Maximum Likelihood Carrier Phase Recovery for Linear Suppressed-Carrier Digital Data Modulations

The problem of ML estimation of the Phase of a general data-modulated carrier is considered. The shortcomings of current iterative approaches to the problem are pointed out, and the correct conceptual approach is proposed. The true ML estimator is then obtained and found to be nonimplementable. However, by specializing to limits of high and low SNR, the general ML estimator is shown to reduce to implementable DA and NDA ML estimators, respectively. The DA receiver's performance in terms of phase tracking and symbol error probability can be analyzed, and even the effects of past decision errors on current system performance can be assessed. For circular signal constellations, the DA receiver has a simple and totally linear structure which is easy to implement. The NDA ML estimator is shown to be equivalent to the common carrier loops. Our emphasis here on explicit computation of the ML phase estimate from the past received signal leads to detection strategies which do not require a carrier loop and a VCO for coherent detection.     

REDUCED COMPLEXITY FREQUENCY ESTIMATOR FOR BURST TRANSMISSION

In burst transmission, carrier recovery is a critical point for synchronization systems. With a feedforward carrier phase recovery algorithm, a small frequency offset can significantly increase the cycle slip rate and then the phase error variance. Therefore, in order to obtain an accurate carrier phase estimation, a precise frequency correction is required. For M-states phase shift keying (M-PSK) modulated signals an unbiased feedforward reduced complexity frequency estimator (RCFE), operating in the non-data aided mode (NDA) is derived from the maximum likelihood (ML) principle. A compromise is realized between noise filtering and estimation slip probability by minimizing the estimator variance. It is optimized to operate at a low signal-to-noise ratio and short bursts. Its performance is compared to that of the ML estimator. The estimator is applied to an all-feedforward synchronization structure with QPSK modulated signals. Global performance of the modem synchronization structure is supplied. © 1996 by John Wiley & Sons, Ltd.     

A suboptimal receiver for joint spatial-temporal filtering andmultiuser detection in mobile radio communications

This paper proposes a suboptimal receiver for joint spatial-temporal filtering and multiuser detection in mobile radio communications using single carrier signaling. The proposed receiver is a reasonable approximation of the maximum likelihood (ML) based optimal receiver described in the present paper. A cascaded connection of an adaptive array antenna and an ML multiuser sequence estimator is the basis of the proposed receiver. The major advantages of the proposed receiver over conventional adaptive array antennas are: (1) delayed path components of desired signals can be effectively combined; (2) interference signals exceeding the degree of freedom; and (3) those having the same incident angle as that of desired path components can both be suppressed. The proposed receiver does not require prohibitively large computational complexity. Results of computer simulations presented in this paper show that the proposed receiver exhibits excellent performance even in severe multipath fading environments     

Iterative detection of turbo-coded offset QPSK in the presence of frequency and clock offsets and AWGN

The key contribution of this paper is to develop transmitter and receiver algorithms in discrete-time for turbo-coded offset QPSK signals. The procedure for simulating a clock offset between the transmitter and receiver is described. Due to the use of up-sampling, matched filtering and a differential correlation approach at the receiver, the time required for detecting the start of frame (SoF) is just around 500 symbols, which is also the length of the preamble. The initial estimate of the SoF and the frequency offset, obtained using the differential correlation approach, is improved using an iterative process. A novel two-step maximum likelihood (ML) frequency offset estimation is proposed, which significantly reduces the complexity over the conventional ML estimation. The decision-directed carrier and timing recovery algorithms use simple first-order IIR filters to track the carrier phase and clock slip. The proposed synchronization and detection techniques perform effectively at an SNR per bit close to 1.5?dB, in the presence of a frequency offset as large as 30% of the symbol-rate and a clock offset of 25?ppm (parts per million). It is shown via simulations that the performance loss with respect to the bare turbo code is only about 0.5?dB, for a preamble length of 500 and a BER of 10^?7. The proposed techniques are well suited for software implementation.     

On orthogonal signaling over the slow nonselective Rician fadingchannel with unknown specular component

Orthogonal signaling over the slow nonselective Rician fading channel is considered. Previous receiver designs have all assumed the amplitude and phase of the specular component of the received carrier to be known completely, but this assumption is entirely unrealistic. The problem is reformulated with unknown random amplitude and phase of the specular component. The optimum maximum likelihood receiver is obtained for equally likely equal-energy orthogonal signals and is shown to be identical to the quadratic receiver for the purely unknown phase channel and the pure Rayleigh fading channel. The error probability performance is analyzed for a fixed known specular amplitude. When specialized to the binary signaling case this error probability result exhibits a performance that is very close to and asymptotically approaches that of the conventional coherent-specular-component case for high SNR. Thus, knowledge of the specular component phase is not important to the optimum receiver     

MPSK信号载波频率盲估计

该文针对调制自动识别中,MPSK信号调制相制和训练序列未知的情况,提出了一种利用定时同步信号的差分相位有效识别MPSK信号相制M,并精确估计其载波频偏的方法。该算法不仅克服了调制制式不明对频偏估计的不利影响,还通过引入线性相位展开和高阶时延相关,大大提高了大频偏、低信噪比下估计的性能,对调制自动识别中MPSK信号的澄清和参数估计起到关键作用。     

Carrier phase synchronization for GMSK signals

Several carrier phase recovery schemes for Gaussian minimum shift keying (GMSK) modulated signals are derived and analysed in terms of squaring loss and acquisition time. Two bandwidths are considered for the GMSK signal: BT_b=0.5 and 0.25, following the recommendations of the Consultative Committee for Space Data Systems. Pre‐encoding is assumed to remove the inherent differential encoding of the GMSK modulations. The carrier phase recovery schemes are derived from the approximate expression of the GMSK signal as an OQPSK signal or as the superposition of two OQPSK signals maximum a posteriori/maximum likelihood phase estimation is considered, with perfect clock reference; both non‐data‐aided and decision–directed schemes are analysed. Moreover, in the case of GMSK with BT_b=0.25, an equalizer is also included in the synchronizer loop to remove inter‐symbol interference. High and low signal to noise ratio (SNR) approximations are considered to simplify the structure of the synchronizers. It is shown that, for the considered BT_b values, the complex synchronizers initially derived do not provide any improvements over their simplified versions; the introduction of the equalizer for GMSK with BT_b=0.25 leads to a better performance. Moreover, it is shown that GMSK with BT_b=0.5 has a better performance than unfiltered OQPSK, which is better than GMSK with BT_b=0.25. The SNR values above which the high SNR approximation turns out to be convenient with respect to the low SNR approximation are also given. Copyright © 2002 John Wiley & Sons, Ltd.     

极低信噪比环境下的载波同步算法研究

在极低信噪比环境下,需要使用纠错能力强的编码比如Turbo码,但Turbo码系统的缺点是要求近乎理想的载波同步。然而,在极低信噪比环境下,Turbo编码系统的同步是具有挑战性的工作。文章提出了一种基于最大均方软输出的扫频和面向判决载波同步相结合的载波同步算法。仿真结果表明,该算法能捕获较大的频偏和相偏,且在极低信噪比环境下,仍能正常工作,其性能非常接近理想同步条件下的性能。     

Specular coherent and noncoherent optimal detection for unresolvedmultipath Ricean fading channels

This paper considers specular coherent and noncoherent optimal detection for unresolved multipath Ricean fading channels with known delays. The focus is on receiver structures and performance. Specular coherent detection employs the carrier phase of the Ricean specular component, while noncoherent detection does not. Therefore, a specular coherent detector must be augmented with a carrier phase estimator for the specular component. The structures considered are generalization of the well-known RAKE receiver to the unresolved multipath case. It is shown that both optimal structures perform a decorrelation operation before combining, which is essential to eliminating error floors under multipath unresolvability conditions. Furthermore, the noncoherent optimal receiver includes an inherent estimator for the specular component phasor. It is shown that the specular coherent and noncoherent structures converge at high SNR. This result is confirmed through analytical and numerical performance evaluation. Little performance gains can be obtained by the use of specular coherent detection for orthogonal frequency-shift keying and to a lesser extent for differential phase-shift keying over mixed mode Ricean/Rayleigh fading channels, making noncoherent demodulation attractive in these cases     

ML iterative soft-decision-directed (ML-ISDD): a carrier synchronization system for short packet turbo coded communication

Modern communication systems are required to provide services based on high data rates burst-mode packet-data transmission, capable of operating at very low SNR conditions. Turbo codes enable the operation at low SNR, close to the Shannon limit. However, carrier frequency and phase synchronization, needed for optimal coherent performance of the receiver, still remains a problem in low SNR and short bursts conditions. This paper proposes a new carrier synchronization method, the Maximum-Likelihood Iterative-Soft-Decision-Directed (ML-ISDD), which uses the turbo-decoder soft decisions to improve the carrier synchronization performance at low SNR values. The ML-ISDD method operates iteratively and jointly with the turbo decoder, enhancing both the turbo-decoder and the synchronization performance. The ML-ISDD method has been shown by simulation to significantly increase the allowed initial frequency and phase uncertainty region, thus allowing the use of very short training sequences for initial carrier synchronization.     

Carrier phase tracking from turbo and LDPC coded signals affected by a frequency offset

This contribution considers carrier phase estimation from coded signals, affected by a frequency offset at low operating signal-to-noise ratio (SNR). We derive a maximum likelihood (ML) based iterative code-aided feedback phase-tracker suited for receivers with iterative maximum-a-posteriori (MAP) detection. Simulations indicate that the proposed synchronizer is considerably more robust against frequency offsets than a feedforward synchronizer.     

TDMA信号的宽范围载波同步译码联合迭代处理

针对时分多址(Time Division Multiple Access,TDMA)信号提出了宽范围的载波同步译码联合迭代处理的方案。该方案主要分为三个部分,首先利用TDMA信号的同步码进行数据辅助同步,对信号中的大频偏和相偏进行粗估计和纠正;然后利用线性调频Z变换(Chirp-Z Transform,CZT)算法针对整突发帧进行非数据辅助同步,精确估计和纠正信号的剩余频偏;最后通过利用译码器输出的软信息进行编码辅助同步,多次迭代得到剩余相偏的精确估计,最终实现载波的精确同步并输出译码结果。实验结果表明,所提方案具有同步捕获范围宽、参数估计精度高、译码输出误比特率低等优点,在低信噪比环境下也能表现出优良性能。     

Performance study of a maximum-likelihood receiver for FFH/BFSKsystems with multitone jamming

We derive the optimum structure of a maximum-likelihood (ML) receiver for a fast frequency-hopped binary frequency-shift-keying (FFH/BFSK) spread-spectrum (SS) communication system operating in the presence of multitone jamming (MTJ) and additive white Gaussian noise (AWGN). It is shown that the side information of noise variance, signal tone amplitude, and multiple interfering tone amplitude at each hop, as well as the computation of nonlinear modified Bessel function are required to implement the optimum ML receiver. We have also derived and analyzed two suboptimum receivers-namely, the ML-I and ML-II receivers-for large and small signal-to-noise ratio (SNR), respectively. Performance comparisons among various receivers show that the ML receiver gives the best performance, while the ML-I and ML-II receivers also outperform the other existing methods under both high and low SNR conditions     

Viterbi detection with simultaneous suboptimal maximum likelihoodcarrier phase estimation

The authors consider maximum-likelihood (ML) detection of convolutionally coded data over the AWGN channel with unknown carrier phase. A receiver is developed for simultaneous ML data decoding and suboptimal ML carrier-phase estimation. The receiver is readily implementable and, for a circular signal constellation, it is totally linear. Computer simulations using two different models of the time-varying carrier phase indicate that the receiver provides good bit error probability performance     

OFDM盲载波间干扰抑制与同步算法研究

针对载波频偏引起的子载波间干扰问题,提出一种基于独立分量分析的OFDM载波频率同步算法。本算法直接实现载波频率同步,可以避免基于导频机制的频偏估计和由频偏估计误差带来的频谱效率降低与性能损失。首先建立含频偏OFDM独立分量分析模型,然后从最大似然原则得到分离的代价函数,结合自然梯度优化得到OFDM源信号实现载波频率同步。理论分析表明,提出的算法不仅具有基于最大似然的频偏补偿性能而且提高了系统的输出信噪比。最后,仿真分析证明了算法的有效性。      

基于数据辅助的MPSK信号频域信噪比估计

为在载波频率精确恢复前提高多进制数字相位调制（MPSK）信号在低信噪比下的估计精度,提出了一种数据辅助的MPSK信号频域信噪比估计算法。算法在符号定时恢复和帧同步后提取同步段符号,相关运算后在频域进行信噪比估计。仿真结果表明,算法估计均值无偏,不受载波频率误差的影响,在符号长度为512、信噪比为-10 dB时,均方误差与克拉美罗界只有0.15 dB的偏差,特别适合于接收信号包含载波频率误差且要求低信噪比下具有较高信噪比估计性能的应用。     

Non Data Aided SNR Estimation for OFDM Signals in Frequency Selective Fading Channels

This paper deals with the problem of non data aided (NDA) signal to noise ratio (SNR) estimation of OFDM signals transmitted through unknown multipath fading channel. Most of present day’s SNR estimators are based on the knowledge of pilot sequences which is not applicable in some contexts such as cognitive radio for example. Moreover in Multipath fading channels SNR also depends on frequency offset which is caused by mismatch between the oscillator in the transmitter and that in the receiver. Previous NDA SNR estimation schemes assumed a perfect synchronization at reception (i.e. τ = 0 and ${\varepsilon = 0}$ ) which results estimation of SNR with less accuracy. The frequency offset attenuates the desired signal and causes intercarrier interference, thus reducing the SNR. In this paper we propose a new NDA SNR estimator which uses periodic redundancy induced by the cyclic prefix, considering SNR degradation due to frequency offset ( ${\varepsilon}$ ).     

Tracking Loops for Carrier Reconstruction in Vestigial Sideband (VSB) Suppressed-Carrier Data Transmission

This paper deals with a tracking-loop-type approximation to the maximum likelihood (ML) estimator of the carrier phase in a suppressed-carrier vestigial sideband (VSB) data-transmission system. Two different tracking loops are considered, the one resembling a Costas loop, the other a data-aided receiver (DAR). The performance of these circuits is analyzed in the presence of thermal noise and intersymbol interference, and the results are compared with those relevant to a conventional scheme wherein a pilot tone is used to reconstruct the carrier at the receiver.     

Digitally Phase Modulated (DPM) Signals

Some properties of digitally phase modulated (DPM) signals are presented. Phase modulation with (overlapping) pulses generated by a digital FIR filter belong to this class, which may be considered to be a practical approximation to continuous phase modulated (CPM) signals. The power spectra of DPM signals are derived analytically. The ability of these signals to operate through an additive white Gaussian noise channel is assessed by calculating their minimum Euclidean distance. Their noise and spectral properties are found to be similar to those of CPM signals. Assuming that a Viterbi decoder is used to resolve symbol interference, the out-of-band power tends to decrease as the pulse duration increases, and the noise immunity is enhanced. At the same time the receiver complexity grows exponentially. Hence, noise immunity and spectrum compactness are achieved at the cost of higher received complexity. Modems for DPM signals are believed to be easier to implement than those for CPM signals. This is because filter design is simple and a residual carrier component can be retained to facilitate carrier regeneration. Furthermore, the accumulated carrier phase does not need to be continuously evaluated in order to perform matched filtering. The analytic results derived are supported by measurements and simulations.     

Frequency estimation of a single complex sinusoid using a generalized Kay estimator

This letter introduces a generalized version of Kay's estimator for the frequency of a single complex sinusoid in complex additive white Gaussian noise. The Kay estimator is a maximum-likelihood (ML) estimator at high signal-to-noise ratio (SNR) based on differential phase measurements with a delay of one symbol interval. In this letter, the corresponding ML estimator with an arbitrary delay in the differential phase measurements is derived. The proposed estimator reduces the variance at low SNR, compared with Kay's original estimator. For certain delay values, explicit expressions for the window function and the corresponding high SNR variance of the proposed generalized Kay (GK) estimator are presented. Furthermore, for some delay values, the window function is nearly uniform and the implementation complexity is reduced, compared with the original Kay estimator. For a delay value of two, we show that the variance at asymptotically high SNR approaches the Cramer-Rao bound as the sequence length tends to infinity. We also explore the effect of exchanging the order of summation and phase extraction for reduced-complexity reasons. The resulting generalized weighted linear predictor estimator and the GK estimator are compared with both autocorrelation-based and periodogram-based estimators in terms of computational complexity, estimation range, and performance at both low and high SNRs.