Pawel A. Dmochowski

The Effects of Limited Channel Knowledge on Cognitive Radio System Capacity

We examine the impact of limited channel knowledge on the secondary user (SU) in a cognitive radio system. Under a minimum signal-to-interference noise ratio (SINR) constraint for the primary user (PU) receiver, we determine the SU capacity under five channel knowledge scenarios. We derive analytical expressions for the capacity cumulative distribution functions and the probability of SU blocking as a function of allowable interference. We show that imperfect knowledge of the PU-PU link gain by the SU-Tx often prohibits SU transmission or necessitates a high interference level at the PU. We also show that errored knowledge of the PU-PU channel is more beneficial than statistical channel knowledge and that imperfect knowledge of the SU-Tx to PU-Rx link has limited impact on SU capacity.

Interference and Deployment Issues for Cognitive Radio Systems in Shadowing Environments

In this paper we describe a model for calculating the aggregate interference encountered by primary receivers in the presence of randomly placed cognitive radios (CRs). We show that incorporating the impact of distance attenuation and lognormal fading on each constituent interferer in the aggregate, leads to a composite interference that cannot be satisfactorily modeled by a lognormal. Using the interference statistics we determine a number of key parameters needed for the deployment of CRs. Examples of these are the exclusion zone radius, needed to protect the primary receiver under different types of fading environments and acceptable interference levels, and the numbers of CRs that can be deployed. We further show that if the CRs have apriori knowledge of the radio environment map (REM), then a much larger number of CRs can be deployed especially in a high density environment. Given REM information, we also look at the CR numbers achieved by two different types of techniques to process the scheduling information.

Frequency domain equalization for high data rate multipath channels

High data rate transmission over multipath channels requires equalizers of long impulse response. In such cases, frequency domain implementation of the block least mean square (BLMS) algorithm offers low complexity growth relative to time domain techniques. The work presented herein is devoted to a study of the fast BLMS (FBLMS) algorithm implemented in the frequency domain using overlap-save sectioning and the fast Fourier transform (FFT). We examine the bit error rate (BER) performance for high data rate quadrature phase shift keying (QPSK) transmission over a multipath channel as well as the computational complexity of the FBLMS equalizer in comparison to the time domain implementation. Finally, we show how normalizing the step size of the FBLMS algorithm according to the power distribution of the input process results in a significant improvement in the equalizer convergence relative to the time domain methods.

Analysis of the M/M/N/N Queue with Two Types of Arrival Process: Applications to Future Mobile Radio Systems

The queueing system considered is essentially a M/M/N/N queue where two types of users compete for the resources. The users may have different arrival and service rates and are denoted as primary or secondary users. The primary users have priority access to the resources, and three levels of priority are considered: perfect priority, partial priority, and no priority. This system models the recently developed cognitive radio concept, a methodology that has been proposed for future mobile radio systems. In this context, the primary users have certain rights to use the resources, whereas the secondary users must make opportunistic use of the resources without impacting too much on the performance of the primary users. For all priority settings, the mean number of primary and secondary users is derived as are the blocking probabilities for both users. When no priority is given to the primary user, the system collapses to a truncated form of two independent M/M/∞ queues. The product form solution for this special case is known, and, here, these results are given in a novel, compact form. In the case of nonzero priority, the dropping probability for the secondary users is also derived.

Precoding Performance with Codebook Feedback in a MIMO-OFDM System

Limited feedback precoding is part of the LTE standard. Despite standardization, important fundamental questions, especially relating to the performance due to the use of codebooks and receiver processing techniques, remain to be explored. In order to understand these questions, we consider a single user in a single cell employing single or multi-stream transmission using a variety of codebooks and a choice of different receiver types. We derive expressions for capacity loss relative to perfect feedback due to the limited size of codebook. When multistream transmission is deployed, we show that codebook feedback manifests itself as inter-stream interference resulting in a capacity loss for all receiver types. In the case of SVD receivers, this interference results in a capacity floor. We define a precoding matrix index (PMI) coherence time and bandwidth and show how these parameters are respectively related to channel coherence time and bandwidth. The PMI coherence parameters shed new light on how often feedback is required, both in time and frequency domains, and help us to determine the capacity penalty if feedback is delayed beyond the coherence parameters. Finally, we show the distribution of PMI and also show that this is environment dependent. This supports the need for codebooks that are adaptable to different environments and are not strictly tied to i.i.d. channels.

Impact of Channel Knowledge on Cognitive Radio System Capacity

We examine the impact of channel knowledge on the secondary user (SU) in a cognitive radio system. Under a minimum signal-to-interference-and-noise ratio (SINR) constraint for the primary user (PU) receiver, we determine the SU capacity under four channel knowledge scenarios. We derive analytical expressions for the capacity cumulative distribution functions which are verified by means of simulations. We show that the lack of exact knowledge of the PU-PU channel gain by the SU-Tx either prohibits SU transmission or necessitates high interference level at the PU. We also show that the lack of exact knowledge of the SU-Tx to PU-Rx link has little or no impact on SU capacity.

On the convergence of massive MIMO systems

In this paper we examine convergence properties of massive MIMO systems with the aim of determining the number of antennas required for massive MIMO gains. We consider three characteristics of a channel matrix and study their asymptotic behaviour. Furthermore, we derive ZF SNR and MF SINR for a scenario of unequal receive powers. In our results we include the effects of spatial correlation. We show that the rate of convergence of channel metrics is much slower than that of the ZF/MF precoder properties.

On the impact of antenna topologies for massive MIMO systems

Approximate expressions for the spatial correlation of cylindrical and uniform rectangular arrays (URA) are derived using measured distributions of angles of departure (AOD) for both the azimuth and zenith domains. We examine massive multiple-input-multiple-output (MIMO) convergence properties of the correlated channels by considering a number of convergence metrics. The per-user matched filter (MF) signal-to-interference-plus-noise ratio (SINR) performance and convergence rate, to respective limiting values, of the two antenna topologies is also explored.

Robust timing epoch tracking for Alamouti space-time coding in flat Rayleigh fading MIMO channels

We propose a very low complexity timing error detector for n/sub T/ = 2 orthogonal space-time block coded M-PSK systems with an arbitrary number of receive antennas. The algorithm uses maximum-likelihood detection variables to estimate the timing error by examining the difference in threshold crossings, similarly to the Mueller and Muller detector. We show that the timing error estimation is independent of the channel state, thus making it very robust in poor channel conditions. The decision directed version of the detector is used to evaluate the tracking performance for BPSK and QPSK signaling in 1-, 2- and 4-receive antenna systems. Symbol error rate as well as mean square estimation error results are presented. We examine the performance as a function of the timing drift and show that the receiver is able to maintain lock up to a normalized timing bandwidth of B/sub T/T = 0.001. Complete channel state estimation is assumed throughout the paper.

Parametric Channel Prediction for Narrowband Mobile MIMO Systems Using Spatio-Temporal Correlation Analysis

In this paper, we propose an ESPRIT-based parametric prediction scheme for narrowband MIMO systems that fully exploits both temporal and spatial correlations in realistic MIMO channels. The proposed predictor uses a vector transmit spatial signature model and two-dimensional ESPRIT for the estimation of the channel parameters. The proposed scheme outperforms existing algorithms and is well suited to both two dimensional azimuth only and three dimensional MIMO spatial channel models.