A systematic approximation for the mean time to lose lock (MTLL) of a coherent third-order PN-code tracking loop has been derived. Such loops are essential in various spread spectrum systems (Global Positioning System, for example). The computation of the MTLL is based on the singular perturbation method. The application of this method to the coherent delay-locked loop (DLL) yields an approximate expression for the MTLL. Therefore, with the proposed loop model the authors are able to analyze this third-order system at a level that gives a well understanding of the nonlinear loop behavior and the exit phenomenon. The influence of a loop offset due to an acceleration rate (jerk) between transmitter and receiver on the optimal filter parameters is described by comparing MTLL and tracking error performance. As intuitively might be expected it turns out that acceleration rate and code rate are exchangeable in the sense that a lower code rate allows a higher acceleration rate (and vice versa) for the same signal-to-noise ratio in order to maintain the same performance. In a case study, GPS code tracking for objects with high jerk is briefly discussed.>

The classical result of Kramers (1940), originally related to chemical reaction rates, is applied in this letter to a second-order all-pole, coherent code tracking delay-locked loop (DLL). A very simple, explicit expression for the leading order term of the mean time to lose lock (MTLL) is presented. The dependence of the MTLL on the loop tension (offset) due to Doppler shift and code clock mismatch is given, and optimal loop parameters which minimize the MTLL are proposed.>

The performance of various AGC configurations, namely presync, postsync and an adaptive (optimal) AGC are analyzed at and above the threshold for a coherent pseudonoise (PN) second-order code tracking loop (delay lock loop, DLL) used in direct sequence spread spectrum systems. At and near the threshold the criterion of performance is chosen to be the mean time to lose lock (MTLL). Applying a recently presented method, analytic expressions for the loop performance are given, and the threshold degradation caused by Doppler rate is derived. Above the threshold, the "worst case" steady state tracking error is chosen as the loop index of performance. The performance and structure of the "globally-optimal" AGC (at and above the threshold region) is derived, and a simplified, practical and still close to optimum adaptive AGC is presented. This configuration can easily be realized by digitally controlling the AGC parameters.>

For the first time an approximation for the mean time to lose lock (MTLL) of a third-order coherent PN-code tracking loop has been derived. Such loops are essential in various spread spectrum systems (Global Positioning System, GPS, for example). The computation of the MTLL is based on the singular perturbation method. The application of this calculus to the coherent delay-locked loop (DLL) yields an algebraic expression for the dominant term of the MTLL. The influence of loop offset due to an acceleration rate (jerk) between the transmitter and receiver as well as the optimal choice of the parameters maximizing the MTLL for the loop filter is described. A case study for code tracking of objects with high jerk guided by the GPS is briefly discussed.>

A microcellular local area network (LAN) for indoor communications is proposed using code-division multiple access (CDMA) and differential phase-shift keying (DPSK) for data modulation. The pseudonoise (PN) codes in the transmitters of the base station are mutually synchronized. For this purpose, sets of Gold code sequences having low cross correlation have been found by an exhaustive computer search. Together with wideband measurements of the indoor radio channel at 900 MHz, a five-path RAKE receiver was designed to combat fading effects and to process the time diversity by using multipath signal reception. Each receiver path is demodulated independently. Several methods of diversity combining of these paths have been investigated. Acquisition and tracking of the spreading code in the receiver are controlled by a digital signal processor (DSP). Experimental results of the CDMA system are presented, showing the behavior in a multipath environment.>

The singular perturbation method is used to approximate the mean time to lose lock (MTLL) for a second-order coherent pseudonoise code tracking delay-lock loop (DLL). Approximate expressions for the MTLL are given. The influence of loop offset due to the Doppler rate is studied, and optimal loop parameters (natural frequency and damping factor) which maximize the MTLL are presented. Upper bounds to the maximum allowable Doppler rates for various operating conditions are given.>