Timing and Frequency Synchronization for the Uplink of an OFDMA System

Frame Synchronization for Coded Systems Over AWGN Channels T. Cassaro and C. N. Georghiades For the additive white Gaussian noise channel, we consider the problem of frame synchronization for coded systems. We present an algorithm that takes advantage of soft information provided by a soft decoder to produce an enhanced estimate of the frame boundary. To reduce complexity, a companion algorithm is introduced that is a hybrid of the optimal uncoded frame synchronizer introduced by Massey and the list synchronizer introduced by Robertson. The high-complexity coded maximum-likelihood frame synchronizer used by Robertson will accordingly be replaced by our algorithm, which operates on decoder-provided soft decisions. The algorithm begins by obtaining a list of high-probability starting positions via the log-likelihood function of the optimal uncoded frame synchronizer. Then, a test$delta$is used to decide if the decision of the optimal uncoded frame synchronizer is sufficient, or whether list synchronization is required. If the test chooses in favor of using the optimal uncoded synchronizer, the estimate is obtained with relative ease. Otherwise, list synchronization is performed and statistics provided by the decoder are used to resolve the frame boundary. Monte Carlo simulations demonstrate that the frame-synchronization error rate (the probability of the synchronizer making an error) achieves the lower bound for signal-to-noise ratio values exceeding 1 dB.     

On sequential frame synchronization in AWGN channels

We present a framework for the analysis of frame synchronization based on synchronization words (SWs), where the detection is based on the following sequential algorithm. The received samples are observed over a window of length equal to the SW; over this window, a metric (e.g., correlation) is computed; an SW is declared if the computed metric is greater than a proper threshold, otherwise the observation window is time-shifted one sample. We assume a Gaussian channel, antipodal signaling, equally distributed data symbols, and coherent detection, where soft values are provided to the frame synchronizer. We state the problem starting from the hypothesis testing theory, deriving the optimum metric [optimum likelihood ratio test (LRT)] according to the Neyman-Pearson lemma. When the data distribution is unknown, we design a simple and effective test based on the generalized LRT (GLRT). We also analyze the performance of the commonly used correlation metric, both with "hard" and "soft" values at the synchronizer input. We show that synchronization can be greatly improved by using the LRT and GLRT metrics instead of correlation and that, among correlation-based tests, sometimes hard correlation is better than soft correlation. The obtained closed-form expressions allow the derivation of the receiver operating characteristic (ROC) curves for the LRT and GLRT synchronizers, showing a remarkable gain with respect to synchronization based on correlation metric.     

Frame Synchronization Algorithm for LDPC Coded Burst Systems

We present a frame synchronization algorithm for low‐density parity‐check (LDPC) coded burst transmissions, which combines a conventional pilots‐assisted frame synchronization algorithm and a code‐aided algorithm based on the mean magnitude of the soft outputs from the LDPC decoder. With moderate computational complexity, the proposed algorithm is more efficient in bandwidth than conventional pilots‐assisted algorithms. When compared with other code‐aided algorithms, the proposed algorithm offers a better trade‐off between complexity and performance. Simulation results in the case of an 8‐PSK system with (1944, 972) LDPC code show that the proposed algorithm can achieve a performance equivalent to that of the perfect frame synchronization, with a bandwidth efficiency loss of 0.06 dB due to the use of pilot symbols.     

On a technique to calculate the exact performance of aconvolutional code

A Markovian technique is described to calculate the exact performance of the Viterbi algorithm used as either a channel decoder or a source encoder for a convolutional code. The probability of information bit error and the expected Hamming distortion are computed for codes of various rates and constraint lengths. The concept of tie-breaking rules is introduced and its influence on decoder performance is examined. Computer simulation is used to verify the accuracy of the results. Finally, we discuss the issue of when a coded system outperforms an uncoded system in light of the new results     

Design Methodology for a DVB Satellite Receiver ASIC

This contribution describes design methodology and implementation of a single-chip timing and carrier synchronizer and channel decoder for digital video broadcasting over satellite (DVB-S). The device consists of an A /D converter with AGC, timing and carrier synchronizer with matched filter, Viterbi decoder including node synchronization, byte and frame synchronizer, convolutional de-interleaver, Reed Solomon decoder, and a descrambler.The system was designed in accordance with the DVB specifications. It is able to perform Viterbi decoding at data rates up to 56 Mbit /s and to sample the analog input values with up to 88 MHz. The chip allows automatic acquisition of the convolutional code rate and the position of the puncturing mask. The symbol synchronization is performed fully digitally by means of interpolation and controlled decimation. Hence, no external analog clock recovery circuit is needed.For algorithm design, system performance evaluation, co-verification of the building blocks, and functional hardware verification an advanced design methodology and the corresponding tool framework are presented which guarantee both short design time and highly reliable results. The chip has been fabricated in a 0.5 µm CMOS technology with three metal layers. A die photograph is included.     

Noncoherent decoder-assisted frame synchronization for packet transmission

We propose a noncoherent decoder-assisted (NDA) frame synchronizer, a two-stage, synchronization scheme based on the list-synchronization principle [P. Robertson, 1992], [M. Howlader and B. Woerner, 2001], for serially concatenated coded differential modulation (SCCD) system [K. R. Narayanan and G. L. Stuber, 1999] in packet transmission. For the first stage, we derive a suitable noncoherent maximum likelihood (SNML) rule, more effective for the noncoherent decoder's operating region of smaller channel phase offsets, to provide a reliable list of potential frame starting positions. For the second stage, we propose a hybrid sync method by exploiting the combined sign difference ratio (SDR) and sync word log-likelihood ratio (SW LLR) information [M. Howlader and B. Woerner, 2001] to obtain more reliable final decisions and reduce computational complexity. Performance and complexity of the proposed scheme are evaluated under constant and time-varying phase offsets in the AWGN channel via Monte Carlo simulation.     

Sufficient conditions on trellis-coded modulation forcode-independent synchronizer performance

The carrier synchronization and symbol timing recovery for two-dimensional trellis-code modulated signals are considered. For many popular carrier and clock synchronizers, and tracking and cycle-slipping performance depends on the trellis code only through the second- and fourth-order moments of the coded channel symbols. For three successively more complicated classes of coded symbol alphabets, simple conditions on the trellis code are derived which are sufficient to yield the same second- and fourth-order moments as for uncoded symbols. For trellis codes satisfying these conditions, the synchronizer performance does not depend on the specific code, and is the same as for uncoded symbols. These sufficient conditions are fulfilled by many codes which have been presented in the literature, some of which are discussed     

Pilotless Frame Synchronization via LDPC Code Constraint Feedback

In traditional receiver architectures, frame synchronization is performed using pilot symbols and a correlation rule. In this paper we show that outputs from the constraint node side of a bipartite decoding graph can be used to achieve frame synchronization in a pilotless low-density parity-check (LDPC) coded transmission, thereby avoiding the bandwidth cost inherent in use of pilot symbols. The complexity of the frame synchronizer is kept relatively low due to its XOR-based approach.     

Decoder-assisted frame synchronization for packet transmission

This paper proposes a novel frame synchronization methodology for packets with convolutionally encoded data. Rather than by placing sync bits in a separate header, the sync bits are placed in a midamble and encoded as part of the data sequence, using the error correction encoder to resolve time ambiguities. The scheme is based on the principle that an error in trellis termination may result in decoding a wrong information bit sequence, while the starting portion of the sequence can be decoded as error free. This frame synchronization technique is extended to the synchronization of turbo-coded systems using a list-based approach, where the first synchronizer provides a list of potential packet starting positions, and the following synchronizer makes the final decision. The performance improvement over conventional synchronization techniques is quantified via simulation     

高速无线数传网格编码信号的简化解码算法

简单分析了网格编码信号在加性白高斯噪声(AWGN)信道中基于相位解码的维特比算法原理,并给出了一个两阶段解码算法的实现过程.该解码算法是基于接受到信号的相位信息进行解码,并带有一个简单的锁相环解决了相位模糊问题.两阶段解码算法对信号中的编码位和未编码位分别进行译码,因此增加了解码器的可移植性.该译码算法在保证译码性能的同时,明显降低了接收机的复杂度.     

The max-log list algorithm (MLLA)-a list-sequence decoding algorithm that provides soft-symbol output

We present a soft decoding algorithm for convolutional codes that simultaneously yields soft-sequence output, i.e., list sequence (LS) decoding, and soft-symbol output. The max-log list algorithm (MLLA) introduced in this paper provides near-optimum soft-symbol output equal to that of the max-log maximum a posteriori (MAP) probability algorithm. Simultaneously, the algorithm produces an ordered list containing LS-MAP estimates. The MLLA exists in an optimum and a suboptimum version that are different in that the optimum version produces optimum LS-MAP decoding for arbitrary list lengths, while the suboptimum low-complexity version only provides the MAP, the second-order MAP, and the third-order MAP sequence estimates. For lists with more than three elements, MAP decoding is not guaranteed, but the LS decoding is close to the optimal. It is demonstrated that the suboptimum/optimum MLLA can be used to obtain the combination of soft-symbol and soft-sequence outputs at lower complexity than a previously published algorithm. Furthermore, the suboptimum MLLA is well suited for operation in an iterative list (turbo) decoder, since it is obtained by only minor modifications of the well-known Max-Log-MAP algorithm frequently used for decoding of the component codes of turbo codes. Another potential area of application for the suboptimum/optimum MLLA is joint source-channel LS decoding. Estimates of complexity and memory use, as well as performance evaluations of the suboptimum/optimum MLLA, are provided in this paper.     

Joint Baud and Frame Synchronization in Direct Detection Optical Communications

The maximum-likelihood frame synchronizer was recently derived for direct-detection optical communications assuming baud synchronization. In this paper we present an extension to those results when pulse-position modulation is used and jointly derive baud and frame synchronization from slot synchronization. The optimum rule is seen to consist of a simple correlation term and a nonlinear correction term. Simulation results for the optimum rule compared to analytical and simulation results for the simple correlation rule show that equivalent performance for the simple correlation rule requires a substantial increase in signal power. To design good synchronization patterns, we use a divergence measure derived from the optimum rule. A simple algorithm is derived to test whether a given sequence is good or not.     

具有低复杂度的 LDPC 已编码非相干酉空时调制系统设计简

提出一种克服无线信道瑞利衰落和高斯白噪声干扰的非相干编码调制MIMO系统方案。纠错码采用IEEE 802.16e中的非规则QC-LDPC码,非相干调制采用基于三角函数的酉空时调制(SC-USTM)。在接收端,推导出SC-USTM的最大后验概率（MAP）解调算法;为了降低复杂度,构造了SC-USTM的双解调器方案;为了改善双解调的性能,在置信传播（BP）迭代解码器和MAP解调器之间引入了迭代反馈机制。仿真实验表明LDPC已编码SC-USTM的MIMO系统比未编码USTM的MIMO系统在 误码率时,性能改善15~17 dB,并且整个系统具有较低的计算复杂度。     

Analysis of error performance for Turbo coded pulse position width modulation

To lower the bit error rate （BER） of the pulse position width modulation （PPM＋PWM）, which is the improved scheme of the pulse position modulation （PPM）, correcting coding technique is necessary. After setting up the analytic model, the Turbo decoder and iterative algorithm for PPM＋PWM are studied, and the system error performance ofuncoded and Turbo coded PPM＋PWM under the Gaussian channel is simulated and analyzed, as well as the effects of the number of iterations and frame size on the bit error rate. The results show that the introduction of Turbo code can get the encoding gain of 4.0-6.9dB, which improves the error performance of system effectively and has advantage in military communications.     

Multiuser ML sequence estimator for convolutionally codedasynchronous DS-CDMA systems

The optimal multiuser sequence estimator is formulated for an asynchronous direct-sequence code-division multiple-access (DS-CDMA) system where each user employs convolutional coding to improve its performance on a nondispersive additive white Gaussian noise (AWGN) channel. It is shown that the decoder may be implemented efficiently using a Viterbi algorithm which operates on a time-varying trellis with a number of states which is exponential in the product of the number of users in the system and the constraint length of the codes used (for the rate 1/2 code case). The asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying (BPSK) receiver (termed asymptotic multiuser coding gain, or AMCG) is then upper and lower bounded. The AMCG parameter unifies the asymptotic coding gain parameter and the asymptotic multiuser efficiency parameter which are traditional figure of merit parameters for single-user coded systems and multiuser uncoded systems, respectively. Finally, some simulations are presented to illustrate the performance of the maximum likelihood sequence estimator (MLSE) at moderate and low bit error rates     

Joint Synchronization and Decoding for Photon-Limited Optical Channels: Code Design and Complexity Reduction

The problem of joint symbol synchronization and decoding of pulse position modulation (PPM) sequences in the deep-space photon-limited optical channel is considered. A new joint synchronizer and decoder for PPM on this channel is presented along with the design of codes having both good error control and synchronization properties for use with PPM signaling on this channel. The new approach presented in this paper provides a significant reduction in synchronizer/decoder complexity when compared to previous methods for joint synchronization and decoding.     

A low-complexity noncoherent iterative space-time demodulator

Turbo coded unitary space-time modulation (USTM) can provide large coding gain as compared to uncoded USTM. Because the noncoherent space-time maximum a posteriori demodulator is very complicated, in this letter, we propose a new low-complexity noncoherent iterative space-time demodulator for the USTM constructed from pilot symbol-assisted modulation. The proposed demodulator utilizes both hard and soft decisions from the turbo decoder to simplify the computational task as well as produce reliable soft outputs. Several examples demonstrate that this demodulator has both low complexity and good error performance.     

Code-aided ML joint synchronization and channel estimation for downlink MC-CDMA

In this paper, we present a novel code-aided joint synchronization and channel estimation algorithm for downlink multicarrier code-division multiple access. The expectation-maximization algorithm is used to locate the maximum-likelihood estimate of the channel impulse response, propagation delay, and carrier frequency offset. The estimator accepts soft information from the decoder in the form of a posteriori probabilities of the coded symbols, and can be interpreted as performing joint estimation and data detection. The performance of the proposed algorithm is verified through computer simulations. Impressive performance gains are visible as compared with a conventional data-aided estimation scheme.     

Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels

The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless communication channels. We propose a soft quasi-ML detector that maximizes the log-likelihood function by deploying a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML SDR detector closely approximates the performance of the optimal ML detector in both coded and uncoded multiple-input, multiple-output (MIMO) channels with quadrature phase-shift keying (QPSK) modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, thus offering more favorable performance/complexity characteristics. In contrast to the existing sphere decoder, the new quasi-ML detector enjoys guaranteed polynomial worst-case complexity. The two detectors exhibit quite comparable performance in a variety of ergodic QPSK MIMO channels, but the complexity of the quasi-ML detector scales better with increasing number of transmit and receive antennas, especially in the region of low signal-to-noise ratio (SNR).     

基于SSCANL译码器的联合迭代检测译码算法

为了提升基于极化码的稀疏码多址接入（sparse code multiple access,SCMA）系统接收机性能,提出了基于简化软消除列表（simplify soft cancellation list,SSCANL）译码器的循环冗余校验（cyclic redundancy check,CRC）辅助联合迭代检测译码接收机方案。该方案中极化码译码器使用SSCANL译码算法,采用译码节点删除技术对软消除列表（soft cancellation list,SCANL）算法所需要的L次软消除译码（soft cancellation, SCAN）进行简化,通过近似删除冻结位节点,简化节点间软信息更新计算过程,从而降低译码算法的计算复杂度。仿真结果表明,SSCANL算法可获得与SCANL算法一致的性能,其计算复杂度与SCANL算法相比有所降低,码率越低,算法复杂度降低效果越好;且基于SSCANL译码器的CRC 辅助联合迭代检测译码接收机方案相较基于SCAN译码器的联合迭代检测译码（joint iterative detection and decoding based on SCAN decoder, JIDD-SCAN）方案、基于SCAN译码器的CRC辅助联合迭代检测译码（CRC aided joint iterative detection and decoding based on SCAN decoder,C-JIDD-SCAN）方案,在误码率为10^-4时,性能分别提升了约0.65 dB、0.59 dB。