On Optimal Detection of Band-Limited PAM Signals with Excess Bandwidth

PAM data transmission receivers accomplishing maximum likelihood sequence detection (MLSD) usually require a matched filter prefilter, a sampler at the symbol rate, and a Viterbi algorithm detector. When the channel is unknown or slowly changing, one must use an adaptive matched filter prefilter. We examine an alternative optimum receiver whose optimality is independent of the matched filter prefilter and which is applicable when the channel is effectively band-limited. The sampler in the proposed receiver operates at a rate faster than the data symbol rate, enabling one to replace the matched filter by a fixed low-pass filter and still ensure that the maximum likelihood detector is supplied with a set of sufficient statistics. It is shown that the matched filter is incorporated within a modified Viterbi detector without increasing the number of states in the algorithm, although the Viterbi detector must perform computations at approximately twice the usual rate. Simulations support the optimality of the new receiver and quantitatively indicate the degradation in performance experienced by some adaptive receivers previously proposed.     

Bidirectional iterative ISI canceller for high-rate DSSS/CCK communications

This paper proposes a new RAKE receiver incorporated with a bidirectional iterative intersymbol interference (ISI) canceller in order to reinforce multipath robustness of high-rate direct-sequence spread-spectrum complementary code keying (DSSS/CCK) systems. The proposed RAKE receiver first combines multipath signal components through a channel matched filter (CMF) and removes postcursor-ISI by employing a codeword decision feedback equalizer (DFE). Then, a CCK codeword detector tentatively determines the current CCK codeword symbol and reuses it to subtract precursor-ISI from the previous symbol. Therefore, the ultimate symbol decision is made using the delayed signal with both postcursor-ISI and precursor-ISI cancelled. The detection performance can be more improved through an iterative refinement processing between the postcursor and the precursor components. Simulation results exhibit a significantly improved error rate performance of the proposed receiver compared with that of the legacy RAKE receiver employing only a postcursor DFE. The additional cost for realization of the proposed receiver is one symbol decision delay and reuse complexity of the DFE and the codeword detector.     

Joint MAP equalization and channel estimation forfrequency-selective and frequency-flat fast-fading channels

This paper presents a new fractionally-spaced maximum a posteriori (MAP) equalizer for data transmission over frequency-selective fading channels. The technique is applicable to any standard modulation technique. The MAP equalizer uses an expanded hypothesis trellis for the purpose of joint channel estimation and equalization. The fading channel is estimated by coupling minimum mean square error techniques with the (fixed size) expanded trellis. The new MAP equalizer is also presented in an iterative (turbo) receiver structure. Both uncoded and conventionally coded systems (including iterative processing) are studied. Even on frequency-flat fading channels, the proposed receiver outperforms conventional techniques. Simulations demonstrate the performance of the proposed equalizer     

The Estimate Feedback Equalizer: A Suboptimum Nonlinear Receiver

A recursive nonlinear equalizer has been developed. The Bayes estimation theory has been used to obtain an unrealizable nonlinear minimum mean-square error (MMSE) receiver for the reception of binary pulse-amplitude-modulation signals in the presence of intersymbol interference and noise. A realizable approximation to the Bayes structure has been derived as the combination of a matched filter and a nonlinear recursive equalizer structure. The equalizer has been made adaptive using a new algorithm that defines and maintains the time frame of reference and is constrained so that the equalizer's parameters always move toward their optimum values. Computer simulations have been used to demonstrate the properties of the estimate feedback equalizer (EFE) and to compare its performance to that of presently known equalizers.     

A robust noncoherent equalizer receiver for fading channels with short memory .I. Basic structure

Traditional equalizers are very sensitive to carrier frequency offsets between the transmitter and receiver. Coherent receivers with frequency estimation algorithms can remove the offset to prevent the equalizer breakdown, but with a penalty in receiver complexity. On the other hand, noncoherent receivers such as differential detectors are inherently robust to the frequency offsets but cannot employ standard equalization techniques due to their nonlinear front-end. We introduce a simple noncoherent equalizer receiver structure for fading channel environments with short memory (up to two-bit intervals). The receiver consists of a whitened matched filter followed by a differential detector and a maximum likelihood sequence estimation (MLSE) equalizer. We examine the performance of this noncoherent equalizer by both analysis and simulation. It is shown that despite the simplicity, this receiver structure is capable of significant performance improvement as compared to an ordinary differential detector while operating with receiver frequency offsets two orders of magnitude greater than a traditional MLSE equalizer. This structure offers an attractive solution for high-bit-rate cordless transmission systems such as Digital Enhanced Cordless Telecommunications (DECT) that use simple noncoherent receivers whose performance can be constrained by channel dispersion. Using DECT as a case study, we show that the equalizer's performance limits are caused by the receiver nonlinearity and can be improved by adaptation of this nonlinearity to channel conditions.     

Digital Transmission Performance on Fading Dispersive Diversity Channels

The reception and detection of a single digit under known channel conditions are investigated. The probability of error for an optimum one-shot receiver instantaneously matched to the channel state is averaged over an ensemble of dispersive diversity channels. The average probability of error as a function of energy to noise ratio is found to be solely dependent on the ratio of rms dispersion width to data symbol width. For these dispersive channels an implicit diversity effect is qualitatively explained in terms of eigenvalues that depend on the ensemble statistic. The one-shot receiver performance provides a bound for practical receivers. In a comparison with a decision feedback equalizer, it is shown that on moderately dispersive channels the equalizer nearly achieves optimum one-shot performance. Since an adaptive version of this equalizer exists, this means data transmission on slowly fading channels is possible at rates above the natural rate suggested by the channel dispersion spread without bandwidth expansion and with small intersymbol interference penalty. The use of one-shot receiver performance curves can also be used as estimates of equalizer performance in situations where computation of the latter is impractical.     

A 50-MHz standard CMOS pulse equalizer for hard disk read channels

A novel pulse equalizer for hard disk systems is discussed. Opposed to classical realizations, it is full CMOS while operating at 50 MHz cutoff frequency. It is explained how the equalizer can be extended with a selective boost of 13 dB around the cutoff frequency for pulse slimming. The equalizer is a gm-C seventh-order, 0.05° equiripple-on-the-phase low-pass filter. It is made out of biquads with matched integrating nodes. The inaccuracies are compensated with a novel tuning system. This guarantees a ripple on the group delay of 2%. The results are confirmed on 0.7-μm CMOS silicon     

Rake-MMSE-equalizer performance for UWB

The performance of a joint rake and minimum mean square error (MMSE) equalizer receiver for high data rate ultra-wideband communications is studied in this paper. The proposed receiver combats inter-symbol interference by taking advantage of the rake and equalizer structure. The receiver performance is investigated using a semianalytical approach and Monte-Carlo simulation. The effects of the number of rake fingers and equalizer taps on the error performance are examined.     

Equalization for DS-UWB Systems—Part I: BPSK Modulation

Ultra-wideband wireless transmission has attracted considerable attention both in academia and industry. For high-rate and short-range transmission, direct sequence based ultra-wideband (DS-UWB) systems are a strong contender for consumer market applications. Due to the large transmission bandwidth, the UWB channel is characterized by a long root-mean-square delay spread and the RAKE receiver cannot always overcome the resulting intersymbol interference. We therefore study equalization for DS-UWB systems. This paper is comprised of two parts. In this first part, we consider DS-UWB with binary phase-shift keying (BPSK) modulation, which is the mandatory transmission mode for DS-UWB systems promoted by the UWB Forum industry alliance. We derive matched filter bounds for optimum equalization taking into account practical constraints like receiver filtering, sampling, and the number of RAKE fingers when RAKE preprocessing is applied at the receiver. Our results show that chip-rate sampling is sufficient for close-to-optimum performance. For analysis of suboptimum equalization strategies we further study the distribution of the zeros of the channel transfer function including RAKE combining. Our findings suggest that linear equalization is well suited for the lower data rate modes of DS-UWB systems, whereas nonlinear equalization is preferable for high-data rate modes. Moreover, we devise equalization schemes with widely linear processing, which improve performance while not increasing equalizer complexity. Simulation and numerical results confirm the significance of our analysis and equalizer designs and show that low-complexity (widely) linear and nonlinear equalizers perform close to the pertinent matched filter bound limit.     

A Hardware Efficient Passband Equalizer Structure for Data Transmission

A passband digital equalizer is proposed which combines the functions of bandpass filtering and phase splitting with that of adaptive equalization. The new equalizer also provides the in-phase and quadrature outputs required for demodulation. Although input sampling is required at several times the symbol rate (for voice-grade channel applications), outputs need be computed only once per baud. This structure economizes either on front-end analog (phase splitter) filtering or on the number of multiplications required in a digital implementation of a phase splitter and an equalizer. The performance of a receiver incorporating the new equalizer is compared, experimentally, with a receiver using a conventional fractionally spaced (T/2) equalizer.     

An Adjustable Narrow Band Microwave Delay Equalizer

A simple low loss microwave delay equalizer for the delay equalization of narrow band microwave bandpass filters has been explored. This equalizer is quite small and does not require the use of additional components such as circulators or hybrids. It exhibits a reflection coefficient of less than 1 percent and possesses two very valuable and convenient features: a continuous adjustment of the delay shape and of the center frequency. The structure is analyzed theoretically, an equivalent circuit is derived, and expressions for both delay and loss are given. Also presented are design data and experimental results concerning the actual delay equalization of a bandpass filter and the temperature behavior of the equalizer and the filter-equalizer combination.     

High-speed CMOS continuous-time complex graphic equalizer formagnetic recording

A high-speed continuous-time CMOS analog adaptive equalizer for use in magnetic recording read channels is presented. The equalizer is implemented as the summation of several bandpass filters covering different frequency bands as in a graphic equalizer. The outputs from each filter are weighted by a complex coefficient and summed, which results in a linear combiner structure guaranteed to converge under least mean square (LMS) adaptation. System-level simulations of our “complex graphic equalizer (CGE)” show that its performance is comparable to that of a ten-tap finite impulse response (FIR) equalizer following a fourth-order low-pass filter when tested with two different sequence detectors: EPR4-MLSD and fixed delay tree search with decision feedback (FDTS/DF). A five-band tunable CGE has been fabricated using a 0.8-μm CMOS technology. The highest band of the fabricated CGE was centered at 80 MHz (corresponding to channel data rate of about 200 Msymbols/s). Measured dynamic range was 68 dB, and measured total harmonic distortion was only -75 dB while consuming 97 mW at 3.3 V. The measured CGE performance agreed within 0.2 dB with the simulation results for an FDTS/DF system with an ideal CGE operating at 2.5 user bits/PW50     

Turbo Equalization with Prediction and Iterative Estimation of Time-Varying Frequency-Selective Channels

Turbo equalization that cooperates with channel prediction and iterative channel estimation is investigated for mobile wireless communications. Frames of information bits are encoded, interleaved, and mapped to symbols for transmission over time-varying frequency-selective fading channels. At the receiver, the Turbo equalizer consists of a maximum a posteriori probability equalizer/demapper and a soft-input soft-output maximum a posteriori probability decoder. With initial channel estimates and sparse pilot insertion across a number of frames, the receiver predicts the channel of the current frame. The effect of error propagation of channel prediction is mitigated by the de-interleaver that is embedded in the Turbo equalizer. The predicted and interpolated channel is refined through a channel estimator that uses the soft estimates of data symbols at each Turbo iteration. Due to the bandlimiting feature of channel variation, the channel estimation error can be smoothed by low-pass filters that follow the channel estimator. Simulation results show that incorporating Turbo equalization with channel prediction and iterative channel estimation can combat time- and frequency-selective fading and improve reception performance.     

Multiuser detection in a horizontal underwater acoustic channelusing array observations

We present a multisensor, multiuser receiver that is capable of operating in an underwater acoustic channel with severe multipath. For each active user, the receiver consists of a multi-input, single-output array processing filter followed by a single-channel adaptive equalizer. The array processing filter is chosen to maximize an averaged performance metric which measures reduction in the interference from multiple asynchronous cochannel users and the reduction in intersymbol interference caused by time spreading of the transmitted signal. The single-channel adaptive equalizer that follows the array processing filter eliminates the remaining intersymbol interference prior to hard symbol decisions. The division of labor between the array processing filter and single-channel equalizer reduces receiver complexity by allowing the array processing filter weights to be based on the fixed deterministic channel component and the single-channel equalizer to be based on the stochastic channel component. Receiver performance is demonstrated using data obtained from two shallow-water acoustic channels where two cochannel users are transmitting in shallow water at 18 and 30 nautical miles from the receiver array     

A robust noncoherent equalizer receiver for fading channels with short memory . II. Modified structure

For pt. I see ibid., vol.5, no.5, p.1040-54 (2002). In Part I, we introduced a robust noncoherent maximum likelihood sequence estimation (MLSE) equalizer receiver structure applicable to radio channels with impulse responses spanning less than two bit intervals. The distinct characteristic of this receiver was its robustness to carrier frequency offsets. However, due to the differential operation prior to the MLSE equalization, we observed some performance degradation, resulting in a delay spread range significantly smaller than an equivalent coherent MLSE equalizer. We propose techniques to significantly improve the performance of the noncoherent equalizer by using a second, complementary differential processor. The performance assessment of the new receiver is presented. In particular, using the Digital Enhanced Cordless Telecommunications system as an example, it is shown that the modified receiver's dispersive channel operation range is almost twice as much as the basic structure, with a multipath diversity gain comparable to a coherent equalizer receiver. On the other hand, unlike coherent structures, it retains low sensitivity to both frequency offsets and modulation index drifts. Finally, we introduce an approach to further extend the receiver's frequency offset tolerance to that of a standard differential detector receiver.     

Improved spatial-temporal equalization for EDGE: a fastselective-direction MMSE timing recovery algorithm and two-stagesoft-output equalizer

The radio interface EDGE (Enhanced Data rates for Global Evolution) is currently being standardized as an evolutionary path from GSM and TDMA-IS136 for third-generation high-speed data wireless systems. For the EDGE system with multiple antennas, spatial-temporal equalization (STE) can reduce intersymbol interference and co-channel interference, thereby increasing the capacity and range. In this paper, we propose two new techniques to improve the performance of a previously proposed STE: a fast timing recovery algorithm for a selective time-reversal equalizer and a two-stage soft-output equalizer. The new timing recovery algorithm determines the estimated burst timing and processing direction by computing the minimum mean-square error (MMSE) for decision feedback equalizers in both the forward and reverse time directions. The two-stage soft-output equalizer is the cascade of a delayed decision-feedback sequence estimator (DDFSE) and maximum a posteriori probability (MAP) estimator. The DDFSE provides better noise variance estimation and channel truncation for the following MAP. The performance of the new STE is evaluated for the EDGE. At 10% block error rate, the two-branch receiver requires a 3-7-dB lower signal-to-interference ratio (SIR) than the previous approach. Compared with the one-branch receiver, the two-branch receiver requires a 4-dB lower SNR with noise only, and a 10-27-dB lower SIR with a single interferer     

Performance analysis of linear MIMO equalizers for multitone DS/SS systems in multipath channels

In [11] the combination of multitone modulation with direct sequence spectrum spreading has been introduced. The performance of a correlation receiver has been evaluated for a multipath channel. In [12] the analysis has been extended to the presence of a multiple access interference. In the present paper we analyze the equalization problem of such a system for a single user scenario. In order to understand the potential of the system we first investigate the steady-state behavior of the MIMO equalizer for an MMSE design. The investigation is carried out for an equalizer following a receiver made of a bank of filters matched to both the symbol shape and the channel, which is a two-path channel. Assuming BPSK symbols an exact expression of the bit error probability before and after equalization is obtained in the form of an integral by means of the characteristic function method. Next adaptive LMS and RLS structures are proposed. The performance of the RLS algorithm is demonstrated.Part of this work has been presented at ICC '95, Seattle, June 1995.This author would like to thank the Belgian NSF for its financial support.This author is a Research assistant of FRIA.     

Channel modeling and system performance for HomePNA 2.0

The new Home Phoneline Networking Alliance (HomePNA) 2.0 system is an attractive proposition for home networking since it potentially allows transmission rates comparable to those of Ethernet, using the existing installed telephone wiring. However, although the transmission standard is designed to be variable rate (variable symbol rate and bits/symbol), not all combinations are mandatory and it is, therefore, instructive to determine the level of receiver complexity required to handle the optional higher rates. An accurate channel model is devised, characterizing the home phone line network around 7 MHz, which allows the performance of the HomePNA 2.0 physical layer to be evaluated. The very good agreement obtained between the measured and modeled channel responses, in both time and frequency domains, enables a high degree of confidence in the simulation results. Due to the considerable dispersion observed in some home phone line channels, a number of equalizer structures are proposed to improve performance in the receiver. These are compared for each of the two possible symbol rates. Computer simulations show that the performance of the system can be greatly improved at the lower rate with a low complexity equalizer, but at the higher rate, which is not mandatory, a much more complex equalizer is required     

Mitigation of channel estimation error in TR–UWB system based on a novel MMSE equalizer

The time reversal (TR) technique combined with the ultra-wideband (UWB) system offers a new potential for decreasing the cost and complexity of the UWB receivers. In spite of TR–UWB's good performance in perfect channel state information (CSI), it is very sensitive to the channel estimation error. The effect of channel imperfection on the TR–UWB system is considered in this paper. At first, based on a minimum mean square error (MMSE) equalizer receiver, a prefilter is calculated in closed form to improve the performance of the TR–UWB system in an imperfect CSI scenario. Furthermore, for comparison purposes, a similar calculation for prefilter is carried out based on a simple matched filter (MF) receiver. Then, in order to improve the MF receiver performance, a two-stage iteration-based algorithm is developed. The initial value for this iteration-based improved algorithm is considered to be a prefilter which is calculated in the TR–UWB system with MMSE equalizer. This optimized algorithm causes the channel estimation error in the TR–UWB system to become zero in some steps. Finally, exhaustive simulations are done to demonstrate the performance advantage attained by the improved algorithm.     

Performance of Volterra and MLSD receivers for nonlinearband-limited satellite systems

This paper evaluates the performance of Volterra equalizers and maximum-likelihood sequence detection (MLSD) receivers for compensation of signal distortion in nonlinear band-limited satellite systems. In addition, the performance of a receiver with a fractionally-spaced equalizer followed by a Volterra equalizer is studied (FSE-Volterra equalizer). For the equalizers, adaptation of the equalizer weights is considered including a multiple-step LMS algorithm which improves the convergence characteristics. Two MLSD receiver structures are considered: the optimum receiver consisting of a matched-filter bank followed by a Viterbi (1967) detector and a suboptimum receiver consisting of a single receiver filter followed by a Viterbi detector. The performance of the MLSD receivers is then compared to that of the equalizers