Improving Frequency Acquisition of a Costas Loop

A Costas loop for tracking a BPSK signal does not acquire when the initial frequency error is comparable to the loop bandwidth. This paper describes methods for deriving control proportional to frequency error so as to improve the frequency acquisition capability by an AFC augmentation. A composite AFC/Costas loop is realized by combining the individual loops. Pull-in from a frequency error much greater than the Costas loop bandwidth is now feasible. The increase in phase error due to the AFC capability is evaluated by a linearized analysis. If the bandwidth of the AFC portion is sufficiently narrow, the degradation is negligible. Improved frequency acquisition can also be realized by a simple modification of the Costas loop to remove the low-pass filter on the quadrature phase detector channel, with negligible degradation to phase tracking.     

Two-Channel Costas Loop Tracking Performance for UQPSK Signals with Arbitrary Data Formats

This paper generalizes and corrects previous results on the tracking performance of two-channel Costas-type carrier synchronization loops. In particular, the mean-square phase jitter performance of these loops is evaluated when the data formats on the two channels are arbitrary. Particular attention is given to the case where the loops contain active arm filters with or without hard limiters following them. For each case, it is demonstrated that selection of the channel gain ratio, as motivated by MAP estimation theory, does not guarantee optimum loop tracking performance. In fact, it is shown that, in some instances, a conventional single-channel Costas loop will outperform the two-channel version with the MAP choice of gain ratio. Instead, it is suggested that the gain ratio be chosen to directly minimize the mean-square phase tracking jitter which is equivalent to minimizing the loop's "squaring loss." When this is done, it is shown that, in some cases, one can obtain significant improvement in this performance measure. In all cases, however, the two-channel loop will now outperform the single-channel version.     

Coupled AGC-Costas Loops with AM/PM Conversion

Costas loops are invariably designed in conjunction with an automatic gain control (AGC) loop for stabilizing performance. In such systems an inherent coupling between the AGC and Costas loops develops, complicating the standard phase referencing analysis. This coupling is further emphasized if the gain control amplifier introduces an AM/PM conversion, which causes power variations to enter the Costas loop as phase variations. In this paper the coupling effect between AGC and Costas loops is developed, leading to a pair of joint, interconnected dynamical tracking loops. Some degree of solution is attainable by assuming a first order AGC loop, and resorting to quasi-stationary analysis for evaluating the phase referencing generation. Results with and without AM/PM are presented, and illustrate how an improper AGC may in fact degrade the phase referencing from the expected performance.     

On false lock in suppressed carrier MPSK tracking loops

The problem of false lock in suppressed-carrier minimum phase-shift keying (MPSK) tracking loops (M>4 in particular), such as Mth power phase-locked loop (PLL) and MPSK Costas loop carrier recovery subsystems, is investigated. It is demonstrated that such tracking loops false lock onto the received signal when the received carrier frequency and the reference signal frequency generated by MPSK tracking loops are mismatched by multiples of 1/M of the MPSK symbol rate. False lock margins (FLMs) for the suppressed carrier MPSK tracking loops are obtained for a noiseless system model as well as for a model corrupted by additive white Gaussian noise (AWGN). Numerical results are presented in order to explain the influence of system parameters, such as the time-bandwidth product of MPSK Costas loop arm filters (or the Mth power PLL prefilter), arm filters' output signal-to-noise ratio and the input signal-to-noise ratio, on the performance of MPSK tracking loops     

Lock detection in Costas loops

Previous analyses of lock detector algorithms for Costas loops have ignored the effects of the inherent correlation between samples of the phase error process. In this work, analysis and simulations are used to quantify the effects of phase correlation on lock detection for the `square law' and `absolute value' type detectors. Results which depict the lock detection probability as a function of loop signal-to-noise ratio for a given false alarm rate are obtained. It is shown that the square law detector experiences less degradation due to phase jitter than the absolute value detector and that the degradation in detector signal-to-noise ratio is more pronounced for squarewave than for sinewave signals     

Novel p.s.k. tanlock loop

A new loop for coherent demodulation of suppressed carrier phase-shift-keyed (p.s.k.) signals is presented. The p.s.k. tanlock loop (p.s.k.-t.l.l.) has a wider tracking range and faster phase acquisition than the Costas or squaring loops usually used for p.s.k. suppressed carrier tracking, but it has a greater tendency to false lock.     

PSK optical homodyne detection using external cavity laser diodesin Costas loop

5-Gb/s optical PSK (phase-shift keying) homodyne detection experiments are discussed. In these experiments, the optical carrier is recovered by a Costas optical phase-locked loop using a multielectrode local oscillator (DFB) laser diode at 1.55 μm with a flat FM response. Although the beat linewidth of 80 kHz is broad compared to the loops in other phase-locked loop (PLL) experiments, phase locking with Costas loop is confirmed at 5 Gb/s by increasing the loop natural frequency. The receiver sensitivity is -42.2 dBm or 93 photon/bit for a 2⁷-1 pseudorandom bit sequence (PRBS) in front of a 90° hydride     

Tracking Performance of Costas Loops with Hard-Limited In-Phase Channel

It is becoming increasingly popular in the design of suppressed carrier receivers, which employ Costas loops for earrier reconstruction, to hard-limit the output of the in-phase channel. Doing so allows replacement of the analog multiplier, which forms the loop error signal, with a chopper-type device which typically exhibits much less dc offset. The false lock behavior of such a hard-limited loop was recently investigated and shown to be quite different from that of the conventional Costas loop without the hard limiter. This paper presents the companion, analysis of the tracking performance of the hard-limited loop and assesses the penalty, if indeed it is a penalty rather than an improvement, in this performance relative to the conventional Costas loop with an analog third multiplier. In particular, for the case ofRCarm filters and NRZ data, the squaring loss (or equivalently the linear loop tracking jitter) is evaluated and illustrated as a function of the ratio of arm filter bandwidth to data rate and data signal-to-noise ratio. Superimposed on these numerical results will be the corresponding ones for the conventional Costas loop. As a finale, the equivalence in operation of the Costas loop with hard-limited in-phase channel and a baseband modulation carrier reconstruction loop referred to as a demod/ remod loop is discussed.     

基于软件的GPS信号捕获跟踪算法研究

对GPS软件接收机的捕获和跟踪部分进行了研究。对于捕获模块,通过对常用串行搜索捕获算法和并行频域搜索捕获算法的比较和分析,提出了一种新型并行码相位搜索捕获算法;对于跟踪模块,提出采用非相干延迟锁相环对码进行跟踪,同时采用Costas环对载波进行跟踪;最后,从捕获和跟踪的GPS信号中提取出导航电文,并根据电文中的参数计算出了用户的位置坐标,并在Matlab中对用户的位置坐标进行了定位解算验证。     

Discrete Time Analyses of Nonuniform Sampling First- and Second-Order Digital Phase Lock Loops

The present paper considers discrete time analyses of firstand second-order digital phase lock loops. These loops are characterized by the fact that they track the zero crossings of the incoming signal; consequently, the sampling intervals are nonuniform. The firstorder loop is analyzed for phase step and frequency step inputs; mean time to skip cycle is also considered. For phase step input, approximate expressions are obtained for the steady-state phase error probability density and phase error variance, the second of which leads directly to a theoretical prediction of threshold. The second-order loop is analyzed for frequency step input. Approximate expressions for the steady-state phase error probability density, phase error variance, and a theoretical prediction of threshold are obtained. The analyses are confirmed by numerical results and simulation.     

Comparison of four FFT-based frequency acquisition techniques forCostas loop BPSK signal demodulation

This paper discussed four open-loop frequency acquisition techniques for suppressed-carrier BPSK signals. The techniques, which do not require accurate symbol timing nor a data preamble sequence, employ fast Fourier transforms (FFT's) on the Costas loop phase detector output to detect the Doppler frequency offset. Performance of the full-, half-, and staggered-symbol integration techniques as well as the low-pass filter technique are compared in terms of the error signal output SNR's. Then, the probability of detecting the frequency offset is computed for the special case when the frequency of the tone to be detected coincides with one of the FFT-bin center frequencies. It is shown that the performance of the integration techniques depends strongly on the symbol timing offset. On the other hand, the detection probability for the one-pole arm filter technique depends directly on the filter bandwidth. The staggered integration technique is shown to have comparable performance to the low-pass filter technique for low-to-medium symbol SNR's but the latter is superior at high symbol SNR's     

Simple baseband synchronisation scheme for tamed frequencymodulation

A novel carrier and clock synchronisation scheme for tamed frequency modulation is presented. It requires one complex sample per bit, like the digital Costas loop for offset in-phase and quadrature modulations, and is based on processing baseband samples of the phase of the received signal. The performance of the synchroniser is assessed by S-curves and simulated acquisition trajectories     

Performance of optical heterodyne PSK systems with Costas loop inmultichannel environment for nonlinear second-order PLL model

Using the nonlinear second-order phase-locked loop (PLL) model the performance of the heterodyne coherent optical phase shift keying (PSK) systems with Costas loop in multichannel environment is considered in this paper for the first time. The shot noise of the corresponding photodiodes and adjacent channel interferences are described through the signal-to-noise ratio (SNR) in the loop bandwidth, while the laser phase noise is described through the normalized frequency fluctuations instead of the phase ones. The theory and results presented in this paper can be applied when analyzing and optimizing the performance in the region where the linear PLL model is not enough good     

Optimum Design and Performance of Costas Recievers Containing Soft Bandpass Limiters

This paper investigates several key questions concerning the mechanization and design of a Costas receiver for reconstruction of a carrier from a suppressed carrier signal. For baseband NRZ encoded data symbols and a soft bandpass limiter preceding the loop, several design issues which are considered herein and which affect acquisition and tracking performance are: (1) The choice of an IF bandwidth. (2) The optimum choice of the Costas arm filter bandwidths as well as the spectral roll-off characteristics. (3) The optimum choice of loop bandwidth to data rate ratio for a given signal-to-noise ratio. (4) The signal suppression factor and the combined limiter-squaring loss. (5) The variations in loop bandwidth and damping with signal level. (6) The choice of the limiter transfer characteristic. (7) Performance degradation due to the presence of a limiter. Various new results in system design are presented and typical numerical results are given and graphically demonstrated in SNR regions of practical interest. The theory is applicable to the design of carrier reconstruction loops required in the implementation of spread spectrum communication receivers.     

Performance Improvement of a Binary Quantized All-Digital Phased-Locked Loop with a New Aided-Acquisition Technique

A nonuniform sampling digital phase-locked loop (DPLL) is proposed with a sequential loop filter, in which two additional phase comparators are added conjointly with an estimation-decision circuit controlling the two distinct modes, acquisition and tracking, in which the loop is to work. These additions provide more freedom to deal with the conflicting requirements of minimum acquisition time and maximum noise rejection in the presence or absence of frequency drift. Using a pseudo-two-dimensional random-walk filter, the stationary phase-error variance and the mean acquisition time have been evaluated by means of a numerical analysis. The comparison between the theoretical analysis and the experiments has proven to be very satisfactory. Substantial reduction of the acquisition time, without severely degrading the noise reduction performance, has been achieved. The improved ability of this modified loop to track frequency drift was also demonstrated. A digital loop "quasi-bandwidth" measure was used in the evaluation of the loop performance, thus allowing for a comparison with other digital loops and to a limited extent with a first-order analog loop. The usual difference in performance favoring the analog loop for high signal-to-noise ratio is shown to be substantially reduced and can be lowered by an appropriate choice of parameters.     

A non-coherent architecture for GNSS digital tracking loops

In this paper, a new, noncoherent architecture for global navigation satellite system tracking loops is proposed and analyzed. A noncoherent phase discriminator, able to extend the integration time beyond the bit duration, is derived from the maximum likelihood principle and integrated into a Costas loop. The discriminator is noncoherent in the sense that the bit information is removed by using a nonlinear operation. By jointly using such a discriminator and noncoherent integrations at the delay lock loop level, a fully noncoherent architecture, able to operate at low carrier-power-to-noise density ratio (C/N ₀), is obtained. The algorithms proposed have been tested by means of live GPS data and compared with existing methodologies, resulting in an effective solution for extending the total integration time.     

Mobile GPS carrier phase tracking using a novel intelligent dual‐loop receiver

Carrier phase information is necessary for accurate measurements in global positioning system (GPS) applications. This paper presents a novel intelligent GPS carrier tracking loop with variable‐bandwidth characteristics for fast acquisition and better tracking capability in the presence of dynamic environments. Our dual‐loop receiver is composed of a frequency‐locked loop‐assisted phase‐locked loop structure, the fuzzy controllers (FCs), and the ATAN discriminator functions. The soft‐computing FCs provide the time‐varying loop gains to perform accurate and reliable control of the dual‐loop paradigm. Once the phase dynamic errors become large under kinematic conditions, the fuzzy loop gains increase adaptively and achieve rapid acquisition. On the other hand, when the tracking errors approach zero in the steady state, the loop gains decrease and the corresponding dual‐loop receiver returns to a narrowband system. Four types of carrier phase signals, i.e. phase offset, decaying sinusoidal phase jitter, frequency offset, and frequency ramp offset, are considered to emulate realistic mobile circumstances. Simulation results show that our proposed receiver does achieve a superior performance over conventional tracking loops in terms of faster settling time and wider acquisition range while preventing the occurrence of cycle slips. Copyright © 2008 John Wiley & Sons, Ltd.     

高动态环境下扩频系统的快速同步方案

提出了一种应用于高动态环境下扩频系统的快速同步方案,通过优化帧结构设计,利用PN序列自相关达到快速的帧捕获,通过对鉴频环路的结构修改,采用FLL和PLL协同工作的方式,利用四相鉴频器跟踪频率变化,进行大频率搜索;利用叉积自动频率跟踪算法联合Costas环作为载波跟踪算法;环路滤波器采用扩展卡尔曼滤波技术,在提升信号捕获速率的同时,降低噪声的影响,提高捕获精度。经仿真验证,可以在相对较低的复杂度下获得良好的性能。     

QPSK扩频调制信号载波跟踪环路设计

扩频接收基带通常需要载波跟踪环来完成本地载波与接收信号载波的同步,科斯塔斯环是常用的非相干载波相位跟踪环,具有较好的鉴相特性。本文基于常规的单路单载波解调的科斯塔斯环原理,对科斯塔斯环做了改进,提出了对双通道平衡QPSK扩频基带所用载波跟踪环科斯塔斯环的改进方法,并推导出环路误差鉴相信号,用Matlab进行了仿真实验,结果证明利用本环路可实现载波稳定跟踪。     

The behavior of a Costas loop in the presence of space telemetrysignals

When the Costas loop is operated in the presence of a residual carrier space telemetry signal, the loop reconstructs its carrier reference from an input signal whose carrier component is not completely suppressed. The telemetry signal investigated in this work is generated by phase shift-keying the data onto a subcarrier and then phase modulating onto the sinusoidal carrier. The telemetry modulation index, telemetry bit rate, subcarrier waveform, and subcarrier frequency are shown to be the key system parameters that contribute to the performance degradation of a Costas loop. Furthermore, the effect of Doppler shift on the loop is also investigated in this work