Ionosphere effects for wideband GNSS signals

Wideband signals show promise for Galileo development and GPS modernization because they provide sharper correlation peaks and thus more accuracy. For instance, the Galileo E5 signal occupies the frequency band from 1164 MHz to 1215 MHz, over 25 times the two-sided bandwidth of the GPS C/A code. However, because the ionosphere is dispersive, different frequency components in the wideband spectrum suffer different delays as they traverse the upper atmosphere. Signal delay due to refraction through the ionosphere is the largest and most variable source of positioning error for single frequency receivers. There are many models to compensate for the ionospheric delay. A classic and well-known formula is the first-order ionospheric delay model, in which the excess group delay is inversely proportional to frequency squared. Dual frequency receivers take advantage of this to compensate for the ionosphere errors by assuming each incoming signal to be a single frequency tone represented by the center frequency. This simplification is effective for narrowband signals, such as the GPS L1 C/A code, whose two-sided bandwidth is only 2 MHz. As the frequency band gets wider, the ionospheric delay variation within the band becomes larger. Thus, we should no longer neglect it as in the narrowband signal case. This motivates us to update the ionosphere model to take into account all frequency elements of the GNSS signals rather than treating them as a single tone. In this paper, we demonstrate the method of calculating ionospheric delay of wideband signals. We first decompose the time domain signal into the frequency domain, apply variable delays to all the frequency components, then transfer the frequency domain signal back to the time domain. The model modifies the total group delay of wideband signals. Moreover, it captures another ionosphere effect, signal deformation, which is not captured by the classical model. A signal traveling through the ionosphere becomes distorted due to varying delay over its bandwidth. We neglect frequency-dependent bending of the signal. We also apply the method to a variety of wideband signals, the Galileo E5b signal, the Galileo E5 signal, and BPSK signals with a range of bandwidths. The simulation results show the ionosphere impact on timedomain signal deformation, power loss of the correlation peak, phase shift in the PLL output, correlation peak symmetry and the frequency spectrum. Throughout the remainder of the paper, "bandwidthν refers to the two-sided bandwidth of a signal.