Christopher Pladdy

Best linear unbiased channel estimation for frequency selective multipath channels with long delay spreads

We provide an iterative channel impulse response (CIR) estimation algorithm for communication systems which utilize a periodically transmitted training sequence within a continuous stream of information symbols. This iterative procedure calculates the (semi-blind) best linear unbiased estimate (BLUE) of the CIR. We first provide a formulation of the received data and correlation processing with the adjacent information symbol correlation taken into account, and we then present the connections of the correlation based CIR estimation scheme to the ordinary least squares CIR estimation. Simulation results are provided to demonstrate the performance of the novel algorithm.

Approximate best linear unbiased channel estimation for frequency selective multipath channels with long delay spreads

We provide an iterative and a non-iterative channel impulse response (CIR) estimation algorithm for communication systems which utilize a periodically transmitted training sequence within a continuous stream of information symbols. The iterative procedure calculates the (semi-blind) best linear unbiased estimate (BLUE) of the CIR. The non-iterative version is an approximation to the BLUE CIR estimate, achieving almost similar performance, with much lower complexity. We first provide a formulation of the received data and correlation processing with the adjacent symbol correlation taken into account, and we then present the connections of the correlation based CIR estimation scheme to the ordinary least squares CIR estimation, and the BLUE CIR estimation. Simulation results are provided to demonstrate the performance of the novel algorithms for 8-VSB ATSC digital TV systems.

Taylor series approximation of semi-blind best linear unbiased channel estimates for the general linear model

We present a low complexity approximate method for semi-blind best linear unbiased estimation (BLUE) of a channel impulse response vector (CIR) for a communication system, which utilizes a periodically transmitted training sequence, within a continuous stream of information symbols. The algorithm achieves slightly degraded results at a much lower complexity than directly computing the BLUE CIR estimate. In addition, the inverse matrix required inverting the weighted normal equations to solve the general least squares problem may be pre-computed and stored at the receiver. The BLUE estimate is obtained by solving the general linear model. The Gauss-Markoff theorem gives the solution in this paper. In the present work we propose a Taylor series approximation in which the full Taylor formula is described. The algorithms give better performance than correlation channel estimates and previous approximations used, (S. Ozen et al., Nov. 2003), at only a slight increase in complexity. The linearization procedure used is similar to that used in the linearization to obtain the extended Kalman filter, and the higher order approximations are similar to those used in obtaining higher order Kalman filter approximations, (A. Gelb et al., 1974).

Iterative Semi-Blind Blue Estimation of Channel State Information for the Asynchronous GMAC with Memory

In this paper we propose an iterative algorithm for estimating the semi-blind BLUE of the channel impulse response with respect to each source transmitter in an asynchronous scalar Gaussian multiple access channel (GMAC) with complex-valued intersymbol interference (ISI). We examine the case for the two-user GMAC where user 1s training arrives during the data portion of user 2. We demonstrate the algorithm with simulation results and contrast these results with other known channel estimation techniques such as correlation and least squares. We prove convergence of the algorithm under certain conditions for which we can realize the iterations as separate contraction mappings. We also give approximate versions of the algorithms which are more suited to real time applications.

Joint data detection and channel estimation for two dominant users in the asynchronous GMAC with memory

In this paper we consider the situation of two strongly interfering signals, superimposed over a background of AWGN. We consider the situation where User 2psilas packet arrives initially and we are able to estimate accurately this userpsilas channel impulse response. Then a packet from User 1 arrives during the data portion of User 2psilas packet. We propose an algorithm for simultaneously estimating the channel impulse response (CIR) of User 2 and detecting the data of User 1, i.e. joint data detection and channel estimation for two dominant users in the asynchronous scalar Gaussian multiple access channel (GMAC) with complex-valued intersymbol interference (ISI). This approach proves to be useful for reestimation of User 2psilas CIR, after cancellation of interference from User 1. We demonstrate the algorithm with simulation results. We give an extension of the algorithm where the estimate of User 1psilas data is used for interference cancellation to refine the estimate of User 2psilas channel. In simulations, this is shown to improve the channel estimate. We also give reduced rank approximations of the algorithm, using the conjugate gradient method, which are more suited to real time applications and which implement noise-reduction for an over-modeled system.

Taylor series approximation of semi-blind BLUE channel estimates with applications to DTV

We present a low-complexity method for approximating the semi-blind best linear unbiased estimate (BLUE) of a channel impulse response (CIR) vector for a communication system, which utilizes a periodically transmitted training sequence. The BLUE, for h, for the general linear model, y = Ah + w + n, where w is correlated noise (dependent on the CIR, h) and the vector n is an Additive White Gaussian Noise (AWGN) process, which is uncorrelated with w is given by h = (ATC(h)−1 A)−1 ATC(h)−1 y. In the present work, we propose a Taylor series approximation for the function F(h) = (ATC(h)−1 A)−1 ATC(h)−1 y. We describe the full Taylor formula for this function and describe algorithms using, first-, second-, and third-order approximations, respectively. The algorithms give better performance than correlation channel estimates and previous approximations used, at only a slight increase in complexity. Our algorithm is derived and works within the framework imposed by the ATSC 8-VSB DTV transmission system, but will generalize to any communication system utilizing a training sequence embedded within data.

Hybrid GBAR/Nonlinear Time-Series Method for Generation of Synthetic VBR Video Traffic

Linear analysis of a data set examines any evident structure in the data through linear correlations and implicitly assumes that any dynamics of the system are modeled linearly, where small perturbations of initial conditions lead to small changes in the unfolding dynamics. Linear analysis attributes all irregular behavior of the system to stochastic external excitation of the system. However, stochastic excitation of linear equations is not the only source of irregularity in the output of a system. For nonlinear chaotic systems, irregular outputs can be produced from deterministic equations of motion in an autonomous manner; that is with time-independent inputs. We use methods from nonlinear time series to generate synthetic VBR video data. We propose a hybrid algorithm which combines methods from nonlinear time-series analysis to produce downsampled VBR data at the relevant time scale and interpolates between this downsampled data by using the GBAR model for synthetic VBR video data. We contrast this hybrid method with the purely stochastic GBAR method and with a purely deterministic nonlinear time-series method, using both H.263 and MPEG4 data. We compare pdfs and autocorrelation functions of the synthetic and true data. For MPEG4 data the characterisitc autocorrelation structure, present due to GOP coding, is reproduced well by the nonlinear deterministic algorithm. Such synthetic VBR video data are useful in many different aspects of performance evaluation and resource allocation for networks.

Constrained DFEs for Reduced Error Propagation: Theoretical Results and an Adaptive Soft Error Variance Controlled DFE

The problem of error propagation in a decision feedback equalizer (DFE) is acknowledged to be an important factor in the functioning of the equalizer. In order to determine conditions which guarantee the non-propagation of errors we formulate the DFE as a dynamical system in the form of a matrix equation. We analyze the propagation of errors in this matrix system and formulate conditions on the system matrices which guarantee: a) Using deterministic analysis, the non-propagation of errors; b) Using a stochastic analysis, the non-propagation of the expected value of the norm of the hard error vector. These conditions translate into constraints on the size of the feedback tap-weights so that there is linear convergence of the errors (or of expected values of norms of errors for the stochastic analysis) with constant C<1. This is equivalent to exponential decay of the hard errors (or of expected values of norms of errors for the stochastic analysis) over time with decay constant C<1. This ensures that errors do not propagate, but decay exponentially with time. The stochastic analysis gives weaker constraints which may be of more practical use in filter design, as the deterministic constraint guards against a worst case scenario for error propagation. The constraints derived in the stochastic case also combine the variance of the soft errors. Hence feedback of soft error variance may be used to adapt the constraint used on the feedback filter, and this motivates an algorithm for a soft error variance controlled adaptive DFE

Approximate best linear unbiased channel estimation for frequency selective channels with long delay spreads: robustness to timing and carrier offsets

We provide an iterative and a non-iterative channel impulse response (CIR) estimation algorithm for communication systems which utilize a periodically transmitted training sequence within a continuous stream of information symbols. The iterative procedure calculates the (semi-blind) best linear unbiased estimate (BLUE) of the CIR. The non-iterative version is an approximation to the BLUE CIR estimate, denoted by a-BLUE, achieving almost similar performance, with much lower complexity. Indeed we show that, with reasonable assumptions, a-BLUE channel estimate can be obtained by using a stored copy of a pre-computed matrix in the receiver which enables the use of the initial CIR estimate by the subsequent equalizer tap weight calculator. Simulation results are provided to demonstrate the performance of the novel algorithms for the 8-VSB ATSC digital TV system. We also provide a simulation study of the robustness of the a-BLUE algorithm to timing and carrier phase offsets.

Approximate best linear unbiased channel estimation for multi-antenna frequency selective channels with applications to digital TV systems

We provide an iterative and a non-iterative channel impulse response (CIR) estimation algorithm for communication receivers with multiple-antenna. Our algorithm is best suited for communication systems which utilize a periodically transmitted training sequence within a continuous stream of information symbols, and the receivers for this particular system are expected work in a severe frequency selective multipath environment with long delay spreads relative to the length of the training sequence. The iterative procedure calculates the (semi-blind) Best Linear Unbiased Estimate (BLUE) of the CIR. The non-iterative version is an approximation to the BLUE CIR estimate, denoted by a-BLUE, achieving almost similar performance, with much lower complexity. Indeed we show that, with reasonable assumptions, a-BLUE channel estimate can be obtained by using a stored copy of a pre-computed matrix in the receiver which enables the use of the initial CIR estimate by the subsequent equalizer tap weight calculator. Simulation results are provided to demonstrate the performance of the novel algorithms for 8-VSB ATSC Digital TV system. We also provide a simulation study of the robustness of the a-BLUE algorithm to timing and carrier phase offsets.