Fractionally-spaced Equalizer Research Articles

Frame-rate Adaptive Fractionally-Spaced Equalization Enabled High-throughput Optical Camera Communication

Frame-rate Adaptive Fractionally-Spaced Equalization Enabled High-throughput Optical Camera Communication

Fractionally-Spaced Equalizers as Clock and Data Recovery Loops

Fractionally-Spaced Equalizers as Clock and Data Recovery Loops

BER analysis of an optimum MIMO linear receiver in optical SDM systems with mode-dependent loss.

Multiple-input multiple-output (MIMO) receivers designed to optimize the minimum mean square error (MMSE) are a common choice in coherent optical communication systems based on spatial division multiplexing (SDM). This kind of receivers naturally integrate both MIMO equalization and matched filtering functions. However, when the optical channel exhibits significant mode-dependent loss (MDL) and/or mode-dependent gain (MDG), the impact of inter-symbol interference (ISI) and crosstalk that arise, even using an ideal MIMO MMSE linear receiver, is barely analyzed. Moreover, due to the random nature of the MDL/MDG model, the resulting ISI, crosstalk, and bit error rate (BER) also become random variables and, hence the system performance is more unpredictable. In this paper, we first evaluate the residual distortion (ISI and crosstalk) after the MIMO receiver and then we study the validity of assuming it as an additional Gaussian noise term independent of the channel noise. Next, the probability density distribution (PDF) of the BER is analyzed, from both an analytical perspective and numerical simulations. For the latter, we use a single-carrier 2-PAM (pulse amplitude modulation) system, with pulse shaping, and the MIMO MMSE receiver implementation by means of a MIMO fractionally-spaced equalizer (FSE). We carry out simulations of the system under different conditions of MDL/MDG level and signal to noise ratio (SNR), measured at the receiver input. Additionally, we address possible fits of the BER PDF to known closed-form distributions, among which the Generalized Extreme Value (GEV) family of distributions is selected, and polynomial functions are proposed that relate the system parameters with the GEV PDF parameters. Finally, we present contour maps of BER according to a giving target of system outage probability (OP) that depend on the MDL/MDG and SNR conditions.

FBMC Receiver Design and Analysis for Medium and Large Scale Antenna Systems

In this paper, we design receivers for filter bank multicarrier-based (FBMC-based) massive MIMO considering practical aspects such as channel estimation and equalization. In particular, we propose a spectrally efficient pilot structure and a channel estimation technique in the uplink to jointly estimate all the users’ channel impulse responses. We mathematically analyze our proposed channel estimator and find the statistics of the channel estimation errors. These statistics are incorporated into our proposed equalizers to deal with the imperfect channel state information (CSI) effect. We revisit the channel equalization problem for FBMC-based massive MIMO, address the shortcomings of the existing equalizers in the literature, and make them more applicable to practical scenarios. The proposed receiver in this paper consists of two stages. In the first stage, a linear combining of the received signals at the base station (BS) antennas provides a coarse channel equalization and removes any multiuser interference. In the second stage, a per subcarrier fractionally spaced equalizer (FSE) takes care of any residual distortion of the channel for the user of interest. We propose an FSE design based on the equivalent channel at the linear combiner output. This enables the applicability of our proposed technique to small and/or distributed antenna setups such as cell-free massive MIMO. Finally, the efficacy of the proposed techniques is corroborated through numerical analysis.

Matched Filtering for MIMO Coherent Optical Communications with Mode-Dependent Loss Channels.

The use of digital signal processors (DSP) to equalize coherent optical communication systems based on spatial division multiplexing (SDM) techniques is widespread in current optical receivers. However, most of DSP implementation approaches found in the literature assume a negligible mode-dependent loss (MDL). This paper is focused on the linear multiple-input multiple-output (MIMO) receiver designed to optimize the minimum mean square error (MMSE) for a coherent SDM optical communication system, without previous assumptions on receiver oversampling or analog front-end realizations. The influence of the roll-off factor of a generic pulse-amplitude modulation (PAM) transmitter on system performance is studied as well. As a main result of the proposed approach, the ability of a simple match filter (MF) based MIMO receiver to completely eliminate inter-symbol interference (ISI) and crosstalk for SDM systems under the assumption of negligible MDL is demonstrated. The performance of the linear MIMO fractionally-spaced equalizer (FSE) receiver for an SDM system with a MDL-impaired channel is then evaluated by numerical simulations using novel system performance indicators, in the form of signal to noise and distortion ratio (SNDR) loss, with respect to the case without MDL. System performance improvements by increasing the transmitter roll-off factor are also quantified.

Fractionally Spaced Equalization and Decision Feedback Sequence Detection for Diffusive MC

In this letter, we consider diffusive molecular communication (MC) systems affected by signal-dependent diffusive noise, inter-symbol interference, and external noise. We design linear and nonlinear fractionally-spaced equalization schemes and a detection scheme which combines decision feedback and sequence detection (DFSD). In contrast to the symbol-rate equalization schemes in the MC literature, the proposed equalization and detection schemes exploit multiple samples of the received signal per symbol interval to achieve lower bit error rates (BERs) than existing schemes. The proposed DFSD scheme achieves a BER which is very close to that achieved by maximum likelihood sequence detection, but with lower computational complexity.

Efficient frequency‐domain linear distortion equaliser in faster‐than‐Nyquist systems

Faster-than-Nyquist (FTN) signalling is regarded as a promising technology in satellite communications for the past few years, however, existing inter-symbol interference (ISI) elimination algorithms for FTN signalling cannot eliminate the linear distortion caused by the input-multiplexing and output-multiplexing filters, which are very common in satellite communications. On the strength of the fractionally-spaced equaliser (FSE), the authors propose a precoding-based frequency-domain linear distortion equaliser (PFLDE) to eliminate the above-mentioned linear distortion in FTN systems. On the one hand, by virtue of fast Fourier transform (FFT) and inverse FFT, the proposed PFLDE lends itself naturally to high-throughput parallel architectures, which are quite essential in high throughput satellite communications. On the other hand, the mean square error performance of the proposed PFLDE is superior to that of the existing time-domain FSEs. Furthermore, combining PFLDE with the existing ISI elimination algorithms for FTN signalling, the satisfactory bit error ratio performance can be obtained.

Depth-L Nyquist (M) Filters and Biorthogonal Partners

In the past, Nyquist filters have been studied by many researchers. A pair of filters are said to be biorthogonal partners of each other if their cascade forms a Nyquist filter. The theory and design of traditional biorthogonal partners have been studied extensively. In this paper, we extend these results to depth-L Nyquist filters and biorthogonal partners. Two potential applications of them are discussed in fractionally spaced equalizer (FSE) and filter bank multicarrier (FBMC) systems. Moreover, the necessary and sufficient condition is derived for the existence of an finite impulse response (FIR) depth-L biorthogonal partner. We find out that the existence depends on the cardinality of the largest so-called congruous-zero set. In addition, we will show how to design these filters by using the eigenfilter method. Finally, performance comparisons are carried out to demonstrate the advantage of depth-L biorthogonal partners. It is shown that the depth-L version is more robust against inter-symbol interference (ISI) and timing synchronization error compared to the traditional biorthogonal partner.

A 2$\times$ Blind Oversampling FSE Receiver With Combined Adaptive Equalization and Infinite-Range Timing Recovery

A 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> blind-oversampling, fractionally spaced equalizer (FSE) receiver is presented as an effective way to combine adaptive equalization and timing recovery in a single control loop. To additionally support plesiochronous clocking, the presented work realizes an infinite-range timing recovery using a set of two four-tap FSEs with a 0.5-UI timing offset, only one of which is selected to recover the data. The selection seamlessly alternates between the two, each time a 0.5-UI timing drift occurs. The optimal time to switch the selection is detected by observing the currently adapted FSE tap coefficients and its main cursor position. An equivalent timing recovery loop model is derived. A current-integrating summer and multi-input regenerative latch help the four-tap FSEs and four-tap decision-feedback equalizers (DFEs) achieve low-power dissipation, respectively. A prototype receiver fabricated in a 28-nm CMOS consumes 3.5 pJ/bit and 0.10 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at 9 Gb/s while compensating for a 22-dB channel loss and 100-ppm frequency offset between the transmitted data and blind sampling clocks.

The Relationship Between the Cyclic Wiener Filter and Fractionally Spaced Equalizers

This paper presents a different interpretation of the cyclic Wiener filter (CWF) for digital (in-phase/quadrature) IQ-modulated signals, such as phase-shift keying (PSK) or quadrature amplitude modulations (QAM). We demonstrate that the CWF can be implemented as a multirate filter instead of the frequency-shift (FRESH) filter implementation found in the literature. The multirate implementation consists of a fractionally spaced equalizer (FSE) followed by a pulse shaping filter, thus establishing a direct relationship between the CWF and FSEs. Afterwards, the results from the study are applied to develop a simple blind adaptive algorithms for signal estimation, which are benchmarked against the most common CWF implementation based on FRESH filters.

An Efficient Stabilization Process for Analog Fractionally Spaced Equalizers

An analog fractionally spaced equalizer (FSE) is an efficient solution for high-speed communication system without a clock and data recovery circuit. However, the FSE might become unstable when a sign–sign least mean square tuning algorithm is used, especially when the transmitter pre-distortion is used. Here, an analytical model of the instability is derived, and a low-cost and efficient stabilization process based on dithering is proposed. The analytical instability model is verified in an experimental setup based on a vertical cavity surface emitting laser. Furthermore, it is experimentally demonstrated that in the case of the instability of the FSE, a clear convergence is achieved when applying the proposed stabilization scheme.

Spectral Analysis of Fractionally-Spaced MMSE Equalizers and Stability of the LMS Algorithm

In the communication systems that use a linear modulation scheme for transmission, the fractionally-spaced (FS) samples of the received signal constitute a wide-sense cyclostationary time series. Hence, the standard Fourier transform techniques cannot be used to study the spectral characteristics of the received FS samples or to derive the transfer function (TF) of the corresponding digital minimum mean-square error (MMSE) receiver. In this paper, an analytical expression for the TF of the FS MMSE equalizer is derived, which includes the effects of the continuous-time to discrete-time (C/D) converter used at the receiver front end. Using this TF, the sources of instability of the FS least-mean-square (LMS) algorithm and the effects of the equalizer length and sampling phase on convergence of the LMS algorithm are explained. For stabilization of the FS LMS algorithm, conditions on the front-end C/D converter are provided, such that, when satisfied the LMS algorithm becomes more stable and the learning characteristics of the modified receiver are better than the leaky-FS LMS algorithm. Theoretical results are corroborated by simulations.

Diversity Pulse Shaped Transmission in Ultra-Dense Small Cell Networks

In ultra-dense small cell networks, spatial multiplexing gain is a challenge because of the different propagation conditions. The channels associated with different transmit–receive pairs can be highly correlated due to the: 1) high probability of line-of-sight (LOS) communication between user equipment (UE) and base station (BS) and 2) insufficient spacing between antenna elements at both UE and BS. In this paper, we propose a novel transmission technique titled Diversity Pulse Shaped Transmission (DPST), to enhance the throughput over the correlated multiple-input multiple-output (MIMO) channels in an ultra-dense small cell network. The fundamental of DPST is to shape transmit signals at adjacent antennas with distinct interpolating filters, introducing pulse shaping diversity. In DPST, each antenna transmits its own data stream with a relative deterministic time offset—which must be a fraction of the symbol period—with respect to the adjacent antenna. The delay is interpolated with the pulse shaped signal generating a virtual MIMO channel that benefits from increased diversity from the receiver perspective. To extract the diversity, the receiver must operate in an oversampled domain, and hence, a fractionally spaced equalizer (FSE) is proposed. The joint impact of DPST and FSE helps the receiver to sense a less correlated channel, eventually enhancing the UE's throughput. Moreover, in order to minimize the spatial correlation, we aim to optimize the deterministic fractional delay. Simulation results show that applying DPST to a correlated channel can approximately enhance the UE throughput by 1.93 $\times$ and 3.76 $\times$ in ${\text{2}}\,\times\, {\text{2}}$ and ${\text{4}}\,\times \,{\text{4}}$ MIMO systems, respectively.

Enhanced frequency-domain fractionally spaced equalization for coherent optical transmission system with colored noise

An enhanced minimum mean-square-error (MMSE) frequency-domain (FD) fractionally spaced equalizer (FSE) for polarization demultiplexing is proposed in the presence of colored noise. The 2-norm of the estimated channel matrix and polynomial fitting of equalization coefficients are introduced to mitigate the colored noise without requiring knowledge of the optical and electrical filtering. Simulation results show that ∼3-dB improvement of equalization performance is achieved compared to conventional MMSE FD-FSE in an 8×112-Gbit/s wavelength-division multiplexing polarization-division multiplexing-quadrature phase shift keying transmission system over a 1200-km single mode fiber link.

Design and Analysis of Broadband Amplify-and-Forward Cooperative Systems: A Fractionally-Spaced Sampling Approach

In this paper, we propose novel fractionally-spaced frequency-domain equalizers for the amplify-and-forward cooperative systems. In the proposed equalization schemes, the sampling rate of the received signal remains at least as high as the Nyquist rate within the digital processing chain of the relay node(s), upon which a true fractionally-spaced equalization becomes feasible at the destination. Based on minimum-mean-square-error (MMSE) criterion, different equalization structures (linear and non-linear) are designed, and approximations for their bit error rate (BER) performance are presented. The BER performance of the proposed schemes are further lower bounded through a matched-filter bound (MFB) analysis which provides insight into system design such as optimum power allocation and relay selection strategy. Our results show that, under certain channel realizations and sampling phase errors (that may occur in the relay and destination terminals), the performance of the conventional symbol-spaced cooperative systems reduces to that of no relay scenario. However, the performance of cooperative systems with the proposed fractionally-spaced equalizers is independent of the samplers' phases, and as a result, full benefit of cooperation is retained.

Study of Fractionally Spaced Equalizers for Bit-Patterned Media Recording

Bit-patterned media recording (BPMR) is a promising technology to enhance the areal density (AD) of hard disk drives beyond the limit imposed by the current perpendicular recording technology. Practically, a $T$ -spaced equalizer is employed in a conventional (symbol-rate) BPMR system to shape the overall channel response to a target response before performing the data-detection process, where $T$ is a bit period. Because the BPMR channel response has a large excess bandwidth, we propose to use a fractionally spaced equalizer (FSE) in the oversampled BPMR system so as to improve the system performance. A design of the FSE and its corresponding 1-D and 2-D targets is given. Thus, we compare the performance of the oversampled BPMR system with the symbol-rate one. Results indicate that the oversampled system performs better than the symbol-rate one in terms of bit-error rate (BER). Specifically, at ${\rm BER} = 10^{-4}$ and no media noise, the oversampled system can provide $\sim 1$ dB gain at the ADs of 2 and 2.5 Tb/in $^{2}$ over the symbol-rate system. In addition, we found that the oversampled system is more robust to media noise than the symbol-rate one.

Iterative Block Fractionally Spaced Nonlinear Equalization for Wideband Channels

For a transmission over frequency-selective channels, we propose a fractionally spaced (FS) iterative block decision feedback equalizer (FS-IBDFE) receiver that combines the advantages of FS equalization, nonlinear processing, and frequency-domain (FD) implementation. The contributions of the letter are as follows: 1) the extension of existing FD iterative equalization schemes considering an FS processing; 2) the design of the FD equalizer coefficients minimizing the mean square error at the detection point; and 3) a simple equalizer design procedure where equalization coefficients are computed in closed form, without matrix inversions. As an example, the performance of the proposed scheme is assessed in a Rayleigh fading channel, and it is seen that the FS-IBDFE significantly outperforms the FS linear equalizer, the non-FS IBDFE, and the noise prediction FS FD equalizer.

Fractionally spaced equalization algorithms in 60GHz communication system

Several fractionally spaced equalizers(FSE) which could be used in 60 GHz systems are presented in this paper. For 60 GHz systems, low-power equalization algorithms are favorable. We focus on FSE in both time domain(TD) and frequency domain(FD) in order to meet different complexity requirements of 60 GHz systems. Compared with symbol spaced equalizer(SSE), FSE can relax the requirement of sampling synchronization hardware significantly. Extensive simulation results show that our equalization algorithms not only eliminate ISI efficiently, but are also robust to timing synchronization errors.

Fractionally spaced equalizer based on dynamically varying modulus algorithm for spectrally efficient channel compensation in SC-FDMA based systems

Orthogonal frequency division multiplexing (OFDM) based wireless communication systems are expected to satisfy the thirst for ever increasing demand on higher spectral efficiency. But, OFDM systems suffer from peak to average power ratio (PAPR) and inter carrier interference (ICI) problems. It is observed that when OFDM is used in the uplink, PAPR problem is more severe and the relative mobility of the user equipments with respect to the base station will cause Doppler spread which leads to ICI. One of the solutions to minimize PAPR and ICI is single carrier frequency division multiple access. But there is a tradeoff in spectral efficiency. The main objective of this paper is to evaluate the performance of fractionally spaced equalizer (FSE) for blind channel estimation based on higher order statistics and to identify any better alternative to improve its performance. Dynamically varying modulus algorithm (DVMA) based FSE is proposed in this paper which is a better alternative for supervised equalization. The simulation results prove that FSE blind equalizer based on DVMA outperform the conventional supervised and blind equalizers.

Recursive Least Squares Fractionally-spaced Blind Equalization Algorithm for Underwater Acoustic Communication

Constant Modulus Algorithm (CMA), Fractionally-spaced Equalizer (FSE) and Recursive Least Squares (RLS)-CMA are investigated, and a low computational complexity RLS-CMA based on FSE with the simplified cost function of CMA (LRLS-FSE-SCMA) was proposed in this paper. To overcome the instability of RLS-CMA, the cost function of CMA is simplified to meet second norm form and an improved RLS-CMA (RLS-SCMA) is obtained. For the input signals of FSE are obtained by oversampling the received signal, the input signals of each sub-equalizer are correlative, and the autocorrelation matrixes of the input signals of each sub-equalizer are little difference. To reduce the computational complexity, we use one of the autocorrelation matrixes instead of the others in RLS-FSESCMA, and then LRLS-FSE-SCMA is obtained. The simulation results under the underwater acoustic channel condition show that LRLS-FSE-SCMA has faster convergence rate and lower steady state error compared with Stochastic Gradient Descent (SGD)-CMA and RLS-SCMA with transversal equalizer, while LRLS-FSE-SCMA has similar performance as RLS-FSE-SCMA with lower computational complexity.