Randomization of alternating codes: Improving incoherent scatter measurements by reducing correlations of gated autocorrelation function estimates

Abstract

Abstract. Incoherent scatter radar autocorrelation function estimates produced by alternating codes are found to contain significant correlations between different lags and different heights. While no correlations are caused by the background thermal noise, the special structure of the alternating code sequences causes clutter or the self-noise contribution of the codes themselves to introduce maximal positive correlations between the different lag estimates. Because of this, postintegration of adjacent heights does not improve the results as much as could be expected. For a high signal-to-noise ratio, alternating code results are worse than estimates produced by similar random codes. In this paper we show that we can correct the situation by randomizing the alternating codes. This is accomplished by multiplying each alternating code sequence in the alternating code cycle by a fixed random-looking sequence. This multiplying sequence can be changed and randomly chosen at the end of each alternating code cycle. The multiplying sequence can also be kept constant with almost equally good results. If this is done, the special structure of the alternating code sequences actually causes the correlations to become less than the correlations produced by random codes. The improvement in accuracy is discussed in various situations. The reasons for the appearance of maximal positive correlations with alternating codes are explained in a mathematical appendix.

Polyphase‐coded incoherent scatter measurements at Millstone Hill

“…[39] Polyphase alternating codes share the same properties with binary alternating codes [Markkanen et al, 2008]. All kinds of alternating codes will thus provide uncorrelated lag profiles in very low signal-to-noise conditions [Lehtinen and Häggström, 1987], whereas randomized codes must be used in order to suppress unwanted correlations in high signal-to-noise conditions [Lehtinen et al, 1997].…”

“…The final polyphase alternating code thus had 10 different phases. Both alternating codes were randomized [Lehtinen et al, 1997] with the binary sequence -+ -+ + -+ -+ ---+ + -+ -+ --+ + --+.…”

Phase-coded pulse aperiodic transmitter coding

“…If this is not the case, the self-noise causes complicated effects, including correlations between different lag profile estimates, which may lead into rather surprising results. Experiment optimisation remains an open question in this case and for example the numerical case studies in Huuskonen and Lehtinen (1996) and Lehtinen et al (1997) show that taking these correlations into account may significantly affect the lag profile and consequently ionospheric parameter estimation variances. In some cases the variances may actually be smaller, and in some cases larger, than simple approximations would imply.…”

Incoherent scatter experiments at Jicamarca using alternating codes

“…This time, all the codes in a scan were multiplied by one of four random patterns that were then rotated from scan to scan. The particular random patterns were the ones tabulated and investigated by Lehtinen et al [ 1997]. The results are shown in the bottom half of Figure 2.…”