Adaptive Frequency-domain Equalization Research Articles

Iterative adaptive frequency-domain equalization based on sliding window strategy over time-varying underwater acoustic channels.

This letter provides a novel iterative adaptive frequency-domain equalization for time-varying underwater acoustic (UWA) channels. The proposed scheme adopts a modified frequency-domain block least mean square algorithm to update the filter weights. A sliding window strategy is developed to deal with the rapid time-varying characteristics of UWA channels. The proposed method enhances the performance through an iterative structure. Experimental results show that the bit error rates of the proposed method can be one order of magnitude lower than those of conventional schemes.

A robust ICI suppression based on an adaptive equalizer for very fast time-varying channels in LTE-R systems

High-speed railway communication implemented based on Long-Term Evolution-Railway (LTE-R) Platform has strict requirements for quality of services to support high data-rate transmission for numerous mobile users. In such environment, there often exists inter-carrier interference. In this paper, we exploit a robust channel estimation method in the time domain for very fast time-varying LTE-railway channels, and then, we propose an effective and adaptive frequency-domain equalizer that can offer a tradeoff between performance and computational complexity. The simulation results show the robustness of our proposed method compared with previous ones. The computational complexity of the proposed method retain at a decent number by exploiting specified properties of channel matrices.

Multi-level quantization and blind equalization based direct transmission method of digital baseband signal

The direct transmission of digital baseband signals has practical significance in the field of Ethernet terminal connection, high-speed digital communication, data transmission of various types of information peripherals. The signal amplitude gradually decays while the transmission distance increases. Also the attenuation is proportional to the signal frequency, resulting in signal distortion and receiving error. It is a common method for digital baseband signal transmission to use pre-emphasis chip and equalizer chip to improve the transmission quality with a wide range of mature applications. This paper describes a new type of digital signal transmission method, as the receiver using analog-to-digital converter, instead of equalizer chip, to achieve the multi-level quantization of receiving time-domain data waveform. The waveform of the transmitted digital high and low level signal is sampled into multi-bit values. Then, the paper realizes adaptive frequency domain equalization based on soft threshold and makes use of multi-level quantization soft information for error correction. Error correcting code is mainly used to correct the error caused by the channel bandwidth limit, external noise or interference in the process of data transmission, so as to improve the stability and reliability of the transmission. The paper uses the two-stage error correcting codec system based on both Turbo and BCH coding, to achieve the high performance of Turbo code, and good characters of respond time and complexity. The transmitter outputs 12.5 MHz pseudo-random sequence through a 199.93 meter unshielded balanced twisted pair transmission medium. And the receiver circuit using a 62.5MSPS analog-to-digital converter over-samples the waveform to 8-level quantity. The output error of a 65536 bit pseudo-random sequence is less than 8 bits, and the error correction can be further improved by 8b-10b codec. Compared with the traditional pre-emphasis and balanced interface ICs connection, the method described in this article has the advantages of longer transmission distance, better flexibility and wider scope of use.

Adaptive Frequency-Domain Equalization in Mode-Division Multiplexing Systems

Long-haul mode-division multiplexing (MDM) employs adaptive multi-input multi-output (MIMO) equalization to compensate for modal crosstalk and modal dispersion. MDM systems must typically use MIMO frequency-domain equalization (FDE) to minimize computational complexity, in contrast to polarization-division-multiplexed systems in single-mode fiber, where time-domain equalization (TDE) has low complexity and is often employed to compensate for polarization effects. We study two adaptive algorithms for MIMO FDE: least mean squares (LMS) and recursive least squares (RLS). We analyze tradeoffs between computational complexity, cyclic prefix efficiency, adaptation time and output symbol-error ratio (SER), and the impact of channel group delay spread and fast Fourier transform (FFT) block length on these. Using FDE, computational complexity increases sublinearly with the number of modes, in contrast to TDE. Adaptation to an initially unknown fiber can be achieved in ~3-5 μs using RLS or ~15-25 μs using LMS in fibers supporting 6-30 modes. As compared to LMS, RLS achieves faster adaptation, higher cyclic prefix efficiency, lower SER, and greater tolerance to mode-dependent loss, but at the cost of higher complexity per FFT block. To ensure low computational complexity and fast adaptation in an MDM system, a low overall group delay spread is required. This is achieved here by a family of graded-index graded depressed-cladding fibers in which the uncoupled group delay spread decreases with an increasing number of modes, in concert with strong mode coupling.

MIMO Signal Processing for Mode-Division Multiplexing: An overview of channel models and signal processing architectures

We present the fundamentals of multiple-input, multiple-output (MIMO) signal processing for mode-division multiplexing (MDM) in multimode fiber (MMF). As an introduction, we review current long-haul optical transmission systems and how continued traffic growth motivates study of new methods to increase transmission capacity per fiber. We describe the key characteristics of MIMO channels in MMF, contrasting these with wireless MIMO channels. We review MMF channel models, the statistics derived from them, and their implications for MDM system performance and complexity. We show that optimizing performance and complexity requires management of channel parameters-particularly group delay (GD) spread and mode-dependent loss and gain-by design of transmission fibers and optical amplifiers, and by control of mode coupling along the link. We describe a family of fibers optimized for low GD spread, which decreases with an increasing number of modes. We compare the performance and complexity of candidate MIMO signal processing architectures in a representative long-haul system design, and show that programmable frequency-domain equalization (FDE) of chromatic dispersion (CD) and adaptive FDE of modal dispersion (MD) is an attractive combination. We review two major algorithms for adaptive FDE of MD-least mean squares (LMS) and recursive least squares (RLS)-and analyze their complexity, throughput efficiency, and convergence time. We demonstrate that, with careful physical link design and judicious choice of signal processing architectures, it is possible to overcome MIMO signal processing challenges in MDM systems.

Steepest-descent method-based adaptive frequency domain equalizer in coherent optical orthogonal frequency division multiplexing with quadrature phase shift keying modulation

An adaptive frequency domain equalizer (A-FDE) in quadrature phase shift keying-coherent optical-orthogonal frequency division multiplexing (QPSK-CO-OFDM) system is proposed in this paper. A-FDE uses steepest descent method to search the optimal equalization parameters. And through applying the adaptive control factor (ACF) to monitor the state of A-FDE, the interference from phase noise (PN) and chromatic dispersion (CD) can be mitigated. The numerical simulation shows that the performance of A-FDE has a remarkable improvement on combating PN and CD comparing with the conventional decision-directed equalizer (DDE). And the A-FDE can achieve the forward-error-correction (FEC) threshold in noisier scenario. Furthermore, because the calculation of ACF only bases on valid data instead of pilot symbols (PSs), A-FDE has low PS overhead merit.

Unique-Word Based Single Carrier Systems with Adaptive Frequency Domain Equalization

Unique-Word Based Single Carrier Systems with Adaptive Frequency Domain Equalization

Adaptive Frequency-Domain Equalization for Mode-Division Multiplexed Transmission

We propose single-carrier adaptive frequency-domain equalization (SC-FDE) for mode-division multiplexed transmission. A two-mode fiber long haul transmission system is simulated. The performances of both FDE and time-domain equalization (TDE) are verified and compared. The FDE approach reduces the computational complexity significantly compared to the TDE while maintaining the same performance. For a two-mode transmission of 2000 km, FDE decreases the complexity by a factor of as much as 77 compared with TDE at the expense of a large memory length of 2048 that may require higher hardware complexity. The dynamic response of the adaptive equalizer is simulated by using a mode scrambler. FDE achieves the same tracking speed as TDE.

Adaptive frequency-domain equalization for the transmission of the fundamental mode in a few-mode fiber

We propose and experimentally demonstrate single-carrier adaptive frequency-domain equalization (SC-FDE) to mitigate multipath interference (MPI) for the transmission of the fundamental mode in a few-mode fiber. The FDE approach reduces computational complexity significantly compared to the time-domain equalization (TDE) approach while maintaining the same performance. Both FDE and TDE methods are evaluated by simulating long-haul fundamental-mode transmission using a few-mode fiber. For the fundamental mode operation, the required tap length of the equalizer depends on the differential mode group delay (DMGD) of a single span rather than DMGD of the entire link.

Adaptive Frequency-Domain Equalization with Narrowband Interference Suppression

Frequency-domain equalization (FDE) is an effective technique that exhibits the property of relatively low complexity which grows with increasing the number of symbols of dispersion in multipath propagation environments for broadband wireless communications compared with the conventional time-domain equalization. However, in practical broadband wireless communications, there exists not only multipath but also narrowband interference (NBI). The conventional FDE methods do not consider NBI and their performance degrades obviously in such case. In this paper, we propose a new optimization criterion which can effectively suppress NBI to obtain the maximum decision signal-to-noise ratio. The proposed scheme employs a conventional adaptive algorithm such as least-mean-square or recursive-least-square and operates in the spatial-frequency domain, which is concerned with the use of FDE and space diversity within block transmission schemes jointly. The simulation results show that the proposed schemes have better error-rate performance with low complexity and can be used even in the presence of strong NBI, compared to other existing adaptive FDE algorithms.

Adaptive frequency-domain equalization in digital coherent optical receivers

We propose a novel frequency-domain adaptive equalizer in digital coherent optical receivers, which can reduce computational complexity of the conventional time-domain adaptive equalizer based on finite-impulse-response (FIR) filters. The proposed equalizer can operate on the input sequence sampled by free-running analog-to-digital converters (ADCs) at the rate of two samples per symbol; therefore, the arbitrary initial sampling phase of ADCs can be adjusted so that the best symbol-spaced sequence is produced. The equalizer can also be configured in the butterfly structure, which enables demultiplexing of polarization tributaries apart from equalization of linear transmission impairments. The performance of the proposed equalization scheme is verified by 40-Gbits/s dual-polarization quadrature phase-shift keying (QPSK) transmission experiments.

Efficient design of block adaptive equalization and diversity combining for space-time block-coded single-carrier systems

In this paper, a weighted space-time block-coding (STBC)-like matrix-wise block adaptive frequency-domain equalization (WSB-FDE), which has a flexibility over the STBC-like matrix-wise block length as compared to a normalized least-mean-square (NLMS)-FDE and a recursive-least-square (RLS)-FDE, is proposed for the cyclic-prefixed STBC single-carrier systems equipped with a diversity combining. In the WSB-FDE, the STBC-like matrix-wise block is first formulated from received blocks. The correction terms of the equalizer coefficients in each block are then updated so as to minimize a weighted squared-norm of the a posteriori error vector for the formulated block. Moreover, a square-root adaptive algorithm based on an unitary Givens rotation is proposed to achieve the numerical stability and computational efficiency in update procedure of the WSB-FDE. The theoretic convergence and the steady-state excess mean-square error (EMSE) of the WSB-FDE are analyzed, where it is observed that the EMSE decreases as the STBC-like matrix-wise block length and the number of antenna increase. Finally, the performance evaluation shows in a typical urban (TU) channel that the bit-error-rate (BER) performance of the WSB-FDE is superior to that of the RLS-FDE as the STBC-like matrix-wise block length increases.

A Weighted Element-Wise Block Adaptive Frequency-Domain Equalization

In this paper, a weighted element-wise block adaptive frequency-domain equalization (WEB-FDE) is proposed for a single-carrier system with the cyclic-prefix. In the WEB-FDE, the one-tap equalizer corresponding to a frequency-bin first preserves input DFT elements (element-wise block). Its coefficient in each block is then calculated by minimizing a weighted squared norm of the a posteriori error. Simulation results in a time-varying typical urban (TU) channel show that the bit-error-rate (BER) performance of the WEB-FDE outperform that of the normalized least-mean-square (NLMS)-FDE and recursive-least-square (RLS)-FDE.

Channel estimation for adaptive frequency-domain equalization

Frequency-domain equalization (FDE) is an effective technique for high-rate wireless communications because of its reduced complexity compared to conventional time-domain equalization (TDE). In this paper, we consider adaptive FDE for single-carrier (SC) systems with explicit channel and noise-power estimation. The channel response is estimated in the frequency domain following two different approaches. The first operates independently on each frequency bin while the second exploits the fading correlation across the signal bandwidth. Least-mean-square (LMS) and recursive-least-square (RLS) algorithms are employed to update the channel estimates. The noise power is estimated using a low-complexity algorithm based on ad hoc reasoning. Compared to other existing receivers employing adaptive FDE, the proposed schemes have better error-rate performance and can be used even in the presence of relatively fast fading.

Adaptive frequency-domain equalization for single-carrier multiple-input multiple-output wireless transmissions

Channel estimation and tracking pose real problems in broadband single-carrier wireless communication systems employing multiple transmit and receive antennas. An alternative to estimating the channel is to adaptively equalize the received symbols. Several adaptive equalization solutions have been researched for systems operating in the time domain. However, these solutions tend to be computationally intensive. A low-complexity alternative is to adaptively equalize the received message in the frequency domain. In this paper, we present an adaptive frequency-domain equalization (FDE) algorithm for implementation in single-carrier (SC) multiple-input multiple-output (MIMO) systems. Furthermore, we outline a novel method of reducing the overhead required to train the proposed equalizer. Finally, we address the issues of complexity and training sequence design. Other computationally efficient adaptive FDE algorithms for use in SC systems employing single transmit and receive antennas, receive diversity, or space-time block codes (STBC) can be found in the literature. However, the algorithm detailed in this paper can be implemented in STBC systems as well as in broadband spatial multiplexing systems, making it suitable for use in high data rate MIMO applications.

Adaptive frequency-domain equalization and diversity combining for broadband wireless communications

We introduce a new kind of adaptive equalizer that operates in the spatial-frequency domain and uses either least mean square (LMS) or recursive least squares (RLS) adaptive processing. We simulate the equalizer's performance in an 8-Mb/s quaternary phase-shift keying (QPSK) link over a frequency-selective Rayleigh fading multipath channel with /spl sim/3 /spl mu/s RMS delay spread, corresponding to 60 symbols of dispersion. With the RLS algorithm and two diversity branches, our results show rapid convergence and channel tracking for a range of mobile speeds (up to /spl sim/100 mi/h). With a mobile speed of 40 mi/h, for example, the equalizer achieves an average bit error rate (BER) of 10/sup -4/ at a signal-to-noise ratio (SNR) of 15 dB, falling short of optimum linear receiver performance by about 4 dB. Moreover, it requires only /spl sim/50 complex operations per detected bit, i.e., /spl sim/400 M operations per second, which is close to achievable with state-of-the-art digital signal processing technology. An equivalent time-domain equalizer, if it converged at all, would require orders-of-magnitude more processing.