Performance Analysis of a Complex Multicode Tracking Loop in Bandlimited Rayleigh Fading Channels

Abstract

This paper presents the root-mean-squared tracking error performance analysis of a class of coherent digital delay-locked loops for multicode direct sequence spread spectrum signals in bandlimited correlated Rayleigh fading channels. In the transmit side, multiple independent PSK-modulated data streams in the in-phase and qudrature phase branches are spread by short mutually orthogonal codes before being further complex spread by a long complex PN code. We assume that the system employs a pilot code channel to assist the receiver's synchronization and channel estimation. The proposed code tracking loop incorporates the pilot-aided channel estimator and derives the timing error from all short-code-spread subchannels. Our analysis takes into account the effects of imperfect channel estimate, correlated frequency selective Rayleigh fading and band-limiting. Numerical results are presented to quantify the impact of the resulting multipath interference within the same code channel and amongst different code channels.

A novel tracking jitter computation method for delay‐locked loops in spread‐spectrum systems

“…which coincides with the more complicated derivation on the basis of the loop transfer function in [1][2][3][4][5][5][6][7]. The square root of the stationary variance in Equation (16) yields the jitter RMS value.…”

“…with vanishing expectation value A;" D 0. The condition with a vanishing loop offset u D 0 requires a fixed receiver according to Equation (6). Contrary, as shown in [1], a maximum MTLL always requires a positive loop offset u > 0.…”

“…The crucial jitter results follow from the simple OU random processes without the integral evaluation that the conventional jitter computation [1][2][3][4][5][5][6][7] requires. We obtain for the second-order Langevin DLL the identical jitter and total loop bandwidth as for the first-order DLL in Section 2, which is due to the identical channel delay functions T .t/ in Equation (4) corresponding to a constant velocity v 0 .…”

“…The design of loops typically involves the optimisation of these measures in terms of the loop parameters, and this is a very expensive task computationally because, for each fixed set of loop parameters, a complete time-domain simulation must be performed. To avoid these high complexities, researchers attempt to obtain the jitter RMS value and the MTLL [1][2][3][4][5][5][6][7] analytically. The key idea in this approach is the computation of a loop transfer function [8][9][10] between the instantaneous channel delay and its loop estimate, a function that depends on the loop's filter and discriminator.…”