RLS-based initialization for per-tone equalizers in DMT receivers

Per-tone equalization has recently been proposed as an alternative receiver structure for discrete multitone-based systems improving upon the well-known structure based on time-domain equalization. Fast initialization of all the equalizer coefficients has been identified as an open problem. In this letter, a recursive initialization scheme based on recursive least squares with inverse updating is presented for the per-tone equalizers. Simulation results show convergence with an acceptably small number of training symbols. Complexity calculations are made for per-tone equalization and for the case where tones are grouped. It is demonstrated with an example that in the latter case, initialization complexity becomes sufficiently low and comparable to complexity during data transmission.     

Fast initialization of equalizers for VSB-based DTV transceivers in multipath channel

This paper proposes a fast initialization technique for equalization of 8-VSB-based digital television (DTV) signal in severe multipath channels. We consider the use of a modified decision feedback equalizer (MDFE) , for fast initialization. The feedback filter (FBF) of the MDFE can be initialized simply by estimating the channel impulse response and only the feedforward filter (FFF) of the MDFE need training for initialization. To overcome the shortage of the training sequence in the VSB DTV signal, we propose a new initialization method by generating a virtual training signal to initialize the FFF of the MDFE. Simulation results show that the proposed scheme can fast initialize the equalizer using less than 5000 symbols, while providing the receiver performance comparable to that of conventional schemes.     

Linear and decision-feedback per tone equalization for DMT-based transmission over IIR channels

The per-tone equalizer (PTEQ) has been presented as an attractive alternative for the classical time-domain equalizer (TEQ) in discrete multitone (DMT) based systems, such as ADSL systems. The PTEQ is based on a linear minimum mean-square-error (L-MMSE) equalizer design for each separate tone. In this paper, we reconsider DMT modulation and equalization in the ADSL context under the realistic assumption of an infinite impulse response (IIR) model for the wireline channel. First, optimum linear zero-forcing (L-ZF) block equalizers for arbitrary IIR model orders and cyclic prefix (CP) lengths are developed. It is shown that these L-ZF block equalizers can be decoupled per tone, hence they lead to an L-ZF PTEQ. Then, based on the L-ZF PTEQ, low-complexity L-MMSE PTEQ extensions are developed: the linear PTEQ extension exploits frequency-domain transmit redundancy from pilot and unused tones; alternatively, a closely related decision-feedback PTEQ extension can be applied. The PTEQ extensions then add flexibility to a DMT-based system design: the CP overhead can be reduced by exploiting frequency-domain transmit redundancy instead, so that a similar bitrate as with the original PTEQ is achieved at a lower memory and computational cost or, alternatively, a higher bitrate is achieved without a considerable cost increase. Both PTEQ extensions are also shown to improve the receiver's robustness to narrow-band interference.     

Echo cancellation in DMT-receivers: circulant decomposition canceler

Asymmetric digital subscriber lines (ADSLs) employ discrete multitone modulation (DMT) as transmission format, where subcarriers are assigned to the up- and/or downstream transmission direction. To separate up- and downstream signals, the ADSL standard allows the use of echo cancellation resulting in improved bit rates, reach, and/or noise margins. In DMT-based modems, typically, the mixed time/frequency (MTF) domain echo canceling scheme, as proposed by Ho et al., is implemented. This technique estimates the echo filter in the frequency domain using the least mean square (LMS) algorithm with the transmitted echo symbols as update directions. Since not every tone of the transmitted echo signal will carry data, i.e., will be excited, the MTF adaptation process does not lead to a good estimate for the echo channel, unless extra power on unused echo tones is transmitted. However, transmitting extra power on such tones is often undesired. In this paper, we present an alternative echo canceling scheme referred to as the circulant decomposition canceler (CDC), which works without extra power requirements and with comparable complexity as the method of Ho et al. Similar to MTF echo canceling, the CDC scheme can easily be incorporated into a multirate environment with different transmit and receive rates and can also cheaply be combined with per-tone equalization and double talk cancellation to allow fast tracking and/or convergence in the presence of a far-end signal.     

Multi-gigabit analog equalizers for plastic opticalfibers

Two new CMOS analog continuous-time equalizers for high-speed short-haul optical fiber communications are presented in this paper. The proposed structures compensate the limited bandwidth-length product of 1-mm SI-POF channels (45 MHz·100 m) and have been designed in a standard 0.18-μm CMOS process. The equalizers are aimed for multi-gigabit short-range applications, targeting up to 2 Gb/s through a 50-m SI-POF. The prototypes operate with a single supply voltage of only 1 V and overcome the severe limitations suffered by the widely used degenerated differential pair due to the low supply voltage.     

Designing low-complexity equalizers for wireless systems

The demand on wireless communications to provide high data rates, high mobility, and high quality of service poses more challenges for designers. To contend with deleterious channel fading effects, both the transmitter and the receiver must be designed appropriately to exploit the diversity embedded in the channels. From the perspective of receiver design, the ultimate goal is to achieve both low complexity and high performance. In this article, we first summarize the complexity and performance of low-complexity receivers, including linear equalizers and decision feedback equalizers, and then we reveal the fundamental condition when LEs and DFEs collect the same diversity as the maximum-likelihood equalizer. Recently, lattice reduction techniques were introduced to enhance the performance of low-complexity equalizers without increasing the complexity significantly. Thus, we also provide a comprehensive review of LR-aided low-complexity equalizers and analyze their performance. Furthermore, we describe the architecture and initial results of a very-large-scale-integration implementation of an LR algorithm.     

Blind per tone equalization of multilevel signals using support vector machines for OFDM in wireless communication

We present an efficient support vector machine (SVM)-based blind per tone equalization for OFDM systems. Blind per tone equalization using constant modulus algorithm (CMA) and multi-modulus algorithm (MMA) are used as the comparison benchmark. The SVM-based cost function utilizes a CMA-like error function and the solution is obtained by means of an iterative re-weighted least squares algorithm (IRWLS). Moreover, like CMA, the error function allows to extend the method to multilevel modulations. In terms of bit error rate (BER), simulation experiments show that the blind per tone equalization using SVM performs better than blind per tone equalization using CMA and MMA.     

Design methods for time-domain equalizers in DMT transceivers

Time-domain equalizers (TEQ) are used in the discrete multitone (DMT) transceivers in order to reduce the duration of the overall response of the transmission system, so that a shorter-length cyclic prefix could be used. The optimum TEQ is the one that results in maximum bit allocation to each block of the DMT. However, the optimum design of TEQs turns out to be a very difficult task. We give the general guidelines that one should follow in the design of TEQ to achieve a good performance. Based on the suggested guidelines, we first propose an eigenapproach design method which results in TEQs with comparable performance to those of a previously reported method, but at a much lower computational cost. Further study of the proposed guidelines reveals that the choice of target-impulse response in the design of TEQ only weakly depends on the channel response. Noting this, we propose a second design method that is even simpler than our first method, but still results in comparable designs to those of our first method and also those obtained from the much more complex methods of the present literature     

FIR channel-shortening equalizers for MIMO ISI channels

Finite-length delay-optimized multi-input multi-output (MIMO) equalizers that optimally shorten the impulse response memory of frequency-selective MIMO channels are derived. The MIMO equalizers are designed to minimize the average energy of the error sequence between the equalized MIMO channel impulse response and an MIMO target impulse response (TIR) with shorter memory. Two criteria for optimizing the MIMO TIR are analyzed and compared. The presented analytical framework encompasses a multitude of previously-studied finite-length equalization techniques     

Adaptive BLAST-type decision-feedback equalizers for DS-CDMA systems

In this paper, we propose two new adaptive equalization algorithms for direct sequence code division multiple access (DS-CDMA) systems operating over time-varying and frequency selective channels. The equalization schemes consist of a number of serially connected stages and detect users in an ordered manner, applying a decision feedback equalizer (DFE) at each stage. Both the equalizer filters and the order in which the users are extracted are updated in a recursive least squares (RLS) manner, efficiently realized through time- and order-update recursions. V-BLAST detection ordering is implemented, that is, the stronger signal is extracted first so that the weaker users can be more easily detected. The spreading codes are unavailable at the receiver of the first scheme, whereas the second algorithm employs the RAKE receiver concept, incorporating knowledge of the spreading sequences to offer performance improvement. The bit error rate (BER) performance of the equalizers is evaluated via simulations, in both mild and severe near-far environments. Their superiority over existing techniques is demonstrated.     

Joint window and time domain equalizer design for bit rate maximization in DMT-receivers

In discrete multitone (DMT) receivers, as for instance in asymmetric digital subscriber lines (ADSLs), the classical equalizer structure consists of a (real) time domain equalizer (TEQ) combined with complex 1-tap frequency domain equalizers (FEQs). Additionally, receiver windowing can be applied to mitigate the bad spectral containment of the demodulating DFT sidelobes. We focus on a combined equalizer and windowing design procedure to maximize the achievable bit rate in DMT-based modems. Whereas the combination of a TEQ with a single window treats all the data carrying tones in a common way, the presented design method can also be used in a "per group" fashion, where smaller groups of tones receive each a different equalizer-window pair. When such groups contain only one single tone, the design procedure can be linked to the performance of an unbiased minimum mean square error (MMSE) per tone equalizer (PTEQ), which then also implicitly implements a per tone window. The general framework introduced Allows us to treat equalizer-only and window-only designs as well, which appear as special cases in a natural way. This set of bit rate maximizing techniques can serve either as practical design methods or as upper bounds for existing (suboptimal) methods. We will also show that for the same achievable bit rate, equalizer taps can be exchanged for windowing coefficients to reduce complexity during data transmission.     

Giga-bit CMOS equalizers for high-speed data links

Consumer electronics are experiencing an explosive growth in bandwidth requirements. This growth is driven by demand for fiber-to-the-home Internet connections, the increasing capabilities of in-home consumer devices as well as the demands of multimedia recording and playback in mobile devices. However, traditional copper channels and previous generations of optical fiber experience dispersive effects at data rates above 1 Gbps, leading to inter-symbol interference (ISI). This paper presents a finite impulse response filter-based feed forward equalizer (FFE) to reduce the effect of ISI on these channels. The efficacy is of the FFE is demonstrated by measuring the eye diagrams of a 10 Gbps signal transmitted through an optical fiber as well as a copper backplane with and without FFE compensation. The proposed FFEs successfully compensate ISI for both the optical and copper backplane links. All circuits are fabricated using a 0.18 μm CMOS process.     

Tunable acoustooptic filters and equalizers for WDM applications

We describe a high performance acoustooptic tunable filter for add-drop application and for signal equalization in WDM telecommunication crossconnects. It results from a thorough investigation in TeO/sub 2/ of bulk collinear interaction, the geometry of which, particularly the direction of propagation of the acoustic wave, has been chosen in order to obtain the best compromise between the spectral resolution of the device and the acoustooptic figure of merit. Less than 40 mW of electric power is needed either to deviate 100% of a selected light wavelength /spl lambda/ at resonance, or to induce a 30-dB attenuation of its intensity. The sidelobes practically vanish for this configuration and the resolution is equal to 0.75 nm (or 94 GHz) for /spl lambda/=1.55 /spl mu/m. Polarization splitters combined with half-wave plates allow to completely get rid of polarization sensitivity problems. The use of optical fibers to collect the signal at the filter outputs, actually contributes to the high performance of the device as a whole. Experiments have been performed by multiplexing three signals in the input fiber, separated by 4, 2, and 1 nm. The transmission of the filter has been examined through the bar and cross state.     

Fast adaptive equalizers for narrow-band TDMA mobile radio

It is pointed out that the future European cellular digital mobile radio system in the 900 MHz band adopts a narrowband time division multiple access (TDMA) scheme with Gaussian minimum-shift keying (GMSK) modulation and burst type transmission. Consequently, very fast adaptation methods are necessary to cope with the time- and frequency-selective distortions produced by Rayleigh and multipath fading. The authors examine a few theoretical aspects of the application of recursive least squares (RLS) adaptation algorithms to the narrowband TDMA mobile radio system and give the relevant performance results for the fast Kalman algorithm, which turns out to be suitable for the considered application. In particular, signature curves, bit error rate, speed of convergence, steady-state behavior, numerical stability, required accuracy, and hardware complexity are discussed. Linear transversal and nonlinear decision-feedback equalizers are considered     

Performance of turbo equalizers for optical PMD channels

This paper investigates the performance of iterative (turbo) equalization to mitigate the effects of a polarization-mode dispersion (PMD) in nonreturn-to-zero (NRZ) intensity-modulated optical-fiber transmission systems. A PMD can lead to severe distortions in the received electrical signal and is a key limiter for the development of high-bit-rate transmission over currently used fibers. In order to reduce the distortions due to a PMD, the performance of symbol-by-symbol maximum a posteriori (sbs-MAP) soft-in/soft-out (SISO) decoders is studied. The SISO algorithms are adapted to the noise statistics of the optical channel where the photo detector leads to a non-Gaussian signal-dependent noise at the receiver side. The modified SISO algorithms are successfully employed for turbo equalization and results show that iterative (turbo) equalization and decoding for the compensation of a PMD can lead to a tremendous reduction in the bit error ratio (BER). Moreover, it is shown that, due to the robustness of mutual information, the extrinsic information transfer (EXIT) chart can be applied for the design of iterative receivers in optical transmission systems even with a non-Gaussian noise.     

Nonlinear effects in LMS adaptive equalizers

An adaptive transversal equalizer based on the least-mean-square (LMS) algorithm, operating in an environment with a temporally correlated interference, can exhibit better steady-state mean-square-error (MSE) performance than the corresponding Wiener filter. This phenomenon is a result of the nonlinear nature of the LMS algorithm and is obscured by traditional analysis approaches that utilize the independence assumption (current filter weight vector assumed to be statistically independent of the current data vector). To analyze this equalizer problem, we use a transfer function approach to develop approximate analytical expressions of the LMS MSE for sinusoidal and autoregressive interference processes. We demonstrate that the degree to which LMS may outperform the corresponding Wiener filter is dependent on system parameters such as signal-to-noise ratio (SNR), signal-to-interference ratio (SIR), equalizer length, and the step-size parameter     

Low complexity adaptation for SISO channel shortening equalizers

Since the days of Digital Subscriber Links (DSL), time domain equalizers (TEQ's) have been used to combat time dispersive channels in Multicarrier Systems. In this paper, we propose computationally inexpensive techniques to recompute TEQ weights in the presence of changes in the channel, especially over fast fading channels. The techniques use no extra information except the perturbation to the channel itself, and provide excellent approximations to the new TEQ weights. Adaptation methods for two existing Channel shortening algorithms are proposed and their performance over randomly varying, randomly perturbed channels is studied. The proposed adaptation techniques are shown to perform admirably well for small changes in channels for OFDM systems.     

Integrated transversal equalizers in high-speed fiber-optic systems

Intersymbol interference (ISI) caused by intermodal dispersion in multimode fibers is the major limiting factor in the achievable data rate or transmission distance in high-speed multimode fiber-optic links for local area networks applications. Compared with optical-domain and other electrical-domain dispersion compensation methods, equalization with transversal filters based on distributed circuit techniques presents a cost-effective and low-power solution. The design of integrated distributed transversal equalizers is described in detail with focus on delay lines and gain stages. This seven-tap distributed transversal equalizer prototype has been implemented in a commercial 0.18-/spl mu/m SiGe BiCMOS process for 10-Gb/s multimode fiber-optic links. A seven-tap distributed transversal equalizer reduces the ISI of a 10-Gb/s signal after 800 m of 50-/spl mu/m multimode fiber from 5 to 1.38 dB, and improves the bit-error rate from about 10/sup -5/ to less than 10/sup -12/.