Low-rate Feedback Link Research Articles

A Random Search Framework for Convergence Analysis of Distributed Beamforming With Feedback

The focus of this work is on the analysis of transmit beamforming schemes with a low-rate feedback link in wireless sensor/relay networks, where nodes in the network need to implement beamforming in a distributed manner. Specifically, the problem of distributed phase alignment is considered, where neither the transmitters nor the receiver has perfect channel state information, but there is a low-rate feedback link from the receiver to the transmitters. In this setting, a framework is proposed for systematically analyzing the performance of distributed beamforming schemes. To illustrate the advantage of this framework, a simple adaptive distributed beamforming scheme that was recently proposed by Mudambai et al. is studied. Two important properties of the received signal magnitude function are derived. Using these properties and the systematic framework, it is shown that the adaptive distributed beamforming scheme converges both in probability and in mean. Furthermore, it is established that the time required for the adaptive scheme to converge in mean scales linearly with respect to the number of sensor/relay nodes.

To Code in Space and Time or Not in Multihop Relay Channels

Multihop relay channels use multiple relay stages, each with multiple relay nodes, to facilitate communication between a source and destination. Previously, distributed space-time coding was used to maximize diversity gain. Assuming a low-rate feedback link from the destination to each relay stage and the source, this paper proposes end-to-end antenna selection strategies as an alternative to distributed space-time coding. One-way (where only the source has data for destination) and two-way (where the destination also has data for the source) multihop relay channels are considered with both the full-duplex and half-duplex relay nodes. For the full-duplex case, end-to-end antenna selection strategies are designed and proven to achieve maximum diversity gain by using a single-antenna path (using single antenna of the source, each relay stage and the destination) with the maximum signal-to-noise ratio at the destination. For the half-duplex case, two paths with the two best signal-to-noise ratios in alternate time slots are used to overcome the rate loss with half-duplex nodes, with a small diversity gain penalty. A multiple stream end-to-end antenna selection strategy for full-duplex multihop relay channel is also proposed to obtain a lower bound on the diversity multiplexing tradeoff of multihop relay channels. Finally, to answer the question of whether to code in space and time or not in a multihop relay channel, end-to-end antenna selection strategy and distributed space-time coding is compared with respect to several important performance metrics such as encoding/decoding complexity, rate of transmission, latency, bit-error-rate performance, and resource requirements.

End-to-End Joint Antenna Selection Strategy and Distributed Compress and Forward Strategy for Relay Channels

Multihop relay channels use multiple relay stages, each with multiple relay nodes, to facilitate communication between a source and destination. Previously, distributed space-time codes were proposed to maximize the achievable diversity-multiplexing tradeoff; however, they fail to achieve all the points of the optimal diversity-multiplexing tradeoff. In the presence of a low-rate feedback link from the destination to each relay stage and the source, this paper proposes an end-to-end antenna selection (EEAS) strategy as an alternative to distributed space-time codes. The EEAS strategy uses a subset of antennas of each relay stage for transmission of the source signal to the destination with amplifying and forwarding at each relay stage. The subsets are chosen such that they maximize the end-to-end mutual information at the destination. The EEAS strategy achieves the corner points of the optimal diversity-multiplexing tradeoff (corresponding to maximum diversity gain and maximum multiplexing gain) and achieves better diversity gain at intermediate values of multiplexing gain, versus the best-known distributed space-time coding strategies. A distributed compress and forward (CF) strategy is also proposed to achieve all points of the optimal diversity-multiplexing tradeoff for a two-hop relay channel with multiple relay nodes.

Quantized Multimode Precoding in Spatially Correlated Multiantenna Channels

Multimode precoding, where the number of independent data-streams is adapted optimally, can be used to maximize the achievable throughput in multi-antenna communication systems. Motivated by standardization efforts embraced by the industry, the focus of this work is on systematic precoder design with realistic assumptions on the spatial correlation, channel state information (CSI) at the transmitter and the receiver, and implementation complexity. For spatial correlation of the channel matrix, we assume a general channel model, based on physical principles, that has been verified by many recent measurement campaigns. We also assume a coherent receiver and knowledge of the spatial statistics at the transmitter along with the presence of an ideal, low-rate feedback link from the receiver to the transmitter. The reverse link is used for codebook-index feedback and the goal of this work is to construct precoder codebooks, adaptable in response to the statistical information, such that the achievable throughput is significantly enhanced over that of a fixed, non-adaptive, i.i.d. codebook design. We illustrate how a codebook of semiunitary precoder matrices localized around some fixed center on the Grassmann manifold can be skewed in response to the spatial correlation via low-complexity maps that can rotate and scale submanifolds on the Grassmann manifold. The skewed codebook in combination with a lowcomplexity statistical power allocation scheme is then shown to bridge the gap in performance between a perfect CSI benchmark and an i.i.d. codebook design.

Interpolation-Based Multi-Mode Precoding for MIMO-OFDM Systems with Limited Feedback

Spatial multiplexing with multi-mode precoding provides a means to achieve both high capacity and high reliability in multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. Multi-mode precoding uses linear transmit precoding that adapts the number of spatial multiplexing data streams or modes, according to the transmit channel state information (CSI). As such, it typically requires complete knowledge of the multi-mode precoding matrices for each subcarrier at the transmitter. In practical scenarios where the CSI is acquired at the receiver and fed back to the transmitter through a low-rate feedback link, this requirement may entail a prohibitive feedback overhead. In this paper, we propose to reduce the feedback requirement by combining codebook-based precoder quantization, to efficiently quantize and represent the optimal precoder on each subcarrier, and multi-mode precoder frequency down-sampling and interpolation, to efficiently reconstruct the precoding matrices on all subcarriers based on the feedback of the indexes of the quantized precoders only on a fraction of the subcarriers. To enable this efficient interpolation-based quantized multimode precoding solution, we introduce (1) a novel precoder codebook design that lends itself to precoder interpolation, across subcarriers, followed by mode selection, (2) a new precoder interpolator and, finally, (3) a clustered mode selection approach that significantly reduces the feedback overhead related to the mode information on each subcarrier. Monte-Carlo bit-error rate (BER) performance simulations demonstrate the effectiveness of the proposed quantized multi-mode precoding solution, at reasonable feedback overhead