Diffusive MIMO Molecular Communications: Channel Estimation, Equalization and Detection

In diffusion-based communication, as for molecular systems, the achievable data rate is low due to the stochastic nature of diffusion which exhibits a severe inter-symbol-interference (ISI). Multiple-Input Multiple-Output (MIMO) multiplexing improves the data rate at the expense of an inter-link interference (ILI). This paper investigates training-based channel estimation schemes for diffusive MIMO (D-MIMO) systems and corresponding equalization methods. Maximum likelihood and least-squares estimators of mean channel are derived, and the training sequence is designed to minimize the mean square error (MSE). Numerical validations in terms of MSE are compared with Cramer-Rao bound derived herein. Equalization is based on decision feedback equalizer (DFE) structure as this is effective in mitigating diffusive ISI/ILI. Zero-forcing, minimum MSE and least-squares criteria have been paired to DFE, and their performances are evaluated in terms of bit error probability. Since D-MIMO systems are severely affected by the ILI because of short transmitters inter-distance, D-MIMO time interleaving is exploited as countermeasure to mitigate the ILI with remarkable performance improvements. The feasibility of a block-type communication including training and data equalization is explored for D-MIMO, and system-level performances are numerically derived.Comment: Accepted paper at IEEE transaction on Communicatio

Digital processing of signals in the presence of inter-symbol interference and additive noise

Imperial Users onl

FPGA-based DOCSIS upstream demodulation

In recent years, the state-of-the-art in field programmable gate array (FPGA) technology has been advancing rapidly. Consequently, the use of FPGAs is being considered in many applications which have traditionally relied upon application-specific integrated circuits (ASICs). FPGA-based designs have a number of advantages over ASIC-based designs, including lower up-front engineering design costs, shorter time-to-market, and the ability to reconfigure devices in the field. However, ASICs have a major advantage in terms of computational resources. As a result, expensive high performance ASIC algorithms must be redesigned to fit the limited resources available in an FPGA. Concurrently, coaxial cable television and internet networks have been undergoing significant upgrades that have largely been driven by a sharp increase in the use of interactive applications. This has intensified demand for the so-called upstream channels, which allow customers to transmit data into the network. The format and protocol of the upstream channels are defined by a set of standards, known as DOCSIS 3.0, which govern the flow of data through the network. Critical to DOCSIS 3.0 compliance is the upstream demodulator, which is responsible for the physical layer reception from all customers. Although upstream demodulators have typically been implemented as ASICs, the design of an FPGA-based upstream demodulator is an intriguing possibility, as FPGA-based demodulators could potentially be upgraded in the field to support future DOCSIS standards. Furthermore, the lower non-recurring engineering costs associated with FPGA-based designs could provide an opportunity for smaller companies to compete in this market. The upstream demodulator must contain complicated synchronization circuitry to detect, measure, and correct for channel distortions. Unfortunately, many of the synchronization algorithms described in the open literature are not suitable for either upstream cable channels or FPGA implementation. In this thesis, computationally inexpensive and robust synchronization algorithms are explored. In particular, algorithms for frequency recovery and equalization are developed. The many data-aided feedforward frequency offset estimators analyzed in the literature have not considered intersymbol interference (ISI) caused by micro-reflections in the channel. It is shown in this thesis that many prominent frequency offset estimation algorithms become biased in the presence of ISI. A novel high-performance frequency offset estimator which is suitable for implementation in an FPGA is derived from first principles. Additionally, a rule is developed for predicting whether a frequency offset estimator will become biased in the presence of ISI. This rule is used to establish a channel excitation sequence which ensures the proposed frequency offset estimator is unbiased. Adaptive equalizers that compensate for the ISI take a relatively long time to converge, necessitating a lengthy training sequence. The convergence time is reduced using a two step technique to seed the equalizer. First, the ISI equivalent model of the channel is estimated in response to a specific short excitation sequence. Then, the estimated channel response is inverted with a novel algorithm to initialize the equalizer. It is shown that the proposed technique, while inexpensive to implement in an FPGA, can decrease the length of the required equalizer training sequence by up to 70 symbols. It is shown that a preamble segment consisting of repeated 11-symbol Barker sequences which is well-suited to timing recovery can also be used effectively for frequency recovery and channel estimation. By performing these three functions sequentially using a single set of preamble symbols, the overall length of the preamble may be further reduced

Mixed Norm Equalization with Applications in Television Multipath Cancellation

Electrical Engineerin

Estimation and detection techniques for doubly-selective channels in wireless communications

A fundamental problem in communications is the estimation of the channel. The signal transmitted through a communications channel undergoes distortions so that it is often received in an unrecognizable form at the receiver. The receiver must expend significant signal processing effort in order to be able to decode the transmit signal from this received signal. This signal processing requires knowledge of how the channel distorts the transmit signal, i.e. channel knowledge. To maintain a reliable link, the channel must be estimated and tracked by the receiver. The estimation of the channel at the receiver often proceeds by transmission of a signal called the 'pilot' which is known a priori to the receiver. The receiver forms its estimate of the transmitted signal based on how this known signal is distorted by the channel, i.e. it estimates the channel from the received signal and the pilot. This design of the pilot is a function of the modulation, the type of training and the channel. [Continues.

Tree-Structured Nonlinear Adaptive Signal Processing

In communication systems, nonlinear adaptive filtering has become increasingly popular in a variety of applications such as channel equalization, echo cancellation and speech coding. However, existing nonlinear adaptive filters such as polynomial (truncated Volterra series) filters and multilayer perceptrons suffer from a number of problems. First, although high Order polynomials can approximate complex nonlinearities, they also train very slowly. Second, there is no systematic and efficient way to select their structure. As for multilayer perceptrons, they have a very complicated structure and train extremely slowly Motivated by the success of classification and regression trees on difficult nonlinear and nonparametfic problems, we propose the idea of a tree-structured piecewise linear adaptive filter. In the proposed method each node in a tree is associated with a linear filter restricted to a polygonal domain, and this is done in such a way that each pruned subtree is associated with a piecewise linear filter. A training sequence is used to adaptively update the filter coefficients and domains at each node, and to select the best pruned subtree and the corresponding piecewise linear filter. The tree structured approach offers several advantages. First, it makes use of standard linear adaptive filtering techniques at each node to find the corresponding Conditional linear filter. Second, it allows for efficient selection of the subtree and the corresponding piecewise linear filter of appropriate complexity. Overall, the approach is computationally efficient and conceptually simple. The tree-structured piecewise linear adaptive filter bears some similarity to classification and regression trees. But it is actually quite different from a classification and regression tree. Here the terminal nodes are not just assigned a region and a class label or a regression value, but rather represent: a linear filter with restricted domain, It is also different in that classification and regression trees are determined in a batch mode offline, whereas the tree-structured adaptive filter is determined recursively in real-time. We first develop the specific structure of a tree-structured piecewise linear adaptive filter and derive a stochastic gradient-based training algorithm. We then carry out a rigorous convergence analysis of the proposed training algorithm for the tree-structured filter. Here we show the mean-square convergence of the adaptively trained tree-structured piecewise linear filter to the optimal tree-structured piecewise linear filter. Same new techniques are developed for analyzing stochastic gradient algorithms with fixed gains and (nonstandard) dependent data. Finally, numerical experiments are performed to show the computational and performance advantages of the tree-structured piecewise linear filter over linear and polynomial filters for equalization of high frequency channels with severe intersymbol interference, echo cancellation in telephone networks and predictive coding of speech signals

A fast-initializing digital equalizer with on-line tracking for data communications

A theory is developed for a digital equalizer for use in reducing intersymbol interference (ISI) on high speed data communications channels. The equalizer is initialized with a single isolated transmitter pulse, provided the signal-to-noise ratio (SNR) is not unusually low, then switches to a decision directed, on-line mode of operation that allows tracking of channel variations. Conditions for optimal tap-gain settings are obtained first for a transversal equalizer structure by using a mean squared error (MSE) criterion, a first order gradient algorithm to determine the adjustable equalizer tap-gains, and a sequence of isolated initializing pulses. Since the rate of tap-gain convergence depends on the eigenvalues of a channel output correlation matrix, convergence can be improved by making a linear transformation on to obtain a new correlation matrix