A new method for decoding phase codes

Virtanen, I.1, Lehtinen, M.2, Nygrén, T.3, Orispää, M.2 and Vierinen, J.2

1 University of Oulu, Oulu, Finland
2 Sodankylä Geophysical Observatory, Sodankylä, Finland
3 Department of Physical Sciences, University of Oulu, Oulu, Finland

Alternating codes are a standard modulation method in the present-day incoherent scatter measurements. Alternating codes consist of sequences of very specific phase patterns. They are very effective but their drawback is the great number of patterns in the whole code sequence when the number of bits is great.

A phase coded modulation produces range ambiguities, which should be removed by means of decoding. Alternating codes are designed in a way which allows the decoding to be made in power domain. Here we present a new decoding method based on stochastic inversion. The method is capable to decode any phase and/or amplitude modulated radar code (including alternating codes), if both the transmitted signal and the ionospheric echoes are recorded in amplitude domain.

In the new method, both the range ambiguity functions and the lagged products are calculated using the measured data. Because each ambiguous lagged product is a linear combination of the unknown true lag values at a number of range gates, the measurements can be combined to make an overdetermined set of linear equations. Each ambiguous lagged product produces a single equation and the coefficients of the unknowns are determined by the range ambiguity function. By means of stochastic inversion, one obtains the most probable values of the unknowns and their a posteriori variances. The practical solution is made using a special software package (FLIPS) that is suitable for big inversion problems. Finally, the ionospheric plasma parameters are fitted to the decoded autocorrelation functions using iterative methods in the same way as in the GUISDAP analysis package.

The main reason to build a new analysis system is that the method is capable of decoding the next generation radar codes which cannot be decoded with the traditional methods. The method also gives much flexibility to the ISR data analysis, allowing lag profile decoding with different range and time resolutions. The only limiting factors are the sampling frequency at the recording stage and the statistical nature of the measurement itself.

Using real data from an alternating code experiment, we present some comparisons between the inversion method and the standard decoding. Both decoded lag profiles and plasma parameters are presented. We also show some first results of experiments with new kinds of binary codes that contain only few different transmission sequences but are still capable to produce very accurate results.