Error propagation and recovery in decision-feedback equalizers for nonlinear channels

©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Nonlinear intersymbol interference is often present in communication and digital storage channels. Decision-feedback equalizers (DFEs) can decrease this nonlinear effect by including appropriate nonlinear feedback filters. Although various applications of these types of equalizers have been published in the literature, the analysis of their stability and error recovery has not appeared. We consider a DFE with a nonlinear feedback filter based on a discrete Volterra series. We extend error propagation, error probability, stability, and error recovery time results for Nth order nonlinear channelsTsimbinos, J. White, L.B

On a Lower Bound for the Redundancy of Reliable Networks with Noisy Gates

A proof is provided that a logarithmic redundancy factor is necessary for the reliable computation of the parity function by means of a network with noisy gates. This result was first stated by R.L. Dobrushin and S.I. Ortyukov (1977). However, the authors believe that the analysis given by Dobrushin and Ortyukov is not entirely correct. The authors establish the result by following the same steps and by replacing the questionable part of their analysis with entirely new arguments

Design of Block Transceivers with Decision Feedback Detection

This paper presents a method for jointly designing the transmitter-receiver pair in a block-by-block communication system that employs (intra-block) decision feedback detection. We provide closed-form expressions for transmitter-receiver pairs that simultaneously minimize the arithmetic mean squared error (MSE) at the decision point (assuming perfect feedback), the geometric MSE, and the bit error rate of a uniformly bit-loaded system at moderate-to-high signal-to-noise ratios. Separate expressions apply for the ``zero-forcing'' and ``minimum MSE'' (MMSE) decision feedback structures. In the MMSE case, the proposed design also maximizes the Gaussian mutual information and suggests that one can approach the capacity of the block transmission system using (independent instances of) the same (Gaussian) code for each element of the block. Our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers, and that they retain their performance advantages in the presence of error propagation.Comment: 14 pages, 8 figures, to appear in the IEEE Transactions on Signal Processin

Blind detection in channels with intersymbol interference

In high speed digital transmission over bandlimited channels, one of the principal impairments, besides additive white Gaussian noise, is intersymbol interference. For unknown channels, adaptive equalization is used to mitigate the interference. Different types of equalizers were proposed in the literature such as linear, decision feedback equalizers and maximum likelihood sequence estimation. The transmitter embeds sequences with the data regularly to help the equalizer adapt to the unknown channel parameters. It is not always appropriate or feasible to send training sequences; in such cases, self adaptive or blind equalizers are used. The past ten years have witnessed an interest in the topic. Most of this interest, however, was devoted to linear equalization In this dissertation we concentrate on blind decision feedback equalization and blind maximum likelihood sequence estimation. We propose a new algorithm: the decorrelation algorithm, for controlling the blind decision feedback equalizer. We investigate properties such as convergence and probability of error. A new algorithm is also proposed for blind maximum likelihood sequence estimation. We use two trellises: one for the data and the other for the channel parameters. The Viterbi algorithm is used to search the two trellises for the best channel and data sequence estimates. We derive an upper bound for this scheme. We also address the problem of ill convergence of the constant modulus algorithm and propose a technique to improve its convergence. Using this technique, global convergence is guaranteed as long as the channel gain exceeds a certain critical value. The question of the Viterbi algorithm\u27s complexity is important for both conventional and blind maximum likelihood sequence estimation. Therefore, in this dissertation, the problem of reducing the complexity of the Viterbi algorithm is also addressed. We introduce the concept of state partitioning and use it to reduce the number of states of the Viterbi algorithm. This technique offers a better complexity/performance tradeoff than previously proposed techniques

Equalization of Linear Time-Dispersive Intra- and Interbuilding Radio Data Channels

Za telekomunikacione sisteme unutar zgrada, koncept “bežičnog je uveo “novi” prenosni medijum, odnosno kanal za prostiranje radio talasa u zatvorenim prostorima, koji se koristi za povezivanje terminala i ostale opreme u lokalnu računarsku mrežu (LAN). Eksperimentalne studije, urađene u cilju opisivanja kanala za prostiranje talasa u zatvorenim prostorima, su pokazale da su karakteristike prostiranja talasa u zatvorenim prostorima: velika slabljenja pri prostiranju, prostiranje po više puteva između predaje i prijema, spore vremenske promene kanala I feding. Neke primene bežičnih kanala u zatvorenim prostorima zahtevaju veoma brz prenos podataka koji je ograničen prostiranjem po više puteva I fedingom. Kad se poveća brzina prenosa podataka, prostiranje po više puteva prouzrokuje interferenciju među simbolima u toku procesa detekcije simbola. Uobičajeni način borbe protib fedinga koji nastaje pri prostiranju po više puteva, a kao posledica toga i interferencije među simbolima, je upotreba adaptivne ekvalizacije na prijemu. Problem osetljivosti digitalnog radio telekomunikacionog sistema u zatvorenim prostorima na prostiranje po više puteva pri promenjivim parametrima kanala i sitema, je obrađen u ovoj tezi, na primeru 4-QAM telekomunikacionog sistema, sa LMS linearnim ekvalizatorom sa kašnjenjem od jednog simbola između susednih koeficijenata kao i sa LMS nelienarnim (DF) ekvalizatorom sa kašnjenjem manjim od jednog simbola između susednih koeficijenata na prijemu. Rešavanju problema je pristupljeno iz 3 pravca. Prvo je data teorijska analiza problema. Metodom simulacija na računaru je izvršena detaljna procena performansi sistema za veoma brzi prenos podataka po disperzivnim kanalima sa sporim fedingom, koriteći statistički eksponencijalni model kanala sa Relejevim fedingom koji je predložen u jednoj studiji, kao i Rajsov model kanala sa fedingom koji se bazira na merenjima izvršenim u radnim prostorijama i fabričkom okruženju. Konačno. Impulsni odzivi kanala izmereni u naučno-istraživačkoj laboratoriji pri različitim uslovima prostiranja, topografijama (konfiguracijama) i frekvencijama, su takođe korišćeni za procenu performansi sistema. Prosečna verovatnoća greške po bitu je korišćena kao performansni kriterijum. Krive prosečne verovatnoće greške po bitu ukazuju da, bilo kod kanala generisanih uz pomoć računara ili kod izmerenih kanala, linearni ekvalizator smanjuje grešku približno 10 puta (odnos signal-šum od 8dB) u poređenju sa neekvalizovanim kanalom, a da DF ekvalizator nadmašuje linearni ekvalizator dalje smanjujući grešku 2 puta (SNR=8dB). Zapravo, počevši od slučaja frekvencijski-ravnog fedinga, ustanovljeno je da ekvalizator može da smanji grešku za kanale generisane uz pomoć računara skoro do normalizovane vrednosti brzine prenosa podataka od 4 (Relejev slučaj), I, 2.2, 1 I 0.5 (Rajsov slučaj) I vrednost Rajsovog faktora od 2, 6.8 I 11dB, respektivno, dok su u slučaju izmerenih kanala vrednosti minimuma krivih verovatnoće greške između 2 i 3, a pozicije minimuma zavise od veličine prostorije i topografije. Posle minimuma, performanse sistema degradiraju kad se bilo brzina prenosa ili disperzija kanala povećaju, zbog negativnog efekta interferencije među sibolima koji potire poboljšanje usled implicitne (vremenske) raznovrsnosti. Kad je odnos signal-šum nizak (do 12dB zakjlučno), primećeno je da se javlja efekat prostiranja greške. Kod DF prijemnika. Ipak, pokazano je da umetanjem nove, “modifikovane” automatske funkcije čišćenja u filtar povratne sprege kod DF ekvalizatora, se značajno može smanjiti neželjen uticaj efekta prostiranja greške, a samim tim i prosečna verovatnoća greške po bitu i do 2 reda veličine. Na kraju, performanse ekvalizatora su upoređene i sa teorijskom performansom prilagođenog filtra za kanale sa Relejevim fedingom, koji predstavljaju performansnu granicu za sve tehnike eliminacije interferencije među simbolima. Ustanovljeno je da DF ekvalizator sa tačnim povratnim simbolima, koji ima bolje performanse od bilo linearnog ili DF ekvalizatora sa detektovanim povratnim simbolima, daje prosečnu verovatnoću greške po bitu samo oko dva puta veću od “optimalnog” prijemnika čije performanse predstavljaju teorijsku granicu najvećeg mogućeg poboljšanja koje se može dobiti korišćenjem mnogo komplikovanijih prijemnika sa detektorima koji odlučuju po principu funkcije najvećeg izgleda.The concept of wireless in-building systems has introduced a “new” medium the indoor radio propagation channel, which can be used for interconnecting terminals and computers in LAN-s. Experimental studies have shown have shown that indoor radiowave propagation can be characterized by large propagation losses, multipath, slow time variations and fading. Some computer applications require very high signaling rates. When the data rate is increased, themultipath propagation in the indoor channel causes intersymbol interference in the detection process, thus adversely affecting the system performance. A common approach to combat multipath fading and hence intersymbol intereference, is to use an adaptive equalizer. This thesis considers a 4-QAM communication system with LMS symbol-spaced linear and LMS fractionally-spaced decifion feedback adaptive equalizer at the receiver. The problem is approached in three ways. The system performance evaluation for high-speed signaling over slowly fading dispersive diversity channels is considered first, using the statistical exponential Rayleigh fading channel model, and the Rician fading channel model. These models are based on propagation measurements performed in office and factory environments. Next, the channel impulse responses measured in the research laboratory building for different propagation environments, topographies and frequencies are used for system performance predictions based on computer simulation. Finally, a theoretical performance analysis of the problem is given. The average bit error rate (BER) is used as the system performance quality measure. The average BER curves indicate, for both computer generated and measured channels, that a linear equalizer reduces the BER by approximately a factor of ten at SNR=8dB compared with unequalized channel case. The decision-feedback equalizer surpasses the linear equalizer by further reducing the BER by approximately a factor of two at SNR=8dB. Using the frequency-flat fading case as a reference the decision-feedback equalizer is shown to be able to reduce the BER almost up to the normalized data rate of 4 for the case of Rayleigh fading, and up to 2.2, 1 and 0.5 for Rician fading with Rice factor values of 2, 6.8 and 11dB, respectively. The error performance curves for the measured channels have their best values between the normalized data rates of 2 and 3, with the actual minimum positions depending on the room size and lay-out. Beyond the BER minima, system performance degrades when either the data rate or the multipath spread is increased. This is ue to the negative effect of intersymbol interference, which offsets the time divesity gains. Low signal-to-noise ratio (SNR ≤ 12dB) are observed to cause error propagation effects in the decision-feedback receiver. Insertion of a novel modified automatic “clear” function in the backward filter of the decision-feedback equalizer significantly reduces the error propagation effect, decreasing the BER by up to two orders of magnitude. Finally, equalizer performance is compared with the theoretical matched filter performance for Rayleign fading diversity channels; this represents a lower bound for all intersymbol interference elimination techniques. The decision-feedback equalizer with correct symbols fed back, being better in performance than either a linear equalizer or the decision-feedback equalizer with detected symbols fed back, is shown to perform worse than the ideal diversity combining receiver by a factor of approximately two, which represents the theoretical limit for possible performance improvement, using much more complex receivers with maximum likelihood detectors

Adaptive Receiver Design for High Speed Optical Communication

Conventional input/output (IO) links consume power, independent of changes in the bandwidth demand by the system they are deployed in. As the system is designed to satisfy the peak bandwidth demand, most of the time the IO links are idle but still consuming power. In big data centers, the overall utilization ratio of IO links is less than 10%, corresponding to a large amount of energy wasted for idle operation. This work demonstrates a 60 Gb/s high sensitivity non-return-to-zero (NRZ) optical receiver in 14 nm FinFET technology with less than 7 ns power-on time. The power on time includes the data detection, analog bias settling, photo-diode DC current cancellation, and phase locking by the clock and data recovery circuit (CDR). The receiver autonomously detects the data demand on the link via a proposed link protocol and does not require any external enable or disable signals. The proposed link protocol is designed to minimize the off-state power consumption and power-on time of the link. In order to achieve high data-rate and high-sensitivity while maintaining the power budget, a 1-tap decision feedback equalization method is applied in digital domain. The sensitivity is measured to be -8 dBm, -11 dBm, and -13 dBm OMA (optical modulation amplitude) at 60 Gb/s, 48 Gb/s, and 32 Gb/s data rates, respectively. The energy efficiency in always-on mode is around 2.2 pJ/bit for all data-rates with the help of supply and bias scaling. The receiver incorporates a phase interpolator based clock-and-data recovery circuit with approximately 80 MHz jitter-tolerance corner frequency, thanks to the low-latency full custom CDR logic design. This work demonstrates the fastest ever reported CMOS optical receiver and runs almost at twice the data-rate of the state-of-the-art CMOS optical receiver by the time of the publication. The data-rate is comparable to BiCMOS optical receivers but at a fraction of the power consumption

Mixed Norm Equalization with Applications in Television Multipath Cancellation

Electrical Engineerin