Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels

We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete-time channel grows logarithmically with the SNR, with a capacity pre-log equal to $1-{Q}/{N}$. Here, $N$ is the number of symbols transmitted within one fading block, and $Q$ is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as $1-1/N$. Since the capacity pre-log corresponding to symbol-rate sampling is $1-Q/N$, our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.Comment: To appear in the IEEE Transactions on Information Theor

Trellis-Based Equalization for Sparse ISI Channels Revisited

Sparse intersymbol-interference (ISI) channels are encountered in a variety of high-data-rate communication systems. Such channels have a large channel memory length, but only a small number of significant channel coefficients. In this paper, trellis-based equalization of sparse ISI channels is revisited. Due to the large channel memory length, the complexity of maximum-likelihood detection, e.g., by means of the Viterbi algorithm (VA), is normally prohibitive. In the first part of the paper, a unified framework based on factor graphs is presented for complexity reduction without loss of optimality. In this new context, two known reduced-complexity algorithms for sparse ISI channels are recapitulated: The multi-trellis VA (M-VA) and the parallel-trellis VA (P-VA). It is shown that the M-VA, although claimed, does not lead to a reduced computational complexity. The P-VA, on the other hand, leads to a significant complexity reduction, but can only be applied for a certain class of sparse channels. In the second part of the paper, a unified approach is investigated to tackle general sparse channels: It is shown that the use of a linear filter at the receiver renders the application of standard reduced-state trellis-based equalizer algorithms feasible, without significant loss of optimality. Numerical results verify the efficiency of the proposed receiver structure.Comment: To be presented at the 2005 IEEE Int. Symp. Inform. Theory (ISIT 2005), September 4-9, 2005, Adelaide, Australi

An overview of data acquisition, signal coding and data analysis techniques for MST radars

An overview is given of the data acquisition, signal processing, and data analysis techniques that are currently in use with high power MST/ST (mesosphere stratosphere troposphere/stratosphere troposphere) radars. This review supplements the works of Rastogi (1983) and Farley (1984) presented at previous MAP workshops. A general description is given of data acquisition and signal processing operations and they are characterized on the basis of their disparate time scales. Then signal coding, a brief description of frequently used codes, and their limitations are discussed, and finally, several aspects of statistical data processing such as signal statistics, power spectrum and autocovariance analysis, outlier removal techniques are discussed

Online Natural Gradient as a Kalman Filter

We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural gradient descent on the log-likelihood of the observations. In the i.i.d. case, this relation is a consequence of the "information filter" phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant interpretations for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.Comment: 3rd version: expanded intr

Efficient Sum-of-Sinusoids based Spatial Consistency for the 3GPP New-Radio Channel Model

Spatial consistency was proposed in the 3GPP TR 38.901 channel model to ensure that closely spaced mobile terminals have similar channels. Future extensions of this model might incorporate mobility at both ends of the link. This requires that all random variables in the model must be correlated in 3 (single-mobility) and up to 6 spatial dimensions (dual-mobility). Existing filtering methods cannot be used due to the large requirements of memory and computing time. The sum-of-sinusoids model promises to be an efficient solution. To use it in the 3GPP channel model, we extended the existing model to a higher number of spatial dimensions and propose a new method to calculate the sinusoid coefficients in order to control the shape of the autocorrelation function. The proposed method shows good results for 2, 3, and 6 dimensions and achieves a four times better approximation accuracy compared to the existing model. This provides a very efficient implementation of the 3GPP proposal and enables the simulation of many communication scenarios that were thought to be impossible to realize with geometry-based stochastic channel models