Niranjay Ravindran

Multiuser MIMO Achievable Rates With Downlink Training and Channel State Feedback

In this paper, we consider a multiple-input-multiple-output (MIMO) fading broadcast channel and compute achievable ergodic rates when channel state information (CSI) is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback schemes are analyzed and compared under various assumptions. Digital feedback is shown to be potentially superior when the feedback channel uses per channel state coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even if simple uncoded modulation is used on the feedback channel. We discuss first the case of an unfaded additive white Gaussian noise (AWGN) feedback channel with orthogonal access and then the case of fading MIMO multiple access (MIMO-MAC). We show that by exploiting the MIMO-MAC nature of the uplink channel, a much better scaling of the feedback channel resource with the number of base station (BS) antennas can be achieved. Finally, for the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ¿ F < 1/2, a fraction 1 - 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.In this paper, we consider a multiple-input-multiple-output (MIMO) fading broadcast channel and compute achievable ergodic rates when channel state information (CSI) is acquired at the receivers vi...

Limited feedback-based block diagonalization for the MIMO broadcast channel

Block diagonalization is a linear preceding technique for the multiple antenna broadcast (downlink) channel that involves transmission of multiple data streams to each receiver such that no multi-user interference is experienced at any of the receivers. This low-complexity scheme operates only a few dB away from capacity but requires very accurate channel knowledge at the transmitter. We consider a limited feedback system where each receiver knows its channel perfectly, but the transmitter is only provided with a finite number of channel feedback bits from each receiver. Using a random quantization argument, we quantify the throughput loss due to imperfect channel knowledge as a function of the feedback level. The quality of channel knowledge must improve proportional to the SNR in order to prevent interference-limitations, and we show that scaling the number of feedback bits linearly with the system SNR is sufficient to maintain a bounded rate loss. Finally, we compare our quantization strategy to an analog feedback scheme and show the superiority of quantized feedback.

SPLATT: Efficient and Parallel Sparse Tensor-Matrix Multiplication

Multi-dimensional arrays, or tensors, are increasingly found in fields such as signal processing and recommender systems. Real-world tensors can be enormous in size and often very sparse. There is a need for efficient, high-performance tools capable of processing the massive sparse tensors of today and the future. This paper introduces SPLATT, a C library with shared-memory parallelism for three-mode tensors. SPLATT contains algorithmic improvements over competing state of the art tools for sparse tensor factorization. SPLATT has a fast, parallel method of multiplying a matricide tensor by a Khatri-Rao product, which is a key kernel in tensor factorization methods. SPLATT uses a novel data structure that exploits the sparsity patterns of tensors. This data structure has a small memory footprint similar to competing methods and allows for the computational improvements featured in our work. We also present a method of finding cache-friendly reordering and utilizing them with a novel form of cache tiling. To our knowledge, this is the first work to investigate reordering and cache tiling in this context. SPLATT averages almost 30x speedup compared to our baseline when using 16 threads and reaches over 80x speedup on NELL-2.

Multi-User Diversity vs. Accurate Channel State Information in MIMO Downlink Channels

In a multiple transmit antenna, single antenna per receiver downlink channel with limited channel state feedback, we consider the following question: given a constraint on the total system-wide feedback load, is it preferable to get low-rate/coarse channel feedback from a large number of receivers or high-rate/high-quality feedback from a smaller number of receivers? Acquiring feedback from many receivers allows multi-user diversity to be exploited, while high-rate feedback allows for very precise selection of beamforming directions. We show that there is a strong preference for obtaining high-quality feedback, and that obtaining near-perfect channel information from as many receivers as possible provides a significantly larger sum rate than collecting a few feedback bits from a large number of users. In terms of system design, this corresponds to a preference for acquiring high-quality feedback from a few users on each time-frequency resource block, as opposed to coarse feedback from many users on each block.

Multi-User Diversity vs. Accurate Channel Feedback for MIMO Broadcast Channels

A multiple transmit antenna, single receive antenna (per receiver) downlink channel with limited channel feedback is considered. Given a constraint on the total system-wide channel feedback, the following question is considered: is it preferable to get low-rate feedback from a large number of receivers or to receive high-rate/high-quality feedback from a smaller number of (randomly selected) receivers? Acquiring feedback from many users allows multi-user diversity to be exploited, while high- rate feedback allows for very precise selection of beamforming directions. It is shown that systems in which a limited number of users feedback high-rate channel information significantly outperform low-rate/many user systems. While capacity increases only double logarithmically with the number of users, the marginal benefit of channel feedback is very significant up to the point where the CSI is essentially perfect.

MIMO Broadcast Channels with Block Diagonalization and Finite Rate Feedback

Block diagonalization is a linear precoding technique for the multiple antenna broadcast (downlink) channel that involves transmission of multiple data streams to each receiver such that no multi-user interference is experienced at any of the receivers. This low-complexity scheme operates only a few dB away from capacity but does require very accurate channel knowledge at the transmitter, which can be very difficult to obtain in fading scenarios. We consider a limited feedback system where each receiver knows its channel perfectly, but the transmitter is only provided with a finite number of channel feedback bits from each receiver. Using a random vector quantization argument, we quantify the throughput loss due to imperfect channel knowledge as a function of the feedback level. The quality of channel knowledge must improve proportional to the SNR in order to prevent interference-limitations, and we show that scaling the number of feedback bits linearly with the system SNR is sufficient to maintain a bounded rate loss. Finally, we investigate a simple scalar quantization scheme that is seen to achieve the same scaling behavior as vector quantization.

Memory-efficient parallel computation of tensor and matrix products for big tensor decomposition

Low-rank tensor decomposition has many applications in signal processing and machine learning, and is becoming increasingly important for analyzing big data. A significant challenge is the computation of intermediate products which can be much larger than the final result of the computation, or even the original tensor. We propose a scheme that allows memory-efficient in-place updates of intermediate matrices. Motivated by recent advances in big tensor decomposition from multiple compressed replicas, we also consider the related problem of memory-efficient tensor compression. The resulting algorithms can be parallelized, and can exploit but do not require sparsity.

Achievable Throughput of MIMO Downlink Beamforming with Limited Channel Information

We consider a MIMO fading broadcast channel and study the achievable throughput of zero-forcing downlink beamforming when the channel state information (CSI) available to the transmitter and/or receivers is imperfect. Each receiver (mobile) acquires imperfect CSI via downlink training pilots, and the transmitter acquires CSI through explicit feedback from each mobile. We analyze both analog and digital (i.e., quantized) channel feedback techniques. Our analysis quantifies the throughput degradation due to limited training, limited feedback resources (measured in feedback channel symbols rather than bits), and errors on the feedback channel. Using these results we are able to quantify scenarios in which digital feedback outperforms analog and also provide guidelines for the optimal allocation of resources to training and channel feedback.

Interactive volume visualization of fluid flow simulation data

Recent development work at the Laboratory for Computational Science & Engineering (LCSE) at the University of Minnesota aimed at increasing the performance of parallel volume rendering of large fluid dynamics simulation data is reported. The goal of the work is interactive visual exploration of data sets that are up to two terabytes in size. A key system design feature in accelerating the rendering performance from such large data sets is replication of the data set on directly attached parallel disk systems at each rendering node. Adaptation of this system for interactive steering and visualization of fluid flow simulations as they run on remote supercomputer systems introduces special additional challenges which will briefly be described.

Optimized multi-antenna communication in ad-hoc networks with opportunistic routing

We consider the problem of using multiple antennas to maximize end-to-end performance in a multi-hop ad hoc wireless network with opportunistic routing. We find that when a single data stream is sent per hop, performance is maximized by aggressively increasing spatial reuse, as opposed to increasing per-hop length or rate. We also show that using spatial multiplexing to transmit multiple streams per hop results in a linear increase in performance with antennas, even with fixed spatial reuse, and is generally superior to sending only a single stream.