Equivalent Discrete-time Channel Research Articles

On the Effects of Channel Sparsity on Joint Estimators in Aeronautical Telemetry

Minimum mean-squared error (MMSE) equalizers are a viable solution to mitigate the frequency selectivity of the aeronautical telemetry channel. Because the MMSE equalizer filter coefficients are a function of the carrier frequency offset (CFO), the equivalent discrete-time channel, and the noise variance, reliable estimates of those parameters are required. The CFO is due primarily to the high velocity of the airborne transmitter. Because the equivalent discrete-time channel in aeronautical telemetry is sparse, the performance of the joint estimator based on a sparse channel estimator is superior to the performance of a traditional nonsparse maximum-likelihood-inspired joint estimator. The improvement is seen in lower estimator error variances for the parameters, particularly for the CFO and channel estimate, and in the postequalizer bit-error rate. Simulation results demonstrate that the postequalizer bit-error rate using the sparse estimator is almost as good as that using ideal estimators.

On Continuous-Time Gaussian Channels.

A continuous-time white Gaussian channel can be formulated using a white Gaussian noise, and a conventional way for examining such a channel is the sampling approach based on the Shannon–Nyquist sampling theorem, where the original continuous-time channel is converted to an equivalent discrete-time channel, to which a great variety of established tools and methodology can be applied. However, one of the key issues of this scheme is that continuous-time feedback and memory cannot be incorporated into the channel model. It turns out that this issue can be circumvented by considering the Brownian motion formulation of a continuous-time white Gaussian channel. Nevertheless, as opposed to the white Gaussian noise formulation, a link that establishes the information-theoretic connection between a continuous-time channel under the Brownian motion formulation and its discrete-time counterparts has long been missing. This paper is to fill this gap by establishing causality-preserving connections between continuous-time Gaussian feedback/memory channels and their associated discrete-time versions in the forms of sampling and approximation theorems, which we believe will play important roles in the long run for further developing continuous-time information theory. As an immediate application of the approximation theorem, we propose the so-called approximation approach to examine continuous-time white Gaussian channels in the point-to-point or multi-user setting. It turns out that the approximation approach, complemented by relevant tools from stochastic calculus, can enhance our understanding of continuous-time Gaussian channels in terms of giving alternative and strengthened interpretation to some long-held folklore, recovering “long-known” results from new perspectives, and rigorously establishing new results predicted by the intuition that the approximation approach carries. More specifically, using the approximation approach complemented by relevant tools from stochastic calculus, we first derive the capacity regions of continuous-time white Gaussian multiple access channels and broadcast channels, and we then analyze how feedback affects their capacity regions: feedback will increase the capacity regions of some continuous-time white Gaussian broadcast channels and interference channels, while it will not increase capacity regions of continuous-time white Gaussian multiple access channels.

Equivalent Discrete-Time Channel Modeling for Molecular Communication With Emphasize on an Absorbing Receiver.

This paper introduces the equivalent discrete-time channel model (EDTCM) to the area of diffusion-based molecular communication (DBMC). Emphasis is on an absorbing receiver, which is based on the so-called first passage time concept. In the wireless communications community the EDTCM is well known. Therefore, it is anticipated that the EDTCM improves the accessibility of DBMC and supports the adaptation of classical wireless communication algorithms to the area of DBMC. Furthermore, the EDTCM has the capability to provide a remarkable reduction of computational complexity compared to random walk based DBMC simulators. Besides the exact EDTCM, three approximations thereof based on binomial, Gaussian, and Poisson approximation are proposed and analyzed in order to further reduce computational complexity. In addition, the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is adapted to all four channel models. Numerical results show the performance of the exact EDTCM, illustrate the performance of the adapted BCJR algorithm, and demonstrate the accuracy of the approximations.

Waveform domain framework for capacity analysis of uplink WCDMA systems

This paper investigates the capacity limit of an uplink WCDMA system considering a continuous-time waveform signal. Various realistic assumptions are incorporated into the problem, which make the study valuable for performance assessment of real cellular networks to identify potentials for performance improvements in practical receiver designs. An equivalent discrete-time channel model is derived based on sufficient statistics for optimal decoding of the transmitted messages. The capacity regions are then characterized using the equivalent channel considering both finite constellation and Gaussian distributed input signals. The capacity with sampling at the receiver is also provided to exemplify the performance loss due to a typical post-processing at the receiver. Moreover, we analyze the asymptotic capacity when the signal-to-noise ratio goes to infinity. The conditions to simultaneously achieve the individual capacities are derived, which reveal the impacts of signature waveform space, channel frequency selectivity and signal constellation on the system performance.

Performance limits of channel parameter estimation for joint communication and positioning

Recently, a system concept for joint communication and positioning has been proposed by the authors. Channel parameter estimation (CPE) is the core part of this system proposal. Parameters of the physical channel, which can be exploited for positioning, are estimated based on the assumption that a priori knowledge about pulse shaping and receive filtering is available. At the same time, channel estimates of the equivalent discrete-time channel model, which are needed for data detection, are obtained inherently. This article focusses on the positioning part of the system proposal. Performance limits for CPE in terms of Cramer-Rao lower bounds are determined for different channel models. The influence of oversampling and of different channel characteristics is investigated. Oversampling proves especially helpful in dense multipath scenarios, which are most challenging. Based on the presented results, oversampling with a factor of two is recommended in order to improve the positioning accuracy. Excessive oversampling like in conventional global positioning system receivers is not necessary.

Joint communication and positioning based on soft channel parameter estimation

A joint communication and positioning system based on maximum-likelihood channel parameter estimation is proposed. The parameters of the physical channel, needed for positioning, and the channel coefficients of the equivalent discrete-time channel model, needed for communication, are estimated jointly using a priori information about pulse shaping and receive filtering. The paper focusses on the positioning part of the system. It is investigated how soft information for the parameter estimates can be obtained. On the basis of confidence regions, two methods for obtaining soft information are proposed. The accuracy of these approximative methods depends on the nonlinearity of the parameter estimation problem, which is analyzed by so-called curvature measures. The performance of the two methods is investigated by means of Monte Carlo simulations. The results are compared with the Cramer-Rao lower bound. It is shown that soft information aids the positioning. Negative effects caused by multipath propagation can be mitigated significantly even without oversampling.

Joint Carrier Frequency Offset and Fast Time-Varying Channel Estimation for MIMO-OFDM Systems

In this paper, a novel pilot-aided algorithm is developed for multiple-input-multiple-output (MIMO) orthogonal frequency-division-multiplexing (OFDM) systems operating in a fast time-varying environment. The algorithm has been designed to work with both the parametric L -path channel model (with known path delays) and the equivalent discrete-time channel model to jointly estimate the multipath Rayleigh channel complex amplitude (CA) and the carrier frequency offset (CFO). Each CA time variation within one OFDM symbol is approximated by a basis expansion model representation. An autoregressive model is built for the parameters to be estimated. The algorithm performs estimation using extended Kalman filtering. The channel matrix is thus easily computed, and the data symbol is estimated without intercarrier interference (ICI) when the channel matrix is QR-decomposed. It is shown that our algorithm is far more robust to high speed than the conventional algorithm, and the performance approaches that of the ideal case for which the channel response and CFO are known.

Low complexity LMMSE turbo equalization for combined error control coded and linearly precoded OFDM

The turbo equalization approach is studied for Orthogonal Frequency Division Multiplexing (OFDM) system with combined error control coding and linear precoding. While previous literatures employed linear precoder of small size for complexity reasons, this paper proposes to use a linear precoder of size larger than or equal to the maximum length of the equivalent discrete-time channel in order to achieve full frequency diversity and reduce complexities of the error control coder/decoder. Also a low complexity Linear Minimum Mean Square Error (LMMSE) turbo equalizer is derived for the receiver. Through simulation and performance analysis, it is shown that the performance of the proposed scheme over frequency selective fading channel reaches the matched filter bound; compared with the same coded OFDM without linear precoding, the proposed scheme shows an Signal-to-Noise Ratio (SNR) improvement of at least 6dB at a bit error rate of 10−6 over a multipath channel with exponential power delay profile. Convergence behavior of the proposed scheme with turbo equalization using various type of linear precoder/transformer, various interleaver size and error control coder of various constraint length is also investigated.

Performance of symbol-sampled receivers over unknown continuous-time Rayleigh channels

The performance of symbol-sampled receivers is usually evaluated via Forney's finite impulse response (FIR) model for the equivalent channel [discrete-time transversal filter (DTTF)]. This model contains a matched filter, and, thus, requires prior knowledge of the continuous-time channel-impulse response. Therefore, if the channel is continuous and unknown, it is unrealistic to use the DTTF model, which leads to an upper bound on the system performance. Using an alternative model for the equivalent discrete-time channel, where the matched filter is replaced by a receive filter matched to the symbol waveform, we propose a framework to quantitatively investigate the performance loss from a theoretical perspective. The theoretical results are corroborated using a practical system.

Sobre o Desempenho de Receptores à Taxa de Símbolos em Canais Contínuos

Symbol-sampled receivers have had their performance evaluated via Forney's discrete-time transversal filter (DTfF) model for the equivalent channel, which contains a standard matched filter and thus assumes previous knowledge of the continuous-time channel impulse response. If the continuous channel is unknown then the DTfF model provides only an upper bound on the system performance. In this paper, we quantify theoretically the performance loss of an alternative, more realistic model for the equivalent discretetime channel relative to the DTTF model, in terms of information capacity. Moreover, the loss is calculated as a function of the parameters of the transmit filter, which is assumed to be a root-raised cosine filter. We then show by means of computer simulations that this performance loss for the case of an iterative, symbol-sampled, semi-blind receiver, with combined maximum-a-posteriori equalization and turbo decoding can be negligible, which agrees with the theoretical prediction.

Joint equalization and decoding for QAM block transmissions

A method of joint equalization and decoding for block transmission with coding across blocks is presented. It is well suited for bandwidth efficient QAM transmission using large transmit symbol alphabets, whereby the blocking structure can be arbitrary in principle. The method consists in multiple iterations of equalization and decoding, whereby information is exchanged back and forth between the decoder and the equalizer. The equalizer is based on Cholesky factorization of the equivalent discrete-time channel matrix (Eur. Trans. Telecommun 10 (1999) 351; Grundlagen der Kommunikationstechnik, Springer, Berlin, 2004). The convergence behavior of the iterative equalization and decoding method is analyzed by means of an upper bound on the extrinsic information transfer. It is shown that the method has improved bit error performance versus separate equalization and decoding without decoder feedback and, thus, yields superior power efficiency.

Efficient simulation of digital transmission over WSSUS channels

This paper proposes an efficient Monte Carlo method which reduces computation for digital communication simulations over a multipath Rayleigh fading, wide-sense-stationary uncorrelated-scattering (WSSUS) channel. An equivalent discrete-time channel representation, which can be realized by a FIR filter with time-variant tap gains, is employed. In the proposed method, the tap gains are generated from a linear transformation of a set of orthogonal zero-mean complex Gaussian random processes. By the central limit theorem, each random process is approximated by summing a finite number of randomly generated phasors (Monte Carlo approximation). When compared with the tap gain generation method, which approximates the physical channel by the Monte Carlo approximation first and then generates the tap gain values, the proposed method demonstrates a considerable reduction in the required simulation time as well as improved accuracy under similar conditions.