Decision Feedback Research Articles

Performance Analysis of Adaptive Equalizers Over Multipath Faded Channels: Error Vector Magnitudes

Due to the increasing popularity of digital transmission systems, the need for channel equalizers has been acknowledged. These techniques are designed to counteract the effects of the inter-symbol interference (ISI) caused by the communication channels. An adaptive equalizer is used to operate on the output of a channel in order to provide an approximation of the transmission medium. An adaptive equalizer usually requires a training period to operate successfully. This method eliminates the effects of the wireless transmission channel and allows the subsequent symbol modulation. The paper presents an overview of the various adaptive equalizers, such as the least mean squares (LMS), decision feedback equalizers (DFE), and the Recursive least squares (RLS). It also explores their performance in terms of error vector magnitudes (EVM) over Rician and Rayleigh channels. The paper looks into the effects of adaptive equalizers on various digital modulation techniques for rectangular quadrature phase shift, amplitude modulation, such as the BPSK, QPSK, 4-QAM, 16-QAM, 64-QAM and 256-QAM. These modulations are analysed and measured in terms of symbol error rates and number of incorrect symbols.

A 0.061-pJ/b/dB 28-Gb/s Gradient-Based Maximum Eye Tracking CDR With 2-Tap DFE Adaptation in 28-nm CMOS

This brief presents a gradient-based maximum eye tracking (GMET) scheme employed in the forwarded-clock receiver, including baud-rate clock and data recovery (CDR) and 2-tap adaptive decision feedback equalization (DFE). By optimizing the widely used gradient ascent method for robust operation, GMET achieves low computational power and high stability. Also, simultaneous adaptation using the unified algorithm enables low power consumption and low design complexity. Compared with the previous baud-rate CDR, superior performance is demonstrated under high-loss conditions. The prototype receiver is fabricated in 28-nm CMOS and occupies an active area of 0.106 mm2. At the data rate of 28 Gb/s, the receiver consumes 47 mW, corresponding to an energy efficiency of 1.68 pJ/b. Furthermore, with a channel loss of 27.7 dB at the Nyquist frequency, joint operation of the CDR and the DFE adaptation offers measured results with a margin of 0.17 unit interval (UI) at a BER lower than 10-12.

Iterative Block Decision Feedback Equalization for the Hybrid Carrier System

Iterative Block Decision Feedback Equalization for the Hybrid Carrier System

An Infrared Small Target Detection Method Based on Attention Mechanism.

The human visual attention system plays an important role in infrared target recognition because it can quickly and accurately recognize infrared small targets and has good scene adaptability. This paper proposes an infrared small target detection method based on an attention mechanism, which consists of three modules: a bottom-up passive attention module, a top-down active attention module, and decision feedback equalization. In the top-down active attention module, given the Gaussian characteristics of infrared small targets, the idea of combining knowledge-experience Gaussian shape features is applied to implement feature extraction, and quaternion cosine transform is performed to achieve multi-dimensional fusion of Gaussian shape features, thereby achieving complementary fusion of multi-dimensional feature information. In the bottom-up passive attention module, considering that the difference in contrast and motion between the target and the background can attract attention easily, an optimal fast local contrast algorithm and improved circular pipeline filtering are adopted to find candidate target regions. Meanwhile, the multi-scale Laplacian of the Gaussian filter is adopted to estimate the optimal size of the infrared small target. The fast local contrast algorithm based on box filter acceleration and structure optimization is employed to extract local contrast features, and candidate target regions can be obtained by using an adaptive threshold. Besides, the mean gray, target size, Gaussian consistency, and circular region constraint are used in pipeline filtering to extract motion regions, and the false-alarm rate is reduced effectively. Finally, decision feedback equalization is adopted to obtain real targets. Experiments are conducted on some real infrared images involving complex backgrounds with sea, sky, and ground clutters, and the experimental results indicate that the proposed method can achieve better detection performance than conventional baseline methods, such as RLCM, ILCM, PQFT, MPCM, and ADMD. Also, mathematical proofs are provided to validate the proposed method.

Practical Frequency-Domain Decision Feedback Equalization Based on Expectation Propagation

Practical Frequency-Domain Decision Feedback Equalization Based on Expectation Propagation

Simplified THP and M-Log-MAP Decoder Based Faster Than Nyquist Signaling for Intra-Datacenter Interconnect

In this paper, a joint application of simplified Tomlinson-Harashima precoding (THP) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -log-maximum a posteriori probability ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -log-MAP) decoder at transceivers is proposed for low complexity faster than Nyquist (FTN) 4-ary pulse amplitude modulation (PAM4) signaling. A THP with only two taps is applied at the transmitter for FTN-induced inter-symbol interference elimination and equalization-induced noise amplification issue mitigation, which effectively relieves the burden of the receiver. At the receiver, a low complexity M-log-MAP decoder is equipped for residual impairments cancellation, thus a feedback channel is not required to accurately obtain the channel state information for the transmitter. Taking advantage of this collaborative approach, the proposed scheme performs much better than applying the two schemes separately. We experimentally demonstrate the proposed scheme in 70, 75, and 80GBaud PAM4 systems with a 32-GHz brick-wall filter, corresponding to 0.914, 0.853, and 0.8 FTN compression factor, respectively. The results show that the 80GBaud PAM4 signal is successfully transmitted over 2-km single mode fiber with the bit-error-rate (BER) under the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> . It is also observed that the proposed scheme shows about 0.7dB receiver sensitivity improvement compared to the error propagation-free decision feedback equalizer, namely the performance upper bound of the THP, at BER of 7% HD-FEC threshold in a 75GBaud FTN PAM4 system. According to the experimental results, the proposed scheme is a promising solution for bandwidth-starved low-cost intra-datacenter interconnect.

Doubly-spread channel equalization based on channel shortening in mobile underwater acoustic communications

The shallow water environments and the movement of autonomous underwater vehicles contribute to the distortion of acoustic signals in both the delay and Doppler domains. Numerous studies have focused on eliminating the distortion in underwater acoustic communications but have struggled to find an optimal trade-off between performance and computational complexity, rendering them impractical for marine engineering applications. In our research, we propose a channel-shortening equalization scheme based on frequency-domain decision feedback equalization (FD-DFE) to address this issue. This approach leverages FD-DFE to reduce the number of multipaths and decreases the Doppler spread of the channel. A time-domain decision feedback equalization based on recursive least squares (RLS-DFE) is then employed to eliminate residual delay and Doppler spreads. The mismatch between the block- and symbol-wise equalization is minimized by an overlapping subblock structure. Numerical simulations have demonstrated the effectiveness of this scheme. Error-free transmissions with a data rate of up to 6 kbps were achieved in a reservoir experiment between an autonomous underwater helicopter (AUH) and a shore-base receiving node.

A Review on the Design of Equalizers for Frequency Selective Channels

Wireless channels rarely fulfill the conditions required for distortion-less transmission. sensible wireless channels suffer from the impact of a non-flat magnitude response and a non-linear section response that leads for distortions within the received signals. what is more effects liketiny scale weakening, massive scale weakening and physicist shifts cause dis- similarity between the transmitted and received signals. Wireless channels not showing the perfect impulse response ends up in the reception of multiple copies of the transmitted signal at the receiver thereby leading to entomb image Interference (ISI). A additive and cascading impact of the on top of mentioned reasons ends up inthe degraded performance of electronic communication systems. to avoid these prejudicial effects, many equalizer styles are projected.This paper focuses on the design aspects of equalizers with an inclination towards decision feedback equalizers, due to their efficiency in nullifying the detrimental effects of practical wireless channels. Keywords: Frequency Selective Channel, Equalizer, Decision Feedback Equalizer, Bit Error Rate (BER), Probability of Error (Pe), Throughput.

Channel State Information Based Equalizer Design for Frequency Selective Channels

Abstract—Equalizer design is an extremely critical aspect for wireless networks. This paper presents an approach combining the decision feedback mechanism and successive signal detection to equalize frequency selective channel effects for signals traversing different run-lengths. In this approach, the errors on comparison between the transmitted signal and received signal are fed to the equalizer to adjust the tap weights. Still the irreversible nature of inter symbol interference is a huge challenge due to multi path propagation mechanisms in wireless channels. It is a common observation that signals traversing a smaller path reach the receiver earlier compared to the multi-path component traversing a longer path. Assuming similar shadowing effects, it is seen that fading effects make it difficult to accurately receive long distance MPCs, thereby degrading the BER performance. It has been shown that the proposed system attains almost similar BER performance irrespective of the shadowing effect or run length of the MPCs. Keywords— Multi Path Component (MPC), Inter Symbol Interference (ISI), Adaptive Equalizer, Channel State Information (CSI), , Bit Error Rate (BER), Probability of Error

A 103 fJ/b/dB, 10–26 Gb/s Receiver With a Dual Feedback Nested Loop CDR for Wide Bandwidth Jitter Tolerance Enhancement

A 10–26 Gb/s energy-efficient receiver incorporating a dual-feedback nested loop clock and data recovery circuit (DF-CDR) is proposed. Combining a direct modulation path on voltage-controlled oscillator (VCO) and phase interpolator (PI)-based phase rotator inside a phase locked loop (PLL), it improves high-frequency jitter tolerance by 0.15 UI. An edge-first equalization scheme is proposed to reduce power and hardware overhead of decision feedback equalizers. Meanwhile, it facilitates adaptive equalization of continuous time linear equalizer, and background offset calibration of the receiver frontend. A three-stage latch comparator is adopted to enable high-speed direct feedback equalizer. By applying PRBS-31 test pattern through a 32 dB loss channel, the receiver is error-free and features the best energy efficiency of 103 fJ/b/dB at 26 Gb/s.

Cosine function variable step-size transform domain least mean square algorithm based on matrix rotation

A novel cosine function variable step-size transform domain least mean square (LMS) algorithm based on matrix rotation (COS-ROTDCT-LMS-DFE) was put forward. Based on the discrete cosine transform domain LMS (DCT-LMS) algorithm, it was first processed by matrix rotation in an anticlockwise direction to resolve the problem of self-interference between signals, which effectively sped up the convergence of the algorithm. Subsequently, a cosine function variable step-size algorithm was developed considering that its curve was characterized by a smooth top and fast rising and falling speed so as to further improve the convergence speed of the algorithm. Subsequently, the decision feedback equalizer (DFE) was introduced into the algorithm to compensate signal distortion and noise. The convergence performance of the algorithm was simulated in typical multipath underwater acoustic channels. The simulation results showed that the convergence performance of the new algorithm was equivalent to that of recursive least squares (RLS). The convergence speed of COS-ROTDCT-LMS-DFE was even better than that of the recursive least square decision feedback equalizer (RLS-DFE) algorithm. The new algorithm performed well in terms of both convergence speed and steady-state error and could be easily implemented.

Children Learn Simple, Adaptive Decision Strategies from Probabilistic Feedback

ABSTRACT In two studies, children learned simple but adaptive decision strategies from decision feedback. In a probabilistic multi-cue decision task, we investigated children's decision strategies under different feedback conditions. In Study 1 (N = 313), 7- and 9-year-old German children learned the selective decision strategy Take-the-Best. Children learned Take-the-Best equally well in both strict and lenient feedback environments, but worse than adult controls. In Study 2 (N = 246), feedback reinforced either the selective Take-the-Best strategy or the holistic Equal-Weight strategy. Results showed that children adapted to both decision environments. Children used both strategies more or less frequently depending on the feedback structure. Adaptation to the environment favoring Equal-Weight was better overall. This was not because the feedback was more effective, but rather because children, especially the younger ones, tended to use the Equal-Weight strategy even in the absence of feedback. Consistent with this, both studies showed an age effect on strategy use: overall, older children used the selective Take-the-Best strategy more often, while younger children used the holistic Equal-Weight strategy more often. Our results show that feedback can quickly improve decisions and increase the use of adaptive decision strategies in children as young as six years old.

Design and verification of DFE re-decision algorithm for PAM6 high-speed transceiver based on FPGA

In this paper, a decision feedback equalizer (DFE) re-decision algorithm for a 6-level pulse-amplitude-modulation (PAM6) high-speed transceiver is proposed. PAM6 is a two-dimensional (2D) modulation. The four outer points are not used in the 2D constellation diagram to reduce the output power. Although the four outer points will not be modulated, they may be encountered during demodulation. This paper considers the above situation and theoretically analyzes the DFE module under the additive white Gaussian noise (AWGN) channel. Compared with the traditional pipelined DFE structure, the proposed algorithm can help solve the four outer points in PAM6. A serializer/deserializer (SerDes) simulation system is built based on a field programmable gate array (FPGA), and the performance of the proposed algorithm is carried out on the simulation system. According to this proposed algorithm, the symbol error rate (SER) of the PAM6 SerDes system can be reduced, and the system performance can be improved. When the DFE tap coefficient is 0.50 and the signal-to-noise ratio (SNR) is 22.0 dB, the proposed algorithm can additionally correct 8.18 % of erroneous symbols. When the DFE tap coefficient is 1.00 and the SNR is 22.0 dB, the proposed algorithm can additionally correct 17.30 % of erroneous symbols.

A 33-Gb/s/Pin 1.09-pJ/Bit Single-Ended PAM-3 Transceiver With Ground-Referenced Signaling and Time-Domain Decision Technique for Multi-Chip Module Memory Interfaces

A three-level pulse amplitude modulation (PAM-3) transceiver (TRX) with improved simultaneous switching output (SSO) noise and reference voltage margin was studied. PAM-3 signaling with an insertion of 3 bits in 2-unit intervals (UI) was implemented using the upper, under, and ground voltages, achieving 150% pin efficiency. The ground-referenced signaling (GRS) charge pump driver reduced SSO noise and maintained ground as the solitary return current path. Capacitive peaking and middle edge-rate boosting were implemented for transmitter (TX) equalization. With the receiver (RX), the ground level was used as a reference voltage for a single-to-differential (S2D) amplifier. PAM-3 signaling was converted to binary data using the time-domain decision technique in comparators. The decision time of comparators for data and reference voltage was compared. This technique shows the increased voltage margin, the reduced decision time, and the decreased error rate. The reduced decision time improved the performance of the PAM-3 decision feedback equalizer (DFE). A clock disabled the circuit, and a low-power return-to-zero (RZ) to non-RZ (NRZ) converter was configured for the proposed comparator output cases. The prototype TRX was fabricated in a 28-nm complementary metal–oxide silicon (CMOS) process with a surface area of 0.006 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> . The total power efficiency was recorded as 1.09 pJ/b at 33 Gb/s/pin. Through the flame retardant-4 (FR-4) 20-mm printed circuit board (PCB) channel and coaxial cable, a bit error rate (BER) of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{-12}$</tex-math> </inline-formula> was measured.

A Decision Feedback Equalization Algorithm Based on Simplified Volterra Structure for PAM4 IM-DD Optical Communication Systems

A novel simplifying Volterra structure algorithm is proposed for an intensity modulation direct detection (IM-DD) optical fiber short distance communication system using the decision feedback equalization algorithm (DFE). Based on this algorithm, the signal damage for the four-level pulse amplitude modulation signal (PAM-4) is compensated, which is caused by device bandwidth limitation and dispersion during transmission. Experiments have been carried out using a 25 GHz Electro-absorption Modulated Laser (EML), showing that PAM-4 signals can transmit over 10 km in standard single-mode fiber (SSMF). The 112 Gbps and 128 Gbps signals can reach the error rate threshold of KP4-FEC (BER = 2 × 10−4) and HD-FEC (BER = 3.8 × 10−3), respectively. The simplified principle and process of the proposed Volterra-based equalization algorithm are presented. Experimental results show that the algorithm complexity is greatly reduced by 75%, which provides effective theoretical support for the commercial application of this algorithm.

Multiple-Input-Multiple-Output Filtered Multitone Time Reversal Acoustic Communications Using Direct Adaptation-Based Turbo Equalization.

This paper proposes using direct adaptation (DA)-based turbo equalization in multiple-input-multiple-output (MIMO) filtered multitone (FMT) time reversal (TR) acoustic communications to jointly suppress noise, residual co-channel interference (CCI) and intersymbol interference (ISI) after the TR process. Soft information-based adaptive decision feedback equalization (ADFE) adjusted according to the recursive expected least squares (RELS) algorithm, including interference cancellation and decoding, is used to construct the DA-based turbo equalization. In the proposed method, soft information is exchanged between soft symbols with soft decisions of decoding iteratively, and interference suppression is proceeded successively and iteratively until the performance is stable. The principle of the proposed method is analyzed, and based on the acoustic channel responses measured in a real experiment, the performance is assessed in relation to that of anther two methods. Compared with the MIMO-FMT TR underwater acoustic communication using interference suppression without error control coding (ECC), the proposed method performs better, benefitting from the ECC included in turbo equalization. Additionally, compared with the MIMO-FMT TR underwater acoustic communication using interference suppression based on hard decision equalization and decoding, the proposed method exhibits superior performance by exploiting soft information.

Asynchronous Sampling-Based Hybrid Equalizer

An equalizer architecture based on asynchronous sampling is described. The circuit implementation is a hybrid feed-forward equalizer (FFE) using three digital postcursor taps realized via level-crossing samplers (LCSs) and inverter-based delays. Utilizing a current mode logic (CML)-based summer stage, an analog main tap and digital postcursor taps are combined into an inductively tuned resistor load. With a 0.67-mV-rms simulated output-referred noise, the FFE has better noise performance than a conventional continuous-time linear equalizer (CTLE) and a slicer/latch-based decision feedback equalizer (DFE) circuit. Moreover, it exhibits very good linearity and group delay performance suitable for an equalizer. Using inverter-based delays enables area efficiency as well as the capability to tune the delay across process voltage and temperature (PVT) variations. Since the FFE is an event-driven combinational logic based on the incoming data, it does not require synchronous sampling coming from a high-speed clock and data recovery (CDR), and it is advantageous for high-speed and multirate operation as its power consumption scales with the data rate. Fabricated in 40-nm CMOS technology, the hybrid FFE achieves energy per bit of 2.7 pJ/bit with a 20-dB Nyquist insertion loss link at the 28.57-Gb/s nonreturn to zero (NRZ) data rate.

Swarm Intelligence Based MMSE Frequency Domain Equalization for MIMO Systems

The automatic upgradation of equalizer weights in channel equalization demands a low-complexity, highly accurate estimation of recovery at the minimum possible time. The low-complexity frequency domain equalization improves the minimum mean square error (MMSE) of the equalization process. Adding the superiority of particle swarm optimization (PSO) to the equalizer coefficient selection process enhances the MMSE. This work proposes frequency-domain channel equalization along with a modified PSO (MPSO) as an adaptive algorithm for equalizer weight selection in MIMO systems. The simulation results validate the performance with the time domain linear and decision feedback equalizer structures for BPSK and QAM systems. The parameters are carefully selected by analyzing MMSE thoroughly under timevarying channel conditions.

A PAM4 transceiver design scheme with threshold adaptive and tap adaptive

To meet the demand of low bit error rate and high bandwidth for high-speed links, a reliable 112 Gb/s four-level pulse amplitude modulation (PAM4) transceiver design scheme with adaptive threshold voltage and adaptive decision feedback equalizer is proposed in this paper. In this scheme, three continuous time linear equalizers (CTLEs) at the front end of receiver are used to compensate the high-frequency, mid-frequency and low-frequency signals, respectively, and the variable gain amplifier (VGA) and saturation amplifier (SatAmp) are used to scale the signal amplitude. In addition to the three data samplers, four auxiliary samplers are also used for threshold adaptation. The sign-sign least mean squares algorithm uses the offset between the data sampler and the auxiliary sampler at the receiver side to drive the auxiliary reference voltage to converge to the signal constellation level, thus ensuring that the eye diagram of the PAM4 received signal has equal spacing and a constant signal–noise ratio for the three eyes in the vertical direction. In addition, the adaptive DFE for PAM4 signaling allows the transceiver to better adapt to the channel and thus achieve better equalizer performance. The simulation results show that the PAM4 transceiver design can compensate up to 25 dB of channel loss with an average eye height of 59.6 mv and an average eye width of 0.27 UI at a bit error rate of 10−12 under the condition of 3-tap feedforward equalizer (FFE) transmitter.

Low complexity nonlinear detection for multiuser hybrid MIMO systems and performance analysis

This paper proposes an analytical framework and a system of distortion-aware receiver structures for single-carrier uplink hybrid beamforming-based multiple-input-multiple-output (MIMO) channels. Proposed single-user processing units cooperate at the base station (BS) in an iterative manner for multi-user symbol detection under hardware impairments. Firstly, in the proposed system, an iterative nonlinear interference cancellation (nIC) based on feedforward neural network (NN) modeling is developed to eliminate the nonlinear distortion effects of power amplifiers (PAs). Furthermore, depending on the fading pattern of the instantaneous channel, it is analytically shown that a large gain may be applied to the distortion signal during the equalization stage, which yields distortion amplification causing a significant decrease in the signal-to-distortion-plus-noise ratio (SDNR). A reduced complexity distortion aware detector, based on a bank of fractionally delayed iterative block decision feedback equalization (IB-DFE) receivers, is introduced to adjust the combiner weights for fractionally delayed IB-DFE outputs so that distortion power is minimized before detection. Consequently, multi-user detection capability is enhanced considerably. Secondly, an asymptotic SDNR analysis is performed. The theoretical analysis, verified via numerical evaluations, clearly shows that distortion amplification limits the achievable SDNR at the BS, and the proposed reduced complexity multi-user receiver architecture improves the BER performance by effectively mitigating this effect.