Information Theory and Reliable Communication

This short tutorial presents two mathematical techniques namely Majorization Theory and Matrix-Monotone Functions, reviews their basic definitions and describes their concepts clearly with many illustrative examples. In addition to this tutorial, new results are presented with respect to Schur-convex functions and regarding the properties of matrix-monotone functions.

The techniques are applied to solve communication and information theoretic problems in wireless communications. The impact of spatial correlation in multiple antenna systems is characterized for many important performance measures, e.g., average mutual information, outage probability, error performance, minimum Eb/N0 and wide-band slope, zero-outage capacity, and capacity region. The impact of user distribution in cellular systems is characterized for different scenarios including perfectly informed transmitters and receivers, regarding, e.g., the average sum rate, the outage sum rate, maximum throughput. Finally, a unified framework for the performance analysis of multiple antenna systems is developed based on matrix-monotone functions. The optimization of transmit strategies for multiple antennas is carried out by optimization of matrix-monotone functions. The results within this framework resemble and complement the various results on optimal transmit strategies in single-user and multiple-user multiple-antenna systems.

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Majorization and Matrix Monotone Functions in Wireless Communications

Outage probabilities and single-hop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks, and there is no systematic approach that permits the convenient comparison of the performance of networks with different geometries and levels of randomness. The uncertainty cube is introduced to categorize the uncertainty present in a network. The three axes of the cube represent the three main potential sources of uncertainty in interference-limited networks: the node distribution, the channel gains (fading), and the channel access scheme (set of transmitting nodes). For the performance analysis, a new parameter, the so- called spatial contention, is defined. It measures the slope of the outage probability in an ALOHA network as a function of the transmit probability p at p = 0. Outage is defined as the event that the signal-to-interference ratio (SIR) is below a certain threshold in a given time slot. It is shown that the spatial contention is sufficient to characterize outage and throughput in large classes of wireless networks, corresponding to different positions on the uncertainty cube. Existing results are placed in this framework, and new ones are derived. Further, interpreting the outage probability as the SIR distribution, the ergodic capacity of unit-distance links is determined and compared to the throughput achievable for fixed (yet optimized) transmission rates.

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Outage, local throughput, and capacity of random wireless networks

A high-speed transmitter and receiver are provided. In one embodiment, a transmitter comprises a baseband processor structured to receive data and to convert the data into a multiplicity of high and low signal values, with each high and low signal value having a first timing interval. A local oscillator generates a clock signal at a second timing interval and a digital circuit combines the high and low signal values with the clock signal to produce a transmission signal directly at a transmission frequency. A receiver is configured to receive the signal. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules that allow a reader to quickly ascertain the subject matter of the disclosure contained herein. This Abstract is submitted with the explicit understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.

High data rate transmitter and receiver

Apparatus and methods of ultra-wideband communication are provided. In one embodiment, an ultra-wideband receiver comprises an envelope detector that detects the amplitude of a received ultra-wideband pulse and generates a waveform representative of the envelope of the received ultra-wideband pulse. A sign detector then determines a sign associated with a data bit encoded on the received ultra-wideband pulse. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules that allow a reader to quickly ascertain the subject matter of the disclosure contained herein. This Abstract is submitted with the explicit understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.

Ultra-wideband communication apparatus and methods

Fading channels, often seen in wireless systems, provide an unfavorable environment for reliable communications. Current methods for evaluating the performance of fading channels include ergodic capacity and 2-capacity. Ergodic capacity quantifies the ultimate reliable communication limit of the fading channel. It is only achievable with infinite coding delay, making it impossible to achieve in practice. 2-capacity, achievable with finite coding delay, does not provide a measure of error-free communications performance. Since practical communication systems are delay-constrained, it is possible to retransmit codewords when errors occur. We provide a new analysis framework that accounts for codeword retransmission in the analysis of fading channels. We introduce new measures, maximum zero-outage throughput and maximum 2-throughput, that predict the performance of practical systems and show that ergodic capacity and 2-capacity are special cases of our definitions. We also provide a measure that characterizes the performance of a system with more complex receiver design, using “incremental diversity” to improve

Throughput Measures for Delay-constrained Communications in Fading Channels

A communications system is disclosed having an improved receiver designed to combat ICI in OFDM modulated signals. The receiver may also be designed to combat ISI in OFDM modulated signals. In one embodiment, the communications system comprises a transmitter that transmits an OFDM modulated signal, and a receiver that receives and demodulates a corrupted version of the OFDM modulated signal. The receiver includes an A/D converter, a transform module, and a detection module. The A/D converter converts the corrupted OFDM-modulated signal into a digital receive signal. The transform module transforms the digital receive signal into the frequency domain. The detection module determines a channel symbol from the frequency component amplitudes while compensating for correlation between the frequency components. In a preferred implementation, the detection module calculates for each frequency component, a weighted sum of the frequency component amplitudes from the transform module. The weighted sum minimizes expected error energy.

Joint detection in OFDM systems

The fading channels seen in many wireless systems provide a particularly hostile environment for reliable communication. Current metrics for evaluating the performance limits of fading channels have shortcomings. Ergodic capacity, representing the ultimate error-free communications limit, only applies to systems with infinite coding delay. Practical systems are delay-limited and must use finite-length codes. For delay-limited systems /spl epsi/-capacity and delay-limited capacity are typically used to quantify the communications performance. However, /spl epsi/-capacity is not an estimate of error-free performance while delay-limited capacity tends to be an overly conservative measure. We model practical systems as a single server queue and quantify the communications performance as the average throughput through the queue. Throughput is maximized by optimally selecting the transmission rate and power control strategy. Using this approach we arrive at striking conclusions. First, we show that a throughput very close to ergodic capacity can be achieved with a small coding delay. Second, the optimal transmission rate for some systems can be higher than the ergodic capacity of the channel. Third, we demonstrate the notion that power adaptation does not improve communication performance does not hold for delay-limited systems.

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Delay-limited throughput maximization for fading channels using rate and power control

In many communication systems, including Digital Subscriber Lines, performance is severely limited by crosstalk interference. Previous work has presented a general framework for designing optimal transmit spectra for crosstalk avoidance. The technique uses the channel, noise, and interference characteristics to setup and solve an optimization problem which maximizes the capacity of neighboring lines, while maintaining spectral compatibility with other services. This joint signaling and optimal power distribution technique yields significant performance gains over conventional fixed spectra in terms of bit-rates and performance margins. In general, the spectra that result from this scheme have both an echo cancelled and frequency division multiplexed region. To ease the analysis, this technique assumed that the echo canceller has perfect echo rejection capability, which in practice is not true. In this paper, we propose an extension to these techniques, in which we factor the performance of practical echo cancellers into the optimization procedure. When echo rejection is not perfect, as is generally the case, our technique shows significant performance gains over previous techniques. As the performance of the echo canceller increases, our technique converges to the same solution.

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Optimal transmit spectra for communication in the presence of crosstalk and imperfect echo cancellation

As the deployment of broadband communication systems such as DSL continues to grow, system performance in terms of capacity and error rates is severely limited by crosstalk interference. In order to continue deploying high speed DSL service, it becomes necessary to mitigate this crosstalk interference. All current crosstalk mitigation techniques require precise knowledge of the crosstalk coupling functions between the twisted pair wires carrying DSL service within a cable binder. In practice, this is near impossible to obtain, without coordination between the different DSL services. In this paper, we present a crosstalk cancellation technique that is blind to the coupling functions between the wire pairs. Our technique uses the statistical properties of the received crosstalk signal (that can be easily estimated), rather than the exact coupling functions themselves, making it very attractive for practical implementation. We show with the help of simulations for a realistic ADSL system with HDSL and T1 crosstalk interference using actual measured crosstalk coupling functions that the proposed blind crosstalk cancellation technique can achieve significant gains in terms of rate and reach improvement for the ADSL system. We also show that the performance of the proposed blind crosstalk cancellation technique is robust to a jitter in the crosstalk symbol timing estimate that is required to construct the cancellation signal. Keywords—crosstalk, NEXT, mitigation, blind, cancellation.

Nadeem Ahmed

Papers

Throughput Measures for Delay-constrained Communications in Fading Channels

Joint detection in OFDM systems

Delay-limited throughput maximization for fading channels using rate and power control

Optimal transmit spectra for communication in the presence of crosstalk and imperfect echo cancellation

Blind Crosstalk Cancellation for DMT Systems