Signal Propagation

CPI has had an active program in signal propagation for several years addressing ionospheric and tropospheric effects originating from ground-based transmitters. Extensive use has been made of the VOACAP model for ground-to-ground propagation and of the Jones-Stephenson and RIBG models for trans-ionospheric propagation. In addition, CPI physicist Dr. Robert Daniell developed his own ray tracing model IECM for use in making ionospheric corrections to signals from radars used to track space objects. The Jones-Stephenson model [R. M. Jones and J. J. Stephenson, U.S. Dept. of Commerce, OT Rpt. 75-76, 1975] was acquired from NRL several years ago and has undergone extensive modifications by CPI physicist Mr. Ray Barnes including the addition of homing algorithms and replacement of the original integration algorithm needed for advancing the signal along its propagation path. The RIBG model [M. H. Reilly, Radio Sci., 26, 971, 1991] was acquired from Dr. Mike Reilly while an employee of NRL. The Jones-Stephenson and RIBG models have been used to investigate signal propagation from 20 MHz to higher frequencies with the emphasis on ionospheric effects in geolocation determinations. Figure 1 provides illustrations of the paths (red curves) taken by signals through two ionospheres under daytime conditions with different altitude distributions of the ionization. The ionospheres are displayed in color and the frequency and elevation angle considered for the illustration are 30 MHz and 5°, respectively. The blue curves show the corresponding straight-line paths that appear with curvature due to the use of a flat-Earth projection for the displays. The total electron content along the straight-line paths (TEC_SL) is the same for both cases (100 TEC units). The displays illustrate different degrees of ray bending due to different distributions of the ionization along the ray paths but constrained to the same TEC_SL values.

Figure 1.

One of CPI's recent activities has been to parameterize ray tracing results that allow for table lookups, thereby eliminating the need for explicit ray tracing in geolocation determinations. The parameterization addresses two key outputs from ray tracing calculations, namely the group and phase path lengths. The former contains information on time delays due to the presence of an ionosphere along the ray path. The latter contains information useful to the determination of ionospheric Doppler effects (i.e., shifts in frequency seen by a moving receiver [in addition to shifts caused by the explicit motion itself] due to changing ray paths that in turn are associated with changing distributions of ionization along these paths). Extensive ray tracing runs using the RIBG model were made for a variety of frequencies, elevation angles, and ionospheres with attention to various parameterizations of the results.

The paper by Strickland et al. [Lookup tables for trans-ionospheric effects on signals, Radio Science, 39, RS1S33, doi:10.1029/2002RS002831, 2004] documents the tables. The above-mentioned path lengths (group and phase) are incorporated as incremental distances (path lengths less their free-space distances) and are expressed as functions of frequency, elevation angle, TEC_SL, and ionospheric slab thickness. A key type of plot of ray tracing results that has been used for constructing the tables is a scatter plot of the incremental path lengths versus TEC_SL at a given frequency and elevation angle. Figure 2 (Figure 7 from the Radio Science paper) shows scatter plots of incremental group path length Δl_g at 25 MHz for elevation angles of 5°, 10°, and 15°. The dashed lines refer to straight-line propagation and serve as references for illustrating the effect of ray bending exhibited in the scatter distributions. The top plot in each stack shows scatter irrespective to slab thickness. The plots beneath these show components for selected ranges of slab thickness and illustrate that this fourth parameter is effective in reducing the scatter exhibited in the full scatter plots. The results also illustrate a reduction in scatter with increasing elevation angle. Less scatter also occurs with increasing frequency. The cause of scatter is details in ionospheric behavior along the true path not accounted for by limiting the ionospheric parameterization to TEC_SL and slab thickness.

Figure 2. Scatter plots of incremental group path length Δlg and their component plots ordered by slab-thickness. Plots are shown for elevation angles of 5°, 10°, and 15° at 25 MHz. The selected results demonstrate the effectiveness of using slab-thickness as a fourth independent variable for the tables. The dashed curves refer to straight-line propagation.

Several global ionospheric models are available for examining ionospheric effects on signals. When using the Jones-Stephenson model, the CPI PIM model [Daniell et al., Radio Sci., 30, 1499-1510, 1995] is normally used with occasional use of ionospheres extracted from RIBG. When ray tracing is performed with this latter model, its own model ionosphere is used that is parametrically coupled to the ray tracing algorithm.

A recent application of the lookup tables may be seen in Barnes et al. [Full-orbit simulations of transionospheric time delay and Doppler, in Proceedings of the Eighth International Ionospheric Effects Symposium, p. 686, ed. J. M. Goodman, 2005]. Several figures are included in the paper that show images of time delay and Doppler as seen from low-Earth and geosynchronous orbits on the dayside and nightside of the orbits. Two of the figures appear below (here designated as Figures 3 and 4). A given circular pattern covers the area on the ground over which a transmitter can be placed whose straight-line elevation angle to the receiver is 5° and greater. A given value within the circular image refers to the signal received with the transmitter placed at this location.

Figure 3. Nightside transionospheric time delay at 30 MHz for receiver on a LEO platform at 1000 km. Upper left: Receiver field-of-view showing time delay for ground-based transmitters whose signals range in elevation angle from 90° (zenith propagation) to 5° (defines boundary of circular area). Upper right: GAIM vertical TEC, orbit path, and receiver location on nightside. Lower left: Bisecting cut through image in upper left from E to W. Lower right: Corresponding bisecting cut from S to N.

Figure 4. Similar to accompanying figure except with the receiver on the dayside of the orbit. Scales have changed due to the significant increase in time delay.