Reference Loop Phase Shift in Adaptive Arrays

Adaptive arrays for use in communication systems require the generation of a so-called reference signal, which is usually derived from the array output. A particular problem associated with this technique, the problem of reference loop phase shift, is discussed. It is shown that phase shift in the reference loop causes the array weights to cycle, and also causes the array to frequency-modulate the signal. In spite of this frequency change, the array maintains a maximum SNR at the output.     

Convergence Rate of the Extended SMI Algorithm for Narrowband Adaptive Arrays

An extended sample matrix inversion (SMI) algorithm can be used for minimizing the mse (mean-squared error) between the output of an N-element adaptive array and a desired reference signal. This algorithm is shown to yield mse within 3 dB of minimum (on the average) after (2N - 1) observations of the antenna element outputs.     

The Performance of an LMS Adaptive Array with Frequency Hopped Signals

The performance of an LMS adaptive array with a frequency hopped, spread spectrum desired signal and a CW interference signal is examined. It is shown that frequency hopping has several effects on an adaptive array. It causes the array to modulate both the amplitude and the phase of the received signal. Also, it causes the array output SINR (signal-to-interference-plus-noise ratio) to vary with time and thus increases the bit error probability for the received signal. Typical curves of the desired signal modulation and the time-varying SINR at the array output are presented. It is shown how the array performance depends on hopping frequency, frequency jump size, interference frequency, signal arrival angles, and signal powers.     

Eliminating Reference Loop Phase Shift in Adaptive Arrays

Adaptive array processors utilizing the Widrow LMS algroithm with an internally generated reference signal have been shown to be subject to weight cycling caused by phase shift in the reference extracting loop. Adaptive compensation schemes that eliminate the reference loop phase shift are suggested here. Two such schemes are proposed. They differ in the amount of hardware complexity needed as well as in the rate at which each one eliminates the phase shift. Computer calculations are used to compare the rates of convergence of the two schemes.     

Phase-Shift-Keyed Signal Detection with Noisy Reference Signals

This paper derives and graphically illustrates the performance characteristics of Phase-Shift-Keyed communication systems where the receiver's phase reference is noisy and derived from the observed waveform by means of a narrow-band tracking filter (a phase-locked loop). In particular, two phase measurement methods are considered. One method requires the transmission of an auxiliary carrier (in practice, this signal is usually referred to as the sync subcarrier). This carrier is tracked at the receiver by means of a phase-locked loop, and the output of this loop is used as a reference signal for performing a coherent detection. The second method is self-synchronizing in that the reference signal is derived from the modulated data signal by means of a squaring-loop. The statistics (and their properties) of the differenced-correlator outputs are derived and graphically illustrated as a function of the signal-to-noise ratio existing in the tracking filter's loop bandwidth and the signal-to-noise ratio in the data channel. Conclusions of these results as well as design trends are presented.     

The Effect of Differential Time Delays in the LMS Feedback Loop

The effect of differential time delay in the feedback loops of an LMS adaptive array is examined. Differential time delay is shown to have two effects on array performance. First, it causes the weights to oscillate during weight transients. Second, it degrades the output signal-to-interference-plus-noise ratio (SINR) from the array. Weight oscillation occurs when the phase shifts in the LMS loop are not matched at the signal carrier frequency. SINR degradation depends on signal bandwidth: the wider the bandwidth, the larger the degradation.     

Adaptive Array Behavior with Periodic Phase Modulated Interference

We consider a least mean square (LMS) adaptive array [1] receiving a phase modulated interference signal. The phase modulation is assumed to be periodic and to have finite bandwidth. Under these assumptions, we determine the time-varying array weights, the modulation on the array output desired signal, and the time-varying output interference-to-noise ratio (INR) and SINR (signal-to-interference-plus-noise ratio). We present numerical results describing the behavior of a 2-element adaptive array that receives an interference signal with sinusoidal phase modulation. We show how each signal parameter (arrival angle, power, modulation index, and modulation frequency) affects the performance of the array.     

Transient Frequency-Error Statistics in Acquisition of Noiseless First-Order Phase Lock Loop

After a certain time interval from the appearance of a reference signal in a synchronizing system employing a first-order phase lock loop (PLL), the probability that the output frequency error will be higher than a maximum tolerated value is determined. The system is assumed to be noise free.     

天线组阵中SUMPLE算法的合成相位漂移补偿

针对SUMPLE算法在低信噪比时存在的相位漂移问题,在分析权值估计误差引起的合成信号相位漂移现象的基础上,提出一种以固定时刻合成权值作为参考的补偿算法。该算法以收敛后某个固定时刻的合成权值作为参考,其他时刻的相位补偿值通过与该参考权值进行相关计算得到。从理论上分析了该算法的可行性,并进行仿真验证。理论分析与仿真结果表明,所给出的相位补偿方法能有效地消除合成信号的相位漂移现象,补偿后的合成信号相位中心稳定。     

Interferences in Phase-Locked Loops

An analysis of the behavior of a second-order phase-locked loop is presented when an unwanted signal is added to the useful signal. Both signals are sinusoidal and unmodulated, and the analysis is made in the absence of additive noise. When the loop remains locked on the useful signal, a parasitic signal exists at the phase detector output. This signal produces a parasitic phase modulation of the VCO and a static phase error in the loop. The parasitic signal amplitude, the parasitic phase modulation index, and the static phase error are calculated. A necessary condition for the loop to remain in lock is derived. When the loop is initially unlocked, locking can occur either on the useful signal or on the unwanted signal, depending on the amplitude ratio and the frequency difference of the two signals. A formula allowing one to compute the pull-in time is obtained. When the loop locks on the useful signal, acquisition can be slower or faster than in the absence of an unwanted signal. The same phenomenon is observed when the loop locks on the unwanted signal.     

An Lms Adaptive Array Using a Pilot Signal

A least mean square (LMS) adaptive array requires a reference signal. When the desired signal contains a pilot signal, it may be used as the reference signal. In this paper the steady-state performance of an LMS adaptive array in which the pilot signal is used as the reference signal is examined. It is shown that the LMS adaptive array occasionally suppresses the desired signal. The loop gain, which is an important parameter, is also considered.     

闭环光纤陀螺的死区现象及克服死区实验

克服死区是闭环光纤陀螺设计中需要考虑的重要问题。运用适当的小角速度测试方法测得了闭环光纤陀螺输出信号中的死区。采用了一种简便的偏置输出相移信号的方法以克服闭环光纤陀螺输出信号中的死区。实验表明,上述方法可以克服死区。     

Interference Canceler Array with Reference Generating Loop

Adaptive arrays utilizing an internally generated reference signal to drive least mean square (LMS) weight determining loops have experienced difficulty arising from phase shifts induced by the reference generating circuits. The phenomenon observed is that the expected value of the weights oscillate in the steady state modulating the incoming signal. A scheme is reported which avoids this problem. It differs from earlier methods in that the reference generator has no infinite limiter so that the amplitude of the reference is not constant and in that one element is left unweighted. Alternative schemes were considered wherein the reference signal is drawn from all the array elements or from the weighted elements only. Only the latter is fully reported here, and is found superior. It is shown that in the presence of a desired signal and independent element noise, the processing scheme proposed produces weights whose expected values converge to a constant nonoscillatory state provided certain mild constraints are satisfied. In particular, if a cos ? ? 1, a being the gain and ? the phase shift of the filter in the reference generator, the weights converge. In addition, the steady state signal-to-noise power ratio (SNR) is determined. It is found that with a cos ? close to unity the SNR is that of an (N-1) element array coherently combined, where N is the number of elements. The SNR falls off with departures of a and ? from 1 and 0, respectively, but not drastically.     

基于DDS+PLL的光源调制与功率稳定控制方法CSCD

量子传感器是基于量子操控技术的研究成果,一般具有高精度、小体积等优势。激光器是量子传感器的核心部件,有抽运和检测功能,激光器的稳定性对量子传感器具有重要的意义。提出了一种直接数字合成法(DDS)与锁相回路(PLL)相结合的方法,对激光器进行调制并抑制调制噪声,实现了激光器的稳定输出。基于现有小型量子传感器装置,在DDS生成4kHz参考信号的情况下实现了激光器电流8kHz调制,抑制了调制时调制电流信号噪声约8dB,并提高了激光器输出光功率的稳定性。     

Antenna array beam steering using time-varying weights

The author presents a new technique of steering an array antenna by introducing time-varying phase weights. It is shown that the technique is equivalent to placing a linear phase and linear frequency offset across the array when transmitting a linear frequency modulated (LFM) waveform. The technique reduces array dispersion and increases the operating bandwidth. An element level signal generator is presented as a possible way of implementing the time-varying weights. A possible array implementation is also shown.<>     

S频段小数分频锁相环频率合成器实现与应用

传统的整数分频锁相环频率合成技术无法在单个环路实现高频率、低分辨率和低相噪的目标,小数分频锁相环在提高鉴相频率的同时减小分频计数值,从而降低相位噪声。针对USB统一测控系统的需要,本文提出基于单片小数分频锁相环的微波频率合成方法。实验结果表明,小数分频锁相环频率合成器具备良好的信号输出特性,可以为测控系统提供低成本频率合成方案。     

Eigenanalysis for interference cancellation with minimum redundancy array structure

In a previous work, the principles of the eigenanalysis method for interference cancellation was studied for uniform regular array (URA) structure, wherein the array elements are equally spaced. The main objective of this paper is to extend the results of that work to adaptive arrays with different geometry termed "minimum redundancy array" (MRA). An efficient method is presented to solve the minimum variance optimization problem and explicit analytical solutions are derived for the optimal weight vector and output noise variance of the eigencanceler. Performance analysis of the general N-element array was first derived and used to extract the performance of MRA. URA is also considered as a special case. The closed-form equation depicts the minimum variance noise residue for the single interference case, while an interactive procedure is suggested for the two interferences case. If there are more than two interferences, we propose to use direct numerical calculation.     

The Effect of Integrator Pole Position on the Performance of an Adaptive Array

The LMS adaptive array requires an integrator in each weight feedback control loop. In practice the integrator is often replaced by a low-pass filter, i.e., by a filter with a single pole at s = - ? (where s is complex frequency). The effect of this pole position on array performance is examined. It is shown that to obtain optimal performance from the array, ? must be less than k?2, where k is the loop gain and ?2 is the thermal noise power per element. When at exceeds k?2, the output signal-to-inter ference-plus-noise ratio from the array is degraded for intermediate values of interference power.     

Regenerative hybrid arrays for interference suppression

The authors propose two regenerative hybrid adaptive arrays in which a self-generated reference signal is obtained through a detection-modulation procedure from the array output. The proposed arrays do not depend on spectrum spreading and are therefore applicable when this feature is not available. It is shown that at steady state the performance of these regenerative hybrid arrays is approximately the same as that of a hybrid array with a perfect reference signal. As to transient behavior, these arrays are shown to converge if the available imperfect steering vector can result in a few dB output signal-to-interference-plus-noise ratio with the self-generated reference disabled     

Optimum Strategies for Minimum Time Frequency Transitions in Phase-Locked Loops

Pontryagin's maximum principle is applied to minimize the time for a phase-locked loop to lock to a step change in frequency. In particular, a Type II phase-locked loop is considered in detail. Phase control and frequency control of the input signal are analyzed with the nonlinearity of the phase detector taken into consideration. It is shown that application of Pontryagin's maximum principle offers a decided advantage in shortening this time by proper control.