Early-late Spacing Research Articles

Continuous Wave Interference Effects on Ranging Performance of Spread Spectrum Receivers

Continuous wave interference (CWI) can induce significant ranging error for a spread spectrum receiver. Since both the spread spectrum signal and CWI are deterministic signals but truncated by the integrate and dump filters, deterministic signal models are built, and then their continuous frequency spectrums and specific signal forms in the processing flow are analyzed. This paper provides analytical expressions for code tracking performance of ranging receivers using coherent early minus late discriminators. The impacts of interference to signal power ratio (ISR), front-end bandwidth, integration time and early-late spacing on ranging bias are taken into account. According to the property of pseudo-random noise (PRN) code, the average magnitude of the code frequency spectrum is presented to investigate the general properties of ranging bias, and the magnitude fluctuations around the average are considered to analyze the properties of ranging bias with specific PRN codes. It is shown that the ranging bias induced by CWI depends on ISR, interference frequency, initial phases, code properties, receiver parameters, etc. Meanwhile, the envelope magnitude of the code frequency spectrum is provided for an easy way of estimating the upper bound of ranging bias. The 32 GPS C/A codes are taken as examples to show their worst cases of ranging performance under CWI.

Generalized Theory of Code Tracking with an Early-Late Discriminator Part I: Lower Bound and Coherent Processing

Code tracking is an important attribute of receivers for Global Positioning System (GPS) and other global navigation satellite systems (GNSS). This paper and its sequel provide analytical expressions for performance of code-tracking loops using early-late discriminators, under small-error conditions. Expressions are provided for output signal-to-noise-plus-interference ratio (SNIR) and code-tracking error for arbitrary signal spectra, and Gaussian noise and interference having arbitrary spectral shapes. This first paper addresses coherent early-late processing (ELP) for given receiver precorrelation bandwidth and given early-late spacing, also providing a tight lower bound on code-tracking error independent of discriminator design. Theoretical expressions are derived, showing that code-tracking accuracy depends on more than merely signal-to-noise ratio and early-late spacing - the shape of signal and interference spectra are important, as is the receiver precorrelation bandwidth.

Generalized Theory of Code Tracking with an Early-Late Discriminator Part II: Noncoherent Processing and Numerical Results

Code tracking is an important attribute of receivers for Global Positioning System (GPS) and other global navigation satellite systems (GNSS). This paper and its antecedent provide analytical expressions for performance of code-tracking loops using early-late discriminators, under small-error conditions. Expressions are provided for output signal-to-noise-plus-interference ratio (SNIR) and code-tracking error, for arbitrary signal spectra, and Gaussian noise and interference having arbitrary spectral shapes. This second paper addresses noncoherent early-late processing (NELP) for given receiver precorrelation bandwidth and given early-late spacing, comparing the results to results for coherent early-late processing (CELP) and to a lower bound (LB) on code-tracking error. Theoretical expressions are derived and compared, and numerical results are provided to examine the effect of different modulation designs and interference conditions.

Half-sine and triangular despreading chip waveforms for coherent delay-locked tracking in DS/SS systems

The performance of a coherent delay-locked tracking scheme for direct-sequence/spread-spectrum systems using half-sine or triangular chip waveforms for early and late despreading sequences is analyzed. The effect of band-limiting on the received signals is considered. Mean time to lose lock (MTLL) and root mean square (rms) tracking error of the delay-locked loop (DLL) are compared with that of a conventional DLL which uses rectangular chip despreading waveforms. Linear and nonlinear (based on the renewal process approach) analyses are employed to evaluate the performance of the DLL. Results show that the use of either the half-sine or triangular chip waveform reduces the rms tracking error and increases the MTLL considerably when the early-late spacing is approximately between 0.7-1.3 chip times. The results apply in particular to the commonly used DLL using one chip early-late spacing. Computer simulation for band-limited signals confirms the analytical results. The use of these despreading chip waveforms also reduces tracking offset in multipath environments.

Performance degradation due to code tracking errors in spread-spectrum code-division multiple-access systems

The influence of code synchronization errors on the performance of direct-sequence spread-spectrum (DS/SS) communication systems is investigated. Insight is gained in the degradation of some basic performance parameters due to the tracking bias of a noncoherent delay lock loop (DLL). The performance parameters investigated are the bit-error probability, throughput and delay. Numerical results show that for receivers with an early-late spacing of d=1, using a noncoherent DLL, the results of a system performance analysis in a fast fading environment can be much too optimistic if the tracking errors are ignored.

Reducing multipath tracking errors in spread-spectrum ranging systems

Analysis of coherent and noncoherent delay lock loops shows that a smaller early-late spacing than the commonly used one chip time reduces multipath tracking errors considerably. The results are especially interesting for spreadspectrum ranging systems such as GPS.