Reference Loop Phase Shift in an N-Element Adaptive Array

Adaptive arrays based on the LMS algorithm require the generation of a reference signal which is usually derived from the array output. A particular problem associated with this technique is that of a phase shift in the reference signal loop. The effects of this phase shift on the performance of an N-element adaptive array are discussed. It is shown that a reference loop phase shift causes the array weights to cycle, thereby frequency translating the signals at the output. The weight-cycling frequency is related to various system parameters of an N-element array. In particular, it is observed that the cycling frequency increases as the number of antennas (N) increases.     

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.     

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。     

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。     

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.     

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.     

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 a Pulsed Interference Signal on an Adaptive Array

The performance of a least mean square (LMS) adaptive array in the presence of a pulsed interference signal is examined. It is shown that a pulsed interference signal has two effects. First, it causes the array to modulate the desired signal envelope (but not its phase). Second, it causes the array output signal-to-interferenceplus-noise ratio (SINR) to vary with time. The desired signal modulation is evaluated as a function of signal arrival angles, powers and interference pulse-repetition frequency (PRF) and pulsewidth. It is shown that the signal modulation is small except when the interference arrives close to the desired signal. To evaluate the effect of the time-varying SINR, it is assumed that the array is used in a differential phase-shift keyed (DPSK) communication system. It is shown that the SINR variation causes a noticeable but not disastrous increase in the bit error probability.     

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.     

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.     

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.     

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     

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.     

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.     

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。     

An Optimum Phase Reference Detector for Fully Modulated Phase-Shift Keyed Signals

Many modern telemetry systems which use phase-shift keying (PSK) have receivers which derive a coherent reference from the fully modulated PSK signal itself and thus conserve the energy which otherwise would be allocated to a discrete reference signal. In this paper, an optimum receiver structure for estimating a phase reference from the PSK signal itself is derived and its realization discussed. It is shown that at low signal-to-noise ratios, the optimum detector can be realized with a Costas loop. Since a Costas loop and squaring loop exhibit identical performance, it follows that either of these simple devices gives optimum performance for low-input signal-to-noise ratios.     

An LMS Adaptive Array for Multipath Fading Reduction

Multipath fading often poses a serious hindrance in radiocommunication. The application of a least-mean-square (LMS)adaptive array to the problem of multipath fading reduction is discussed. However, it is known that multipath components are in general correlated with one another. We examine the effect of the correlation on the performance of the LMS adaptive array. When the correlation coefficient does not equal or approximate 1, the LMS adaptive array suppresses the multipath signals significantly by nulling. On the other hand, when the correlation coefficient nearly equals 1, the LMS adaptive array prevents the output signalpower from decreasing. Therefore, the LMS adaptive array mayreduce the multipath fading effectively for any correlation coefficient value. A reference signal in the LMS adaptive array is also discussed. It is shown that synchronization in the referencesignal generation must be extremely accurate. Moreover, aprocessor configuration is proposed which may generate thereference signal with the required accuracy.     

空域滤波器组对雷达阵列合成距离像的影响分析

为了简化雷达系统硬件设计和降低成本,可以使用多个窄带成分来合成宽带信号,从而获得满足实际需要的合成距离像。针对合成宽带信号和雷达阵列的特点,详细分析了结合合成宽带信号及传统空域滤波器组情况下所合成距离像的失真原因,指出合成距离像的失真由形状变形和位置平移两部分组成,且这两种失真分别由各个空域滤波器输出幅度和相位的波动所引起。同时,推导出计算对应相位和幅度失真度的理论公式,并由此给出了当合成距离像存在可接受失真时阵列的临界条件。计算机数值仿真结果验证了以上结论。     

An Adaptive Interference Canceling Array Utilizing Hybrid Techniques

The steady state properties of an adaptive array utilizing prior knowledge of both approximate signal arrival direction and signal characteristics are presented. The method combines the features of a directionally constrained array and an array with a self-generated reference signal. Explicit results are obtained for output signal, interference, and noise powers assuming a single interferer is present. The inclusion of a self-generated reference circuit is shown to reduce the sensitivity to pointing error typical of arrays utilizing a zero order directional constraint, the improvement being a consequence of the reduction of the desired signal component fed back to the sidelobe canceling circuit. A relationship between the degree of sensitivity reduction and the quality of the reference signal is developed. Results of computations of signal to interference plus noise ratios for a 7-element 10-wavelength nonuniformly spaced array as a function of pointing error are presented. These results show the behavior with one interferer inside and outside the beamwidth of the quiescent array and with multiple interferers for various degrees of perfection of the reference generating circuit. In all cases the computations confirm that the otherwise severe effects of small pointing errors are substantially reduced.     

Phase-Locked Loop Behavior near Threshold

The phase-locked loop behavior is analyzed following the quasilinearization Booton's method. When the loop is locked on an unmodulated input signal with a static phase error, the phase detector nonlinearity produces an interaction between the static phase error and the voltage-controlled-oscillator (VCO) noise phase fluctuations. Formulas allowing one to compute the static phase error increase and the VCO phase variance increase are derived. When the input signal is phase modulated, there is an interaction between the static phase error, the VCO noise phase fluctuations, and the input signal phase modulation. Formulas are obtained that allow one to compute the loop loss of performances (static phase error increase and VCO phase variance increase) and the coherent phase demodulator output signal-to-noise ratio decrease. Finally, a slight modification to Booton's procedure is proposed, leading to results in better agreement with experimental data.