Yiyue Wu

Code diversity in multiple antenna wireless communication

The standard approach to the design of individual space-time codes is based on optimizing diversity and coding gain. This geometric approach leads to remarkable examples, such as the Golden Code, for which the complexity of maximum likelihood (ML) decoding is considerable. Code diversity is an alternative approach where a small number of feedback bits are used to select from a family of space-time codes. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match ML decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. One method of implementing code diversity is the use of feedback to adapt the phase of a transmitted signal. Phase adaptation with the 4times4 quasi-orthogonal space-time code (QOSTBC) is shown to be almost information lossless; that is, this form of space-time coding does not reduce the capacity of the underlying multiple antenna wireless channel. Code diversity can also be used to improve performance of multi-user detection by reducing interference between users. Phase adaptation with two Alamouti users makes it possible for the zero forcing (ZF) or decorrelating detector to match the performance of ML joint detection.

Highly parallel decoding of space-time codes on graphics processing units

Graphics Processing Units (GPUs) with a few hundred extremely simple processors represent a paradigm shift for highly parallel computations. We use this emergent GPU architecture to provide a first demonstration of the feasibility of real time ML decoding (in software) of a high rate space-time block code that is representative of codes incorporated in 4th generation wireless standards such as WiMAX and LTE. The decoding algorithm is conditional optimization which reduces to a parallel calculation that is a natural fit to the architecture of low cost GPUs. Experimental results demonstrate that asymptotically the GPU implementation is more than 700 times faster than a standard serial implementation. These results suggest that GPU architectures have the potential to improve the cost / performance tradeoff of 4th generation wireless base stations. Additional benefits might include reducing the time required for system development and the time required for configuration and testing of wireless base stations.

On the capacity of the discrete-time channel with uniform output quantization

This paper provides new insight into the classical problem of determining both the capacity of the discrete-time channel with uniform output quantization and the capacity achieving input distribution. It builds on earlier work by Gallager and Witsenhausen to provide a detailed analysis of two particular quantization schemes. The first is saturation quantization where overflows are mapped to the nearest quantization bin, and the second is modulo quantization where overflows are mapped to the nearest quantization bin after reduction by some modulus. Both the capacity of modulo quantization and the capacity achieving input distribution are determined. When the additive noise is gaussian and relatively small, the capacity of saturation quantization is shown to be bounded below by that of modulo quantization. In the limit of arbitrarily many uniform quantization levels, it is shown that the difference between the upper and lower bounds on capacity given by Ihara is only 0.26 bits.

Compressive blind source separation

The central goal of compressive sensing is to reconstruct a signal that is sparse or compressible in some basis using very few measurements. However reconstruction is often not the ultimate goal and it is of considerable interest to be able to deduce attributes of the signal from the measurements without explicitly reconstructing the full signal. This paper solves the blind source separation problem not in the high dimensional data domain, but in the low dimensional measurement domain. It develops a Bayesian inference framework that integrates hidden Markov models for sources with compressive measurement. Posterior probabilities are calculated using a Markov Chain Monte Carlo (MCMC) algorithm. Simulation results are provided for one-dimensional signals and for two-dimensional images, where hidden Markov tree models of the wavelet coefficients are considered. The integrated Bayesian framework is shown to outperform standard approaches where the mixtures are separated in the data domain.

Circulant space-time codes for integration with beamforming

This paper provides a framework for designing space-time codes to take advantage of a small number of feedback bits from the receiver. The new codes are based on circulant matrices and simple conditions are derived that guarantee full rate and full diversity. In the absence of feedback, Symbol Error Rate (SER) performance is shown to be similar to that of Diagonal Algebraic Space-Time (DAST) codes, both for Maximum Likelihood (ML) decoding and for suboptimal linear decoding. Decoding complexity of circulant codes is similar to the DAST codes and encoding is slightly less complex. In the presence of a small number of feedback bits from the receiver the circulant construction is shown to permit integration of space-time coding with a fixed set of beams by simply advancing the phase on one of the antennas. This integration is not possible within the DAST framework. Integration of space-time codes with beamforming makes it possible to achieve ML decoding performance with only linear decoding complexity or to improve upon ML performance of the original code.

Construction of High Rate Super-Orthogonal Space-Time Block Codes

It is standard practice to integrate outer trellis codes with inner space-time block codes to increase coding gain, but the drawback is a decrease in rate. Jafarkhani and Seshadri [1] have introduced an alternative method of combining multiple inner othogonal space-time codes with outer trellis codes that both preserves rate and increases coding gain. However their work is limited to orthogonal codes, for which the achievable rate is typically low. This paper presents a method of achieving higher transmission rates by integrating higher rate non-orthogonal space with outer trellis codes, and new methods are introduced to avoid catastrophic codes. The method is presented with reference to the particular example of the Silver Code, but it applies to all multiplexed orthogonal designs and to more general codes.

On optimal precoding in wireless multicast systems

Precoding has been extensively studied for point-to-point communications, including the problems of constructing the precoding codebook and selecting the best precoder. This paper investigates precoding for a multicast channel in which a base station is sending the same information to all users and each user sends back the index of its best precoding matrix. It is assumed that users do not collaborate and that no channel state information is known at the base station. Optimization problems are formulated to reduce the packet drop rate. A set of probabilistic algorithms that effectively reduce the average package drop rate are presented. It is shown numerically that these new schemes lead to significant improvements.

Regularized blind detection for MIMO communications

Multiple-Input Multiple-Output (MIMO) systems improve the throughput and reliability of wireless communications. Perfect Channel State Information (CSI) is needed at the receiver to perform coherent detection and achieve the optimal gain of the system. In fast fading and low SNR regimes, it is hard or impossible to obtain perfect CSI, which leads the receiver to operate without knowledge of the CSI and perform blind detection. In reality CSI may be available to the receiver but this CSI may be insufficient to support coherent detection. In this paper, we fill the gap between coherent and blind detection by considering a more realistic model where the receiver knows the statistics of the channel, that is Channel Distribution Information (CDI). We propose a new detection algorithm, called Regularized Blind Detection (RBD), where coherent and blind detection can be viewed as special cases in our model. The algorithm estimates CDI from any training symbols that are available and maximizes performance given the estimated CDI. Simulations demonstrate significant improvement in performance over blind detection. Our work can be viewed as a systematic exploration of space between coherent and blind detection with a strong Bayesian statistic flavor.

Enabling Code Diversity for Mobile Radio Channels using Long-Range Fading Prediction

Code diversity integrates space-time coding with beamforming by using a small number of feedback bits to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where Channel State Information (CSI) is used to instruct the transmitter how to choose the code. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match Maximum-Likelihood (ML) decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. Prior analysis of code diversity did not take into account the effect of the mobile speed and the delay in the feedback channel. This paper demonstrates the practicality of code diversity in space-time coded systems by showing that performance gains based on instantaneous feedback are largely preserved when long-range prediction of time-varying correlated fading channels is employed to compensate for the effect of the feedback delay. To maintain prediction accuracy for realistic SNR, noise reduction that employs oversampled pilots is used prior to fading prediction. We also propose a robust low pilot rate method that utilizes interleaving to improve the spectral efficiency. Simulations are presented for two channel models: the conventional Jakes model and a realistic physical channel model where the parameters associated with the reflectors vary in time and the arrival rays have different strengths and asymmetric arrival angles.

On the Effect of Feedback Delay on Limited-Rate Beamforming Systems

The use of beamforming to enable higher data rates in telecommunications is widely appreciated, but performance gains are typically calculated assuming delay-free feedback from the receiver and neglecting processing time. This paper introduces a mathematical framework based on outage probability that measures the extent to which current channel state information is accurate. Performance gains from beamforming can then be evaluated as a function of the currency of system state. Results are provided for Multiple Input Single Output (MISO) and for Multiuser Multiple Input Multiple Output (MU-MIMO) systems. Outage probabilities and effective diversity orders are calculated for widely used methods of beamforming such as Transmit Antenna Selection as a function of the speed of channel variation.