Channel Coding and Bit-error Probability
The design of codes to mitigate channel errors usually involves starting with some basic standard approach for the bandwidths and channel errors involved, and then opening a text book to find error correction performance vs parameterization or running a monte carlo simulation on a few coding types for the particular design-to channel.
There are known techniques for predicting error correction from SNR, by generating the distance spectrum of a code. We consolidated these techniques from across all standard coding types and symbol constellations:
- Natural and Gray mapping
- Low-density Parity check codes
- Turbo codes
- Parity check codes
- Punctured codes
- Reed-Solomon outer code
These were built into a software tool that allows combining any of these together, as well as using both inner and outer codes, to predict channel BEP coding performance.
The encoding can be specified by either a polynomial generator matrix or TCM polynomials. The code trellis distance spectrum is computed using Euclidean squared distance if a signal constellation is provided, or using the Hamming distance otherwise. The number of distance spectral lines can be constrained by either count or maximum distance considered. Bit error probabilities are computed from the distance spectrum as a function of bit SNR.
Channel Coding Performance Evaluation Tool: java tool webpage
Mobile fading -- Sat Comm, Stationary Users
For satellite to stationary user systems, where it is not guaranteed that users will place themselves in favorable outdoor locations, a fading model which statistically captures link impairment is desirable.
Performed a survey of available data at L and S band to understand likelihood of fading in target environments, and fit of standard Ricean/Rayleigh/LogNormal model parameters to base link budget on. Tied to physics when possible so reliance on sparse phenomenological data for interpolation was not necessary. Also important to not rely solely on fading knowledge, but delay spectrum from multipath which creates CDMA asynchronous degradation and inter-symbol noise.
Models developed were also a function of antenna type, since multipath is a function polarization changes and beam patterns.
See survey report for the TRW Odyssey program for more information.
Mobile fading -- Mobile environment
For communication from a satellite to a ground-mobile user, extra information is required to mitigate channel fading vs a stationary satellite-to-ground link above.
The simplest change from the stationary environment is that mobile users tend to be traveling down roads, so it is important to take a subset of fading experiments which operate under these conditions.
The most important change from stationary is that moving will create its own fade diversity, which can be exploited. Rather than having a large fade margin to handle stationary users, we can instead use a smaller power margin but rely statistically on fade variations with an architecture designed to interleave over longer time spans. In the case of broadcast satellite radio, and if longish latencies are allowed (valid for music channels or talk w/o callers), multiple streams can be broadcast with 10's of seconds of relative delay, to mitigate ~10s long tree/building shadows.
For more information, see slides on mobile fade mitigation architectures.
Satellite power control
For bi-directional satellite communication links both up and down through the troposphere, knowledge of the attenuation in one direction can help predict the attenuation in the other. If the carrier frequencies are identical for up vs down, the atmospheric differences would be extremely small, but typically uplink and downlink frequencies are well separated. Because of asymmetry between satellite resources and distributed ground resources, it is often desirable to attempt to predict and correct transmit power in one direction based on the observed attenuation on the other. The following plot shows the correlation between 27GHz attentuation vs 20GHz attenuation in Florida throughout the year 1996. The horizontal axis is 20GHz attenuation, and the vertical axis is prediction error at 27GHz. The color bands represent normalized histograms of error in the z direction, where the inner blue band shows 1sigma, green 2sigma, and so on.
Rain effects on RF noise figure and SNR
Given the attenuation of signal by rain, the "optical depth" of the sky is then also known, and the increase in receiver noise can be determined as a function of sky temperature assumption, and receiver noise filter. The following diagram shows total SNR degradation from both rain signal attenuation and an increase in sky thermal temperature.