Performance of First-Order Digital Phase-Locked Loops in Mobile Radio Channels

The performance of a first-order digital phase-locked loop (DPLL) using nonuniform sampling is studied in the mobile radio environments. The mobile radio channel is characterized by introducing fast Rayleigh fading and random phase variation to the signal envelope and phase, respectively. The nonlinear stochastic difference equation describing the loop operation in fading environments is introduced. The joint probability density function (pdf) of the random variables of this equation is derived by transformation of random variables for fast Rayleigh fading channels. A closed-form expression for the transition probability of the ChapmanKolmogorov (C-K) equation is obtained for phase step plus noise input and for frequency step plus noise input. The probability density function of the steady-state phase error is obtained by solving the C-K equation numerically.     

Phase-Locked Loops with Limiter Phase Detectors in the Presence of Noise

A nonlinear mathematical model of phase-locked loops with limiter phase detectors in the presence of noise is presented. The model, which is an extension of the well-known baseband model of loops with sinusoidal phase detectors without limiters, incorporates a modified nonlinear phase detector characteristic, the form of which is changed if the input carrier-to-noise ratio alters, as well as a modified phase noise as an input to the model. Both the modified phase detector characteristic and the spectral density of the modified noise term are calculated specifically for sinusoidal, triangular, and sawtooth types of limiter phase detectors, allowing the application of various methods to determine the loop noise performance. As an example, the phase error variance of a first-order phase-locked loop is calculated, thereby showing a strong dependence on the specific phase detector realization.     

Tracking Properties of Phase-Locked Loops in Optical Communication Systems

This paper analyzes the performance of a phase-locked loop driven by the photodetector current in an optical receiver. The variance of the phase-errors of the loop is found as a function of the relevant system parameters. The results are in good agreement with experimental data obtained via computer simulation.     

选择性放大传送协同通信在Nakagami信道中的性能分析

该文根据两个统计独立非负随机变量的调和平均值的概率密度函数在零点的变化特性,分析了选择性放大传送协同协议在Nakagami衰落信道中的性能,得出了高信噪比时系统误符号率的闭合表达式。理论分析和数值仿真结果表明,在Nakagami信道中选择性放大传送协同协议可获得和传统放大传送协同协议一样的分集阶数,并且具有更优的误符号率性能。     

Secure Communication Over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.     

混沌扩频通信系统在多径Rayleigh衰落信道中的性能分析

本文研究了混沌直接扩频信号在多径Rayleigh衰落信道中传输时的抗多径干扰和多址干扰的特性。对于所给出的混沌扩频通信系统,当加入多径干扰和信道噪声时,给出了理论误码率与实际误码率的比较,数值结果表明在多径衰落信道中,混沌扩频通信系统抗多径干扰的性能很好;同时对混沌直接扩频信号的奇、偶互相关函数进行了计算,结果表明混沌扩频通信系统具有良好的抗多址干扰能力。     

Burst Synchronization of Phase-Locked Loops

Locking a phase-locked loop (PLL) with a sinusoid that is 100-percent AM modulated by a low-duty cycle square wave (i.e., comes in bursts) is an old and well-known technique. Despite this, certain aspects of the technique have not been systematically considered. One of the most important aspects is how to avoid sidelockan undesired mode where the loop locks to a frequency other than the sinusoid's frequency. In this paper, we explain how sidelock arises, how it can be avoided and how to provide a good lock while still avoiding sidelock. Throughout the paper our emphasis is on the situation, that is usually not considered, where the sinusoid's frequency can be considerably different than the center frequency of the voltagecontrolled oscillator (VCO).     

在多径衰落信道上FD／SSMA系统的性能分析

多载波频率分集扩展频谱码分多址系统是一种基于多载波传播,与直接序列扩展频谱码分多址系统存在时间－频率对偶关系的扩频多址通信方案。在多径传输信道下,基于ＦＤ／ＳＳＭＡ信号的锐自相关和低互相关特性,本文提出了ＦＤ／ＳＳＭＡ系统可以采用路径分集接收的方案。分析和模拟计算表明,在多径衰落信道下,采用路径分集方案时ＦＤ／ＳＳＭＡ系统的性能将得到明显的改善。     

在多径衰落信道下FD/SSMA系统的性能分析

多载波频率分集扩展频谱码分多址系统（ＦＤ／ＳＳＭＡ）是一种基于多载波传输,与直接序列扩展频谱码分多址系统（ＤＳ／ＳＳＭＡ）存在时间－频率对偶关系的扩频多址通信方案。在多径传输信道下,基于ＦＤ／ＳＳＭＡ信号的锐自相关和低互相关特性,本文提出ＦＤ／ＳＳＭＡ系统可以采用路径分集接收的方案。分析和模拟计算表明,在多径衰落信道下,采用路径分集方案时ＦＤ／ＳＳＭＡ系统的性能将得到明显的改善。     

An Approach to the Analysis of Performance of Quasi-Optimum Digital Phase-Locked Loops

An approach to the analysis of performance of quasioptimum digital phase-locked loops (DPLL's) is presented. An expression for the characteristic function of the prior error in the state estimate is derived, and from this expression an infinite dimensional equation for the prior error variance is obtained. The prior errorvariance equation is a function of the communication system model and the DPLL gain and is independent of the method used to derive the DPLL gain. Two approximations are discussed for reducing the prior error-variance equation to finite dimension. The effectiveness of one approximation in analyzing DPLL performance is studied.     

Quantization Effects in All-Digital Phase-Locked Loops

This brief analyzes the impact of the quantization noise sources in all-digital phase-locked loops (ADPLLs), recently employed as frequency synthesizers. In general, the in-band phase noise is not only caused by the phase quantization of the time-to-digital converter, but also by the frequency quantization of the digitally controlled oscillator (DCO). The delta-sigma modulator placed at the DCO input refines the frequency quantization and adds another source of in-band PLL noise. Interestingly, the higher the modulator order, the higher this source of in-band phase noise. A method for the estimation of all the quantization noise contributors is provided, which is proven by mixed-mode simulations.     

On Frequency Sweeping in Phase-Locked Loops

The following experimental study describes a new representation of the behavior that a second-order phase-locked loop (PLL) shows in the presence of linear frequency sweeping. This paper differs from previously published results in that it presents a general experimental analysis of the PLL during a sweep which is independent of a specific in-lock detection. Hence, the results represent a useful tool for the design of an in-lock detector in PLL sweep systems.     

瑞利衰落信道下MMRT的性能分析

为了提高系统性能减少系统功耗和硬件复杂度等,该文提出一种在基站采用最少选择最大比发射的发送分集技术,即MMRT。利用随机矩阵和排序统计的理论知识,该文对MMRT技术进行了详细的性能分析。并得到其在瑞利衰落信道下的中断概率、误码率等的确切表达式。最后通过仿真试验验证了理论分析的正确性。     

On the Pull-In Range of Phase-Locked Loops

The problem of determining the pull-in range of phaselocked loops is solved indirectly by evaluating the limit cycles of the loop in which the frequency error has a constant average. The analytical results derived here are in complete agreement with simulation results.     

瑞利衰落信道MDPSK相位比较解调性能

本文提出一种适合于瑞利衰落信道多进制差分相移键控系统相位比较解调的性能分析方法，推导出符号错误率解析表示式，考虑了瑞利衰落、时间选择性衰落和高斯白噪声对体制性能的影响，并针对衰落功率谱为高斯型和矩形分别对二进制、四进制和八进制情形进行了数值计算。     

Statistical Behavior of Second-Order Phase-Locked Loops in the Presence of a Mixture of Impulsive and Gaussian Noise

An equation is found for the steady-state probability density function of the modulo-2π-reduced phase error of a secondorder phase-locked loop (PLL) with a proportional-proportional-plus-integral control type filter. The equation involves a certain conditional expectation which has been evaluated in an approximate way following the same approach used by previous authors in the case of sole Gaussian noise. With this approximation the equation becomes of the same type as that pertinent to a first-order system and therefore it can be solved with a method described by Ohlson in [3]. Theoretical results obtained in this way are complemented by experimental observations gathered by simulating the PPL on a digital computer.     

Asymptotic Performance of Linear Receivers in MIMO Fading Channels

Linear receivers are an attractive low-complexity alternative to optimal processing for multiple-antenna multiple-input multiple-output (MIMO) communications. In this paper, we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-signal-to noise-ratio (SNR) regime in terms of the diversity-multiplexing tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas.As far as the DMT is concerned, we report a negative result: we show that both linear zero-forcing (ZF) and linear minimum mean- square error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and deAcircnot coding is performed across the antennas. We also provide an apAcircnot proximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and nonasymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of an MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear reAcircnot ceiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.     

MIMO衰落信道上MR-MQAM性能分析

使用矩生成函数方法分别推导了Nakagami衰落信道上多分辨率M进制正交幅度调制(MR-MQAM)的平均误比特率(BER)闭合表达式,发送和接收分别采用选择合并/最大比合并(SC/MRC)和正交空时分组编码(OSTBC).数值计算结果表明在相同的天线设置条件下,SC/MRC方案的平均误比特率性能要优于OSTBC.     

Performance Analysis of Land Mobile Satellite Communication Systems with Equal-Gain Combining over Shadowed-Rice Fading Channels

An accurate model for performance analysis of land mobile satellite (LMS) channels is the Shadowed-Rice (SR) fading model. Recently, an approximate SR model has been proposed by the author for LMS channels. Compared with the existing models, the proposed model is analytically tractable and makes it possible to approximate very accurately the probability density function (PDF) of the SR random variable (RV) by a finite weighted sum of Rice PDFs. In this paper and based on the proposed model, the statistics of the sum of independent SR RVs is studied. While this problem is well understood for common fading models such as the Rayleigh, Rice, and Nakagami, a minor attention has been devoted to the SR case. In this paper and by using the well-known Beaulieu series approach, the PDF and the Cumulative distribution function (CDF) of the sum of independent SR RVs are derived in the form of infinite convergent series. In this regard, analytical, closed-form expressions are derived for the coefficients of the Beaulieu series. To give an application of the presented results, the performance of LMS communication system employing equal-gain combining (EGC) diversity techniques over SR fading channel is investigated and novel closed-form expression is derived for the outage probability of the system.