Decision Feedback Algorithm Research Articles

Energy Efficiency for Faster-than-Nyquist Data Transmission Using Processing Algorithms with Decision Feedback

One of the ways to increase the volume of transmitted information is to increase the bit rate above the Nyquist barrier. However, an increase in bit rate in the case of FTN (Faster-Than-Nyquist) signals leads to an increase in energy costs for receiving information on channels with limited bandwidth, for example, in Digital Video Broadcasting satellite systems like DVB-S2/S2X. It is possible to minimize energy losses by using the processing algorithm “maximum likelihood sequence estimation”. However, the computational complexity of this algorithm is extremely high, which limits its use, especially in terrestrial mobile satellite terminals. We propose a new bit-by-bit decision feedback algorithm with maximum likelihood ratio estimation of subsequent symbols in the observation interval. This algorithm provides minimal energy costs comparable to the method “maximum likelihood sequence estimation” at speeds 2–3 times higher than the Nyquist barrier. At the same time, the complexity is two orders of magnitude less. It is shown by simulation for a channel with additive noise that energy losses in relation to the potential bit error rate (BER) are less than 4.5 dB. In the presence of Rayleigh fading, the application of the proposed algorithm makes it possible to provide the processing of FTN signals for double bit rates in urban areas with energy costs equal to 12 dB when using an equalizer. We give numerical estimations of the increase in computational complexity for the proposed processing algorithm. It is shown that an increase in the bit rate by 1.5 times leads to an increase in the computational complexity by more than an order of magnitude. The same conclusion can be reformulated in another form: for the proposed algorithm, each decibel of energy gain is achieved by increasing the number of computational operations by 1.5×105. It is experimentally shown that additional energy losses due to non-ideal phase and timing synchronization are no more than 1 dB when the proposed algorithm is applied in a fading channel. The energy costs in fading channels relative to a stationary channel for twice the Nyquist rate are equal to 13.8 dB when using an equalizer.

H∞ filter-based dynamic joint carrier frequency offset and linear phase noise tracking for CO-OFDM systems.

In this paper, a robust, dynamic and joint carrier frequency offset (CFO) and linear phase noise (LPN) tracking algorithm is proposed by utilizing the H∞ filter for CO-OFDM systems. The dynamic tracking is implemented by Bayesian filtering which time-recursively updates the posterior state estimates based on the prior state information and calculated gain. To improve the robustness of the dynamic tracking process against the uncertainty of the noise terms, we adopt the H∞ filter, which designs a min-max optimization problem with a performance bound-defined constraint. The H∞ filter obtains the state estimates by limiting the worst-case estimation error, which guarantees its robustness to the system uncertain noise terms and external disturbances. After the joint estimation of CFO and LPN, we then propose a decision-feedback algorithm to achieve accurate signal detection. The accuracy and robustness of the proposed algorithm are verified in an 88.9 Gb/s 16-QAM CO-OFDM system, by comparing with the conventional extended Kalman filter (EKF) and Gaussian particle filter (GPF). Simulation results show that the MSEs of CFO and LPN by H∞ filter can reach the Cramér-Rao Lower Bounds (CRLBs) as well as the Bayesian CRLB (BCRLB), and possesses excellent noise and chromatic dispersion (CD) tolerance.

Low-Complexity Multistage Optimal Detection for SVD-Based Hybrid Millimeter Wave MIMO Systems

The singular value decomposition (SVD) based hybrid processing for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems attempts to eliminate mutual interference between data streams by processing the original channel matrix to an approximate diagonal matrix. However, the non-zero off-diagonal entries will result in performance loss. To improve the performance with low-complexity, we propose a multistage optimal detection algorithm for SVD-based hybrid mmWave MIMO systems. At the first stage, a decision criterion is proposed by effectively exploiting the characteristic that the magnitudes of off-diagonal entries of the baseband channel matrix are relatively small. Through this decision criterion, some elements of global optimal solution can be determined. The ratio of the determined elements to all elements is analyzed to reveal the advantage of proposed decision criterion. At the second stage, we further propose a decision feedback algorithm to detect more elements of global optimal solution. If all elements are determined, the detection is complete, otherwise it enters the third stage. In the case of third stage, we apply the maximum likelihood (ML) detection algorithm to solve the residual small-scale optimization problem containing only few undetermined elements. Numerical experiments show that the number of elements required to be determined by ML detection is relatively very small or zero, in most situations, that is why the algorithm has a significantly lower complexity.

A novel phase noise compensation algorithm combining the DF algorithm with LCSC algorithm in CO-OFDM systems

A novel phase noise (PN) compensation algorithm based on the decision feedback (DF) algorithm and the linear combination self cancellation (LCSC) algorithm is proposed to improve the system performance degradation caused by laser linewidth in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. In this proposed LCSC-DF algorithm, the LCSC algorithm is used to precode the subcarrier information at the transmitter and decode the demodulation information and inter-carrier interference (ICI) related information at the receiver. And then the pilot information is used to obtain the final compensation signal by the improved DF algorithm. The simulation results show that the PN compensation performance of the proposed LCSC-DF algorithm is better than that of the DF algorithm. Furthermore, with the increase of the signal to noise ratio (SNR), its bit error rate (BER) performance approaches to that of the SC-DF algorithm at the larger PN linewidth. The subcarriers utilization ratio of the proposed algorithm is higher than that of the SC-DF algorithm. As a result, the proposed algorithm can effectively improve the performance of the system.

Improved high gain circuit and DFE algorithm for underwater photoelectric signal recovery

Underwater long-distance optical communications, due to the influence of light scattering and absorption, it will cause severe signal attenuation, in addition, multipath propagation effects and Doppler effect of light will cause serious signal distortion. Based on the problems, an improved amplifier with Direct Current (DC) servo loop is proposed. The amplifier overcomes the shortcoming of conventional amplifiers and has high gain, wide dynamic range. Further, in order to overcome the time varying interference, an improved decision feedback equalizer (DFE) model and algorithm is given, the model can achieve faster convergence and smaller steady-state error. The new algorithms take Marr function as a basic function, and two parameters α and β used to shape the profile of functions. Experiments show that the method can greatly improve the transmission distance of underwater optical communications (UOC).

Experimental Demonstration of CO-OFDM Systems Using Superimposed Pilot

We investigate the superimposed pilot (SP)-based channel estimation (CE) for long-haul coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. With specifically designed SP, we demonstrate the impacts that both SP and phase noise have on the performance of CE, from which we obtain the optimal signal-to-pilot power ratio. To enhance the estimation quality of the SP-aided scheme, we exploit an iterative decision feedback algorithm, and in turn, improve the system performance. Experimental results show that the SP-aided CE behaves robust to the phase noise when lasers with moderate linewidth (<;100 KHz), and can offer similar performance as the conventional preamble based methods without scarifying bandwidth efficiency. A CO-OFDM transmission over 5000 km of standard single mode fiber is successfully demonstrated using the SP-aided CE scheme, which shows a spectral efficiency gain of ~10%.

Low-Complexity Iterative Row-Column Soft Decision Feedback Algorithm for 2-D Inter-Symbol Interference Channel Detection With Gaussian Approximation

In this paper, we study the complexity reduction problem of the iterative row-column soft decision feedback algorithm (IRCSDFA) for 2-D inter-symbol interference (ISI) detection. Specifically, Gaussian approximation (GA) is employed in both the component row and column detectors of the IRCSDFA in order to reduce its computational complexity. With the employment of GA, the state space dimension of the ISI trellis of either component detector can be reduced enormously (i.e., the number of branches in one ISI trellis section decreases). Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is then employed to perform detection over the GA-simplified ISI trellis. For brevity, we refer to the IRCSDFA with BCJR detection over the GA-simplified ISI trellis as “IRCSDFA-GA-BCJR”. Next, the iteration scheduling of component detectors and decoder in coded 2-D ISI channels with low density parity check (LDPC) coding and IRCSDFA-GA-BCJR detection is studied. Specifically, three iteration schemes: single detector (row or column) scheme, alternate detector scheme, and combined detector scheme, are considered, with the last scheme showing the best coded performance. Finally, the computational complexity of the proposed IRCSDFA-GA-BCJR is analyzed, and shown to have significant reduction with a cost of only about 0.3 and 0.35 dB in coded BER/FER performance loss compared to the conventional IRCSDFA without GA and the optimal symbol-based BCJR algorithm, respectively.

상수 모듈러스 오차의 정보 포텐셜에 기본을 둔 결정궤환 알고리듬

이 논문에서는 상수 모듈러스 오차의 정보 포텐셜에 대해 소개하고 채널왜곡에 의해 나타나는 큰 출력차이에 대해 상수 모듈러스 오차의 정보 포텐셜은 비교적 안정된 변화율을 나타난다는 특성이 결정궤환 구조의 오차 전파를 막을 수 있다는 점에 근거하여, 상수 모듈러스 오차의 정보 포텐셜의 견지에서 표현된 비용함수를 바탕으로 비선형 결정궤환 구조의 이퀄라이져 알고리듬을 제안하였다. 두 가지 채널 환경에 대한 시뮬레이션 결과로부터 스펙트럼 널이 없는 채널모델에서는 기존의 선형방식보다 3 dB 정도 향상된 정상상태 MSE 를 나타냈으며, 스펙트럼 널이 존재하는 열악한 채널 모델에 대해서는 오히려 약 9 dB 이상의 성능향상을 나타냈다. In this paper, a blind decision feedback algorithm is proposed based on the ideas that the derivative of information potential for constant modulus errors stays relatively undisturbed even when large output differences are induced by severe channel distortions and this property can prevent the error propagation that is one of the main problems in decision feedback structures. From the simulation results of the steady state MSE, the proposed blind equalizer algorithm with decision feedback has yielded about 3 dB performance enhancement in the channel model without spectrum nulls and above 9 dB in severe channel characteristics with spectrum nulls.

오류 확률에 근거한 결정 궤환 방식의 통신 등화 알고리듬

For intersymbol interference (ISI) compensation from communication channels with multi-path fading and impulsive noise, a decision feedback equalizer algorithm that minimizes Euclidean distance of error probability is proposed. The Euclidean distance of error probability is defined as the quadratic distance between the probability error signal and Dirac-delta function. By minimizing the distance with respect to equalizer weight based on decision feedback structures, the proposed decision feedback algorithm has shown to have significant effect of residual ISI cancellation on severe multipath channels as well as robustness against impulsive noise.

Efficient Detection Algorithms for MIMO Communication Systems

In this paper, two new efficient detection algorithms, Type 1 (T1) with better complexity-performance tradeoff and Type 2 (T2) with lower complexity, are derived from one generalized framework for multiple-input multiple-output (MIMO) communication systems. The proposed generalized detection framework constructed by parallel interference cancellation (PIC), group, and iteration techniques provides three parameters and three sub-algorithms to generate two efficient detection algorithms and conventional BLAST-ordered decision feedback (BODF), grouped, iterative, and B-Chase detection algorithms. Since the group interference suppression (GIS) technique is applied to the proposed detection algorithms, the complexities of the preprocessing (PP) and tree search (TS) can be reduced. In (8,8) system with uncoded 16-QAM inputs, one example of the T1 algorithm can save complexity by 21.2% at the penalty of 0.6 dB loss compared with the B-Chase detector. The T2 algorithm not only reduces complexity by 21.9% but also outperforms the BODF algorithm by 3.1 dB.

Iterative Soft Decision Feedback Zig-Zag Equalizer for 2D Intersymbol Interference Channels

We present a novel iterative soft decision feedback zig-zag algorithm for detection of binary images corrupted by two dimensional intersymbol interference and additive white Gaussian noise. The algorithm exchanges soft information between maximum-a-posteriori detectors employing different zigzag scan directions. Each detector exploits soft-decision feedback from the other zig-zag detectors. Simulation results for the 2 × 2 averaging mask channel show that, at low signal-to-noise ratios, the new algorithm gains about 1 dB over an iterative row column soft decision feedback algorithm and over a separable mask algorithm, two of the best previously published schemes. When the zig-zag algorithm is concatenated with the row-column algorithm, the concatenated system performs as well as or better than four of the best previously published algorithms, at both low and high signal-to-noise ratios, for a variety of 2 × 2 and 3 × 3 convolution masks; in several cases, the system performs within less than 0.1 dB of the maximum-likelihood performance bound.

Row-Column Soft-Decision Feedback Algorithm for Two-Dimensional Intersymbol Interference

We present a novel iterative row-column soft decision feedback algorithm (IRCSDFA) for detection of binary images corrupted by 2-D intersymbol interference and additive white Gaussian noise. The algorithm exchanges weighted soft information between row and column maximum a posteriori (MAP) detectors. Each MAP detector exploits soft-decision feedback from previously processed rows or columns. The new algorithm gains about 0.3 dB over the previously best published results for the 2times2 averaging mask. For a non-separable 3times3 mask, the IRCSDFA gains 0.8 dB over a previous soft-input/soft-output iterative algorithm which decomposes the 2-D convolution into 1-D row and column operations.

Equalization techniques based on fast RLS algorithms to improve mobile reception performance of 8-VSB receivers

This paper presents fast and robust equalization techniques to improve ATSC DTV reception for fixed, portable, pedestrian, and mobile receivers. There are many strong and dynamic echoes affecting portable, pedestrian, and mobile reception. The conventional decision feedback equalizer using least mean square algorithm is stable and shows good performance in handling the static multipath channel. The equalizer however has difficulty in handling strong echoes and shows poor performance in tracking high Doppler frequencies. To combat strong and dynamic echoes, a fast converging equalizer using a fast transversal decision feedback algorithm combined with the least mean square method is proposed and investigated.

Noncoherent detection for trellis-coded MPSK

This letter shows several methods for improving the decoding of noncoherent trellis-coded M-ary phase-shift keying. We propose two new metrics for the basic decision-feedback algorithm. These metrics are derived based on the idea of reducing the effect of incorrect amplitude of the reference signal. We also propose a new decoding algorithm that uses a simple way to estimate the metric of the future sequence.

A reduced-complexity algorithm for combined equalization and decoding

This paper presents a new application of a suboptimal trellis decoding algorithm for combined equalization and decoding. The proposed algorithm can outperform the reduced-state sequence estimator (RSSE) of the same order of complexity. The algorithm, termed estimated future decision-feedback algorithm (EFDFA), was originally proposed for the problem of noncoherent decoding with multiple-symbol overlapped observations and is now reformulated for the problem of intersymbol interference inflicted channels. The EFDFA uses the RSSE as a building block. The performance improvement is achieved by using estimated future symbols in the decision process. The estimated future symbols are obtained by RSSE decoding time-reversed blocks of the input. The same technique can be used to greatly enhance the performance of the conventional decision-feedback equalizer. An analysis of the performance of the EFDFA based on the performance of the RSSE is described. The EFDFA can be configured as an adaptive equalizer capable of operating in a time-varying environment, and is shown to perform well in fading conditions. With only minor additional complexity, the EFDFA is also capable of producing soft outputs.

Adaptive differential detection using linear prediction for M-ary DPSK

This paper proposes a novel adaptive differential detection scheme (adaptive DD), which can significantly reduce the irreducible bit-error rate (BER) of M-ary DPSK due to Doppler spread by the adaptive linear prediction of the reference signal. The predictor coefficient is adapted to changing channel conditions by using the recursive least-square (RLS) algorithm. A phase sequence estimation based on the M-state Viterbi algorithm (VA) and another based on the decision feedback algorithm (DFA) are presented. A theoretical BER analysis is presented for adaptive DD-DFA. BER performances of 2 and 4DPSK in Rayleigh fading channels are evaluated by computer simulations. When the RLS forgetting factor of /spl beta/=1 is used, simulation results show that the irreducible BER of 4DPSK can be reduced to 7.2/spl times/10/sup -5/ (3.9/spl times/10/sup -4/) for VA (DFA) while conventional DD offers 3.9/spl times/10/sup -3/ when f/sub D/T/sub b/ (maximum Doppler frequency times bit duration)=0.01 and average E/sub b//N/sub 0/ (signal energy per bit-to-additive white Gaussian noise (AWGN) power spectrum density ratio)=60 dB, where most errors are produced by Doppler spread. Adaptive DD is also effective in AWGN channels-simulations show that for the case of 4DPSK, a performance gain of 1.2 (0.7) dB is achieved over conventional DD for VA (DFA) at BER=10/sup -3/.

Modelling and equalization of rapidly fading channels

Basis expansion ideas are employed in order to equalize frequency-selective, rapidly fading channels. For certain multipath fading channels (e.g. the mobile radio channel), the time variations of the coefficients can be modelled as a combination of a small number of complex exponentials, under the assumption of linearly changing path delays. Based on this observation, novel adaptive and decision feedback algorithms are derived which exploit such an explicit modelling of the channel's variations. The problem of estimating the frequencies of the exponentials is also addressed using second- and higher-order cyclic statistics. By integrating ideas from cyclostationary signal analysis, both batch and recursive methods are developed. Finally, some illustrative simulations are presented.

Modelling and equalization of rapidly fading channels

Basis expansion ideas are employed in order to equalize frequency-selective, rapidly fading channels. For certain multipath fading channels (e.g. the mobile radio channel), the time variations of the coefficients can be modelled as a combination of a small number of complex exponentials, under the assumption of linearly changing path delays. Based on this observation, novel adaptive and decision feedback algorithms are derived which exploit such an explicit modelling of the channel's variations. The problem of estimating the frequencies of the exponentials is also addressed using second- and higher-order cyclic statistics. By integrating ideas from cyclostationary signal analysis, both batch and recursive methods are developed. Finally, some illustrative simulations are presented.

Decoding algorithms for noncoherent trellis coded modulation

Noncoherent decoding of trellis codes using multiple-symbol overlapped observations was shown previously to achieve close to the coherent performance. Optimal decoding by the Viterbi algorithm for L-symbol observations requires a number of states which grows exponentially with L. Two novel suboptimal algorithms are presented, for which the number of states is the same as the original code, yielding a complexity depending weakly on L. For practical values of L, both algorithms are substantially less complex than the optimal algorithm. The first algorithm, the basic decision feedback algorithm (BDFA), is a low complexity feedback decoding scheme, based on the Viterbi algorithm. This algorithm is shown to suffer from increased error probability and from error propagation. A slight modification to this algorithm can, in most cases, reduce these effects significantly. The second algorithm uses the BDFA as a basic building block. This algorithm is based on a novel concept called "estimated future" and its performance is very close to optimum for most practical eases with some additional complexity and memory requirements as compared to the first algorithm. Performance analysis and simulation results are also given.

Adaptive phase diversity for MDPSK reception

Adaptive phase diversity reception that uses only differentially detected phase information is proposed for the differential phase detection (DPD) of Rayleigh faded M-ary differentially encoded phase shift keying (MDPSK) signals. An M-state Viterbi algorithm (VA) is used both for MDPSK phase detection and adaptive estimation of the phase error variance of each diversity branch. The phase error variance is estimated along the surviving path in the trellis, where each state in the trellis represents one MDPSK phase, and its inverse is used as the diversity combining weight. Simple yet efficient MDPSK phase detection based on a decision feedback algorithm (DFA) is also presented. Since there is no need to measure the received instantaneous power for diversity combining, the proposed diversity reception scheme is considered to be very practical. The average bit error rate (BER) performance in the presence of additive white Gaussian noise (AWGN), Doppler spread, multipath delay spread and cochannel interference (CCI) is evaluated by computer simulations for 4DPSK signal transmission in Rayleigh fading channels.