minimum BER BF schemes for both uncoded and coded MIMO-OFDM systems.

Transmit Beamforming for Frequency-Selective Channels

In this paper, we propose beamforming schemes for frequency-selective channels with decision-feedback equalization (DFE) at the receiver. We consider both finite impulse response (FIR) and infinite impulse response (IIR) beamforming filters (BFFs). In case of IIR beamforming, we are able to derive closed-form expressions for the optimum BFFs. In addition, we provide an efficient numerical method for recursive calculation of the optimum FIR BFFs. Simulation and numerical results for typical GSM/EDGE channels confirm the significant performance gains achievable with beamforming compared to single-antenna transmission and optimized delay diversity.