Decision Feedback Equalizer Research Articles

An Estimated δ-Based Iterative Block Decision Feedback Equalization in SC-FDE System

We provide a novel nonlinear frequency domain equalization algorithm for the frequency domain equalization of an SC-FDE system by improving the classical iterative block decision feedback equalization (IBDFE) algorithm and applying δ estimation to the improved algorithm. The improvement of the IBDFE algorithm is carried out by replacing the ZF equalization in the feedback branch with the MMSE equalization and eliminating the iteration of the correlation factor, thus reducing the noise error and the computational complexity of the original algorithm. δ estimation can estimate residual inter-symbol interference in the signal after MMSE equalization and reject it, thus further improving the equalization accuracy. The simulation results show that the performance of the novel algorithm is better than that of the IBDFE algorithm with similar complexity, or the complexity of the novel algorithm is lower than that of the IBDFE algorithm with similar performance.

Research on Co-Channel Interference Cancellation for Underwater Acoustic MIMO Communications

Multiple-input–multiple-output (MIMO) communication systems utilize multiple transmitters to send different pieces of information in parallel. This offers a promising way to communicate at a high data rate over bandwidth-limited underwater acoustic channels. However, underwater acoustic MIMO communication not only suffers from serious inter-symbol interference, but also critical co-channel interference (CoI), both of which degrade the communication performance. In this paper, we propose a new framework for underwater acoustic MIMO communications. The proposed framework consists of a CoI-cancellation-based channel estimation method and channel-estimation-based decision feedback equalizer (CE-DFE) with CoI cancellation functionalities for underwater acoustic MIMO communication. We introduce a new channel estimation model that projects the received signal to a specific subspace where the interference is free; therefore, the CoI is cancelled. We also introduce a CE-DFE with CoI cancellation by appending some filters from traditional CE-DFE. In addition, the traditional direct adaptive decision feedback equalization (DA-DFE) method and the proposed method are compared in terms of communication performance and computational complexity. Finally, the sea trial experiment demonstrates the effectiveness and merits of the proposed method. The proposed method achieves a more than 1 dB of output SNR over traditional DA-DFE, and is less sensitive to parameters. The proposed method provides a new approach to the design of robust underwater acoustic MODEM.

Design Techniques for 48-Gb/s 2.4-pJ/b PAM-4 Baud-Rate CDR With Stochastic Phase Detector

This article presents design techniques for a PAM-4 baud-rate digital clock and data recovery (CDR) circuit utilizing a stochastic phase detector (SPD). The proposed baud-rate phase detector (PD) is designed in an inductive and stochastic way, so there is a clear difference from the existing deductive and logical method used in sign-sign Mueller–Müller PD (SS-MMPD), a representative baud-rate PD. By collecting the histograms of the sequential PAM-4 patterns under EARLY and LATE sampling phases and calculating optimal weights, the SPD exhibits optimized phase-locking characteristic that maximizes the PAM-4 vertical eye opening (VEO) compared with the conventional logical approaches. In addition, unlike SS-MMPD, which may suffer from a severe multiple-locking problem, the SPD tracks a unique and optimal sampling phase even with an adaptive decision-feedback equalizer (DFE). For verification, a prototype PAM-4 receiver is fabricated in 40-nm CMOS technology and occupies 0.24 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Tested with PRBS-7 patterns, it achieves a bit error rate (BER) of less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-11}$ </tex-math></inline-formula> and energy efficiency of 2.4 pJ/b at 48 Gb/s.

A 56-Gb/s PAM-4 Transmitter/Receiver Chipset With Nonlinear FFE for VCSEL-Based Optical Links in 40-nm CMOS

This article presents a 56-Gb/s four-level pulse amplitude modulation (PAM-4) transmitter/receiver (TX/RX) chipset for optical link. The optical transmitter (TX) adopts a digital-to-analog converter (DAC)-based structure with a two-tap nonlinear PAM-4 feed-forward equalizer (FFE) implemented in the digital domain to compensate for the asymmetric responses from the vertical cavity surface-emitting laser (VCSEL). The 56-Gb/s PAM-4 receiver (RX) is connected to the photodiode (PD) and transimpedance amplifier (TIA) module for optical application. The interconnection loss from the RX chip to the PD+TIA module is compensated by the RX continuous-time linear equalizer (CTLE) and the one-tap decision-feedback equalizer (DFE). The pattern-filter-based bang-bang phase detector in the RX improves the jitter performance. Both TX and RX are fabricated in the 40-nm CMOS. The VCSEL TX demonstrates a 56-Gb/s compensated PAM-4 waveform with −0.9-dBm outer optical modulation amplitude (OMA) while consuming only 97 mW of power (1.73 pJ/b). The RX achieves 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−12</sup> bit error rate (BER) with 0.08 UI margin under 10-dB interconnection loss while dissipating 278 mW of power (4.96 pJ/b).

Serially Connected Bidirectional Double EP-Based DFE for Turbo Equalization

In this letter, a new serially connected bidirectional double expectation propagation (EP)-based decision feedback equalizer (SBI-DEP-DFE) for turbo equalization over inter-symbol interference (ISI) channels is proposed. By cascading the normal and time-reversed DEP-DFEs without inner iterations, the bidirectional structure resembles inner iterations, and the SBI-DEP-DFE can emulate the EP behavior and harvest time-reverse diversity. Simulation results illustrate that the SBI-DEP-DFE achieves remarkably better performance than the state-of-the-art existing EP-based DFE, with a complexity just twice that of the minimum mean square error-based linear turbo equalizer. It also outperforms the EP-based linear receivers under certain conditions.

Implementation Adaptive Decision Feedback Equalizer for Time-Reversal Communication in Shallow Water Environment

Underwater wireless communications are growing very fast along with human needs for applications such as defense, state security, underwater control and monitoring systems. Until now, an acoustic signal is a practical way to achieve long distance communication in the ocean. However, the underwater acoustic channel faces many challenges including limited available bandwidth, long delays, time-variability, and Doppler-spread. These challenges can reduce the reliability of the communication system and the achievement of high data-rate becomes a challenge. Adaptive decision feedback equalization is a method to compensate for the distortion of information signals on the underwater acoustic channel. On the other hand, time reversal is an effective method of overcoming intersymbol interference (ISI) problems which is the effect of multipath phenomena in underwater channels. Spatial focusing on time reversal can reduce the co-existing system disturbances and its temporal focusing makes the received power concentrated within a few taps so that the equalizer design work becomes much simpler. The temporal focusing can also increase the transmission rate. This paper shows that the combination of time reversal and adaptive DFE (TR-DFE) has superior performance than TR and DFE itself. By modifying the step-size parameters in the adaptive DFE, the TR-DFE level of convergence and performance can be improved. The geometry-based modeling which is used proves that distance and multipath variation greatly affect the quality of time reversal communication on the underwater acoustic channel.

Comparison of low-complexity sparse and weight-sharing nonlinear equalizers for C-band 100-Gbit/s DSB PAM-4 transmission over 60-km SSMF.

To cope with the nonlinear distortions and the chromatic dispersion (CD) induced power fading in double-side band (DSB) intensity modulation and direct detection (IM/DD) transmission systems, high-performance Volterra nonlinear equalizers (VNLEs) including Volterra feed-forward equalizer (VFFE) and Volterra decision-feedback equalizer (VDFE) are widely applied. However, the conventional VNLEs have high computational complexity, especially for longer memory lengths. In this paper, based on sparse and weight-sharing strategies for significant kernel reduction, we propose four low-complexity NLEs including a sparse diagonally pruned VDFE (S-DP-VDFE), a sparse diagonally pruned absolute-term DFE (S-DP-ATDFE), a weight-sharing DP-VDFE (WS-DP-VDFE), and a weight-sharing DP-ATDFE (WS-DP-ATDFE), and present a comprehensive comparison among them in terms of computational complexity and bit error ratio (BER) performance in a C-band 100-Gbit/s PAM-4 transmission system over 60-km standard single-mode fiber (SSMF). The experimental results show that the proposed S-DP-VDFE and WS-DP-VDFE not only exhibit comparable performance with the conventional DP-VDFE but also reduce the complexity by 54.5% and 45.9%, respectively. While the proposed S-DP-ATDFE and WS-DP-ATDFE yield lower complexity at the expense of a slight performance degradation. Compared with the proposed S-DP-VDFE, S-DP-ATDFE, and WS-DP-VDFE, the proposed WS-DP-ATDFE with the lowest number of real-valued multiplications of 45 achieves up to 90.9%, 81.6%, and 95.8% complexity reduction, respectively, at the 7% hard-decision forward error correction (HD-FEC) BER limit of 3.8 × 10-3. The proposed low-complexity WS-DP-ATDFE shows great potential in low-cost and high-performance IM/DD optical transmission systems.

Generalized Receiver with Decision-Feedback Equalizer for Multicode Wideband DS-CDMA

In the present paper, a chip-level minimum mean-square-error (MMSE) decision-feedback equalizer for the downlink receiver of multicode wideband direct sequence code-division multiple access (DS-CDMA) wireless communication systems over frequency-selective channels is investigated. Firstly, the MMSE per sym-bol achievable by an optimal decision-feedback equalizer is derived, assuming that all interchip interference (ICI) of the desired user can be eliminated. The MMSE of the decision-feedback equalizer is always less than or at most equal to that of linear equalizers. When all the active codes belong to the desired user, the ideal deci-sion-feedback equalizer is able to eliminate multicode interference and approach the performance of the single-code case at high signal-to-noise ratio (SNR) range. Secondly, we apply the hypothesis-feedback equalizer or tentative-chip decision-feedback equalizer in the multicode scenario. The tentative-chip decision-feedback equ-alizer outperforms the chip-level linear equalizer and the decision-feedback equalizer that only feeds back the symbols already decided. The performance gain increases with SNR, but decreases with the number of active codes owned by the other users. When all the active codes are assigned to the desired user, the tentative-chip decision-feedback equalizer eliminates the multicode interference and achieves single-user performance at the high SNR, similarly, to the ideal decision-feedback equalizer. The asymptotic performance of the decision-feed-back equalizer is confirmed through the bit error rate (BER) simulation over various channels.

Complex-valued decision feedback equalizer for optical IMDD signals with adaptive manipulations in time and amplitude domains.

In this work, we innovatively equalize optical intensity-modulated and directly detected (IMDD) four-level pulse amplitude modulation (PAM-4) signals using a complex-valued decision feedback equalizer (CDFE). Through mapping adjacent symbols of PAM-4 signals onto the complex domain, the influence of strongest inter-symbol interference (ISI) can be alleviated during the decision process in a decision feedback equalizer (DFE), effectively combating burst-error propagation when signals are noisy. Moreover, signal-adaptive manipulations of DFE parameters in both the time and the amplitude domain are performed by using an ultra-stable timing recovery and level-adaptive decision. Performance evaluations are made on vertical cavity surface emitting laser (VCSEL) modulated and multimode fiber (MMF) transmitted 100-Gbit/s optical PAM-4 signals. Based on experimental results of the short-reach optical communication, the proposed DFE outperforms the traditional DFE with a 0.5-dB system power budget gain at the 7% overhead (OH) forward error correction (FEC) bit error rate (BER) threshold.

A Gigabit VLC Receiver That Incorporates a Fluorescent Antenna and a SiPM

In this paper we demonstrate a novel optical receiver for visible light communications that combines a fluorescent antenna and a silicon photomultiplier (SiPM). The fluorescent antenna is configured in a slab geometry to collect and absorb an incoming optical data signal, and to waveguide the resulting fluorescence to an edge where it is detected by the SiPM. The antenna incorporates the fluorophore, pentafluorene, selected for its very high bandwidth of 245 MHz, high photoluminescence quantum yield of 90%, and emission spectrum that matches the wavelengths most efficiently detected by the SiPM. The performance of a receiver, comprising the fluorescent antenna and a J-series 30020 SiPM manufactured by ON Semiconductor, was assessed in a 30 cm data link with a 405 nm GaN laser diode transmitter, both in the dark and under 500 lux of ambient white light. The fluorescent antenna successfully rejects ambient light by a factor of 20, limited by extrinsic scattering in the thin film. Using on-off-keying with decision feedback equalization, a maximum data rate of 1.4 Gbps was demonstrated in 500 lux of ambient light. Using the pentafluorene antenna plus a BG3 filter, provides a 200 fold suppression of ambient light, and can increase the data rate of the receiver at low signal powers by up to a factor of 2. When operating in ambient light the composite receiver requires only 2.5 times more signal power than when it operates in the dark, with this power penalty reducing to a factor of 1.2 at 1 Gbps.

Automatic Optimization of Volterra Equalizer With Deep Reinforcement Learning for Intensity-Modulated Direct-Detection Optical Communications

Volterra nonlinear equalizer (VNLE) is widely investigated for linear and nonlinear distortions compensation in optical communication systems. Despite the powerful equalization ability, the required high computation complexity limits its real-time implementation on the hardware. To simplify the complexity, the structure of the VNLE needs to be well optimized. Traditionally, manual optimization of the VNLE structure is blind, and traversal search is inefficient and may result in multiple structures. Therefore, the optimal VNLE structure with the best equalization performance and the lowest equalization complexity for the same performance are still unclear. In this paper, a novel search method named AutoVolterra is proposed to efficiently find the optimal structure of VNLE by using deep reinforcement learning to learn the functional relationship between structure parameters and optimization objectives. Experimental demonstration of 50-Gb/s PAM-4 signal transmission in a bandwidth-limited intensity modulation and direct detection system is performed to verify the effectiveness of AutoVolterra. Both AutoVolterra and greedy search are applied to Volterra feedforward equalizer, Volterra decision feedback equalizer and Volterra-Pruning. The bit error ratio and equalizer's complexity results suggest that the structure searched by AutoVolterra can optimize the equalization performance, and also significantly reduce the complexity, and improve the pruning quality of VNLE to assist real-time implementation on the hardware. Besides, AutoVolterra can also provide a reliable equalization performance benchmark and complexity benchmark to help us verify the actual capabilities of other algorithms.

Analytical method for joint optimization of FFE and DFE equalizations for multi-level signals

Abstract Channel equalization is the efficient method for recovering distorted signal and correspondingly reducing bit error rate (BER). Different type of equalizations, like feed forward equalization (FFE) and decision feedback equalization (DFE) are canceling channel effect and recovering channel response. Separate optimization of tap coefficients for FFE and DFE does not give optimal result. In this case FFE and DFE tap coefficients are found separately and they are not collaborating. Therefore, the final equalization result is not global optimal. In the present paper new analytical method for finding best tap coefficients for FFE and DFE joint equalization is introduced. The proposed method can be used for both NRZ and PAM4 signals. The idea of the methodology is to combine FFE and DFE tap coefficients into one optimization problem and allow them to collaborate and lead to the global optimal solution. The proposed joint optimization method is fast, easy to implement and efficient. The method has been tested for several measured channels and the analysis of the results are discussed.

A 5.2 Gb/s Receiver for Next-Generation 8K Displays in 180 nm CMOS Process

This article presents a high-speed receiver for next-generation 8K ultra-high-definition TVs. The receiver supports error-free communication between the timing controller and the display driver integrated circuits (DDIs) across various channels. Because the receiver must be co-integrated with pixel drivers in the DDI, it must be implemented in a process with high-voltage devices, which poses significant challenges in achieving beyond 5-Gb/s operation. We propose techniques for overcoming such process-induced speed limitations. They include a level-shifting passive continuous-time linear equalizer (CTLE), an active CTLE with extended bandwidth using a negative capacitor, a speculative decision feedback equalizer with a down-sampled edge-sampling path, and a low-dropout regulator with parallel error amplifiers to achieve all-band power supply rejection. A reference-less clock and data recovery circuit with a new frequency detector is also described. Fabricated in a 180-nm CMOS process, the prototype receiver operates at 5.2 Gb/s and can compensate up to 29-dB channel loss while consuming 120 mA from a 1.8-V supply.

Underwater wireless optical communication utilizing low-complexity sparse pruned-term-based nonlinear decision-feedback equalization.

The nonlinearity of the light-emitting diode (LED) in underwater wireless optical communication (UWOC) systems is considered the one major limiting factor that degrades the system's performance. Volterra series-based nonlinear equalization is widely employed to mitigate such nonlinearity in communication systems. However, the conventional Volterra series-based model is of high complexity, especially for the nonlinearity of higher-order terms or longer memory lengths. In this paper, by pruning away some negligible beating terms and adaptively picking out some of the dominant terms while discarding the trivial ones, we propose and experimentally demonstrate a sparse pruned-term-based nonlinear decision-feedback equalization (SPT-NDFE) scheme for the LED-based UWOC system with an inappreciable performance degradation as compared to systems without the pruning strategy. Meanwhile, by replacing the self/cross beating terms with the terms formed by the absolute operation of a sum of two input samples instead of the product operation terms, a sparse pruned-term-based absolute operation nonlinear decision-feedback equalization (SPT-ANDFE) scheme is also introduced to further reduce complexity. The experimental results show that the SPT-NDFE scheme exhibits comparable performance as compared to the conventional NDFE (nonlinear decision-feedback equalization) scheme with lower complexity (the nonlinear coefficients are reduced by 63.63% as compared to the conventional NDFE scheme). While the SPT-ANDFE scheme yields suboptimal performance with further reduced complexity at the expense of a slight performance degradation, the robustness of the proposed schemes in different turbidity waters is experimentally verified. The proposed channel equalization schemes with low complexity and high performance are promising for power/energy-sensitive UWOC systems.

Performance and Complexity Analysis of Conventional and Deep Learning Equalizers for the High-Speed IMDD PON

To accommodate the exponential growth of network services in the five-generation (5G) and beyond wireless system, 50 Gb/s/λ passive optical network (PON) is developed for mobile xhaul applications. Intensity modulation and direct detection (IMDD) technology together with digital signal procession (DSP) is being considered as the promising solution for 50 Gb/s/λ PON due to its low cost, low power consumption, and compact footprint. Different DSP algorithms with varied structures are proposed for linear and nonlinear impairments compensation in the high-speed PON, while the performance and complexity analysis of these algorithms is still missing. To find the most efficient equalizers, in this paper, four conventional equalizers, including feed-forward equalizer, decision feedback equalizer (DFE), Volterra equalizer (Vol) and Volterra DFE equalizer (Vol-DFE), together with two deep learning equalizers namely fully-connected neural network, and long short-term memory equalizer are experimentally compared in a 10G optics based 50G-PON system in terms of the equalization performance, computation complexity, optimization difficulty, and generalization ability. After the evaluation of our proposed fair comparison algorithm, we consider Vol-DFE is the most efficient one considering both performance and complexity. Attributes to the strong and efficient equalization capability of Vol-DFE, C-band 50 Gb/s PAM-4 signal transmission can be supported in a 10G optics based IMDD system with a 3 dB bandwidth of 6.11 GHz, and a power budget up to 38 dB can be achieved.

ML-Assisted Equalization for 50-Gb/s/λ O-Band CWDM Transmission Over 100-km SMF

We propose and demonstrate a bidirectional Vanilla recurrent neural network (Vanilla-RNN) based equalization scheme for O-band coarse wavelength division multiplexed (CWDM) transmission. Based on a 4 × 50-Gb/s intensity modulation and direct detection (IM/DD) system, we demonstrate the significantly better bit error rate (BER) performance of the Vanilla-RNN scheme over the conventional decision feedback equalizer (DFE) for both Nyquist on-off keying (OOK) and Nyquist 4-ary pulse amplitude modulation (PAM4) formats. It is shown that the Vanilla-RNN equalizer is capable of compensating for both linear and nonlinear impairments induced by the transceiver and the single-mode fiber (SMF). As a result, up to 100-km and 75-km SMF transmission can be achieved for OOK and PAM4 transmission, respectively. Furthermore, through the comparison with other equalization schemes, including the linear equalizer, 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> -order Volterra equalizer, and Volterra+DFE, it is demonstrated that the Vanilla-RNN equalizer achieves the best BER performance. In the meantime, it also exhibits lower implementation complexity when compared to Volterra-based schemes. Our results show that the Vanilla-RNN scheme is a viable solution for realizing simple and effective equalization. This work serves as an exploration and offers useful insights for future implementations of reach-extended O-band CWDM IM/DD systems.

On the Sum Capacity Achieving Precoders and Their CSI Requirements for MIMO-BC

Dirty paper coding (DPC) precoders achieve the sum capacity of Gaussian MIMO broadcast channels. However, most systems employ zero-forcing (ZF) and MMSE precoders that are near-optimal at high SNR if the base station (BS) has a large number of antennas, but achievable sum rates with ZF and MMSE precoders are significantly below sum capacity otherwise. We show that capacity achieving DPC precoding requires CSI that scales only as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(M^{2})$ </tex-math></inline-formula> for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -antenna user (not full CSI as is generally assumed) irrespective of the number of BS antennas. Moreover, easily computable generalized decision feedback equalizers significantly outperform MMSE and ZF precoders.

Research on blind equalization algorithm of high-speed visible light communication signal based on machine learning and Marketing

In order to solve the problem of high communication error rate caused by inter symbol interference in high-speed visible light communication signal blind equalization algorithm, a high-speed visible light communication signal blind equalization algorithm is designed based on machine learning. The visible light communication channel model is constructed, and a fusion length limited coding mode is set to make the signal transmitted by visible light communication more in line with the overall response of the channel. The decision feedback equalizer is selected as the equalizer, and the channel cascade impulse response condition is set to compensate the distorted output of the channel. The blind equalization algorithm is designed to classify the data by unsupervised learning, and the extreme point of the error function is found through iterative calculation to optimize the equalizer. The simulation results show that under the same SNR test conditions, the bit error rate of the proposed algorithm is significantly lower than that of the blind equalization algorithm based on LMS and BP neural network. Under the condition of SNR = 20dB, the bit error rate is significantly reduced to the order of 10-5, with high communication quality. The VLC system uses an LED backlight display with a CMOS camera. In general, this panel is used to display marketing information. By adjusting the brightness of the CMOS camera's rolling shutter effect (RSE), additional data, such as dynamic content, may be wirelessly sent. NR (noise to signal) ratio of VLC can't keep up with the variety of material being shown on the screen. It is possible to significantly enhance the CMOS RSE pattern decomposition by using a grayscale value distribution (GVD) and a machine learning method (MLA).

Low power low area VLSI implementation of adaptive FIR filter using DA for decision feed back equalizer

In this paper, a low-complexity pipelined adaptive FIR filter is designed using Distributed Arithmetic (DA) architecture for signal processing applications. Generally adaptive filters will occupy more area and power consumption because of using memories in the filters for partial product (PP) generation. To get rid of this, We use the pipeline concept to reduce the registers in the filters and also to reduce the area further compressor adders are used in the adaptive filter architectures instead of using normal adders. With these two concepts the area and power consumption of the adaptive filters will be reduced. The proposed design is coded in Verilog HDL language and synthesized in Synapsis design compiler tool with SAED 90 nm technology for finding the area, power, minimum sampling period, maximum sampling frequency, area delay product (ADP), power delay product (PDP). By using proposed adaptive filter we can design and implement higher order filters more easily and also the complexity of the proposed design is very less when compared with the existing designs. When we observe the synthesis results the proposed design will occupy 30% less area when compared with the two memories based existing architecture. Also the power consumption is 25% less when compared with the block based adaptive filters. The ADP and PDP of the proposed design is very less when compared with existing architectures. The proposed design is well suited for signal processing application designs such as adaptive decision feed back equalizers for removing the signal noises and inter symbol interference, hearing aids, ECG signal analysis and software defined radio.

A 2.5–32 Gb/s Gen 5-PCIe Receiver With Multi-Rate CDR Engine and Hybrid DFE

This brief presents a 2.5 &#x2013; 32 Gb/s Gen 5-PCIe receiver with a multi-rate clock and data recovery (CDR) engine and a hybrid decision feedback equalizer (DFE). The receiver for the PCIe requires wide-range operation and compensation for high insertion loss. The proposed multi-rate CDR engine enables the receiver to operate with multi-rate clocking schemes according to the data rates, which does not need any additional high-speed analog circuits normally used for wide-range operation. In addition, the hybrid DFE architecture not only meets the DFE feedback timing constraint and but also reduces the equalization power. By using clock gating, the receiver can save power when operating at lower generations such as Gen 1, 2, 3, and 4. The prototype chip is fabricated in a 40-nm CMOS technology and occupies an active area of 0.14 mm². The receiver achieves BER less than 10^&#x2212;12 with various PCIe channels, satisfying PCIe jitter tolerance masks. It consumes 62.7 mW at 32 Gb/s, compensating for 27.5-dB inserting loss, and the figure of merit (energy efficiency per channel loss at Nyquist frequency) of 0.07 pJ/b/dB is achieved.