In this work, the steady state mean square tracking error of first order correlation loops is minimized by varying the locally generated cross correlation function produced by the voltage controlled oscillator. This analysis should assist in the design of modified first order delay locked loops used for pseudonoise code synchronization in direct sequence spread spectrum receivers. The optimum cross correlation waveform is generated by filtering a replica of the originally transmitted signal. The optimal filter imposes a 90 degree phase shift at all frequencies and has an amplitude response that is a function of the channel signal to noise ratio. In the general case, this filter is not a differentiator, as is commonly assumed. The analytical difficulty of solving multi-dimensional, nonlinear, integral equations prevents us from finding a closed form solution. However, a number of asymptotic cases are analyzed and sample results from numerical evaluations are presented

Meeting Name

1990 IEEE Military Communications Conference, MILCOM '90 (1990: Sep. 30-Oct. 3, Monterey, CA)


Electrical and Computer Engineering

Keywords and Phrases

PLL; SNR; Correlators; Cross Correlation Function; Cross Correlation Waveforms; Delay-Locked Loop; Direct Sequence Spread-Spectrum Receivers; Filtering and Prediction Theory; First Order Correlation Loops; High Signal-To-Noise Ratios; Linear Time-Invariant Filter; Mean Square Tracking Error; Nonsinusoidal Signals; Optimal Reference Waveform; Optimization; Periodic Signals; Phase; Phase-Locked Loop; Phase-Locked Loops; Pseudonoise Code Synchronization; Radio Receivers; Spread Spectrum Communication; Steady State Error; Time Delay; Voltage Controlled Oscillator

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type





© 1990 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Sep 1990