SUMMARYThe new M-code signals of GPS and the signals proposed for the future Galileo systems are of splitspectrum type, where the pseudorandom (PRN) code is multiplied with rectangular sub-carriers in one or several stages. Sine and cosine binary-offset-carrier (BOC) modulations are examples of modulations, which split the signal spectrum and create ambiguities in the envelope of the autocorrelation function (ACF) of the modulated signals. Thus, the acquisition of split-spectrum signals, based on the ambiguous ACF, poses some challenges, which might be overcome at the expense of higher complexity (e.g. by decreasing the step in searching the timing hypotheses). Recently, two techniques that deal with the ambiguities of the ACF have been proposed, and they were referred to as 'sideband (SB) techniques' (by Betz, Fishman et al.) or 'BPSK-like' techniques (by Martin, Heiries et al.), since they use SB correlation channels and the obtained ACF looks similar to the ACF of a BPSK-modulated PRN code. These techniques allow the use of a higher search step compared with the ambiguous ACF situation. However, both these techniques use SB-selection filters and modified reference PRN codes at the receivers, which affect the implementational complexity. Moreover, the 'BPSK-like' techniques have been so far studied for even BOC-modulation orders (i.e. integer ratio between the sub-carrier frequency and the chip rate) and they fail to work for odd BOC-modulation orders (or equivalently for split-spectrum signals with significant zero-frequency content). We propose here three reduced-complexity methods that remove the ambiguities of the ACF of the split-spectrum signals and work for both even and odd BOC-modulation orders. Two of the proposed methods are extensions of the previously mentioned techniques, and the third one is introduced by the authors and called the unsuppressed adjacent lobes (UAL) technique. We argue via theoretical analysis the choice of the parameters of the proposed methods and we compare the alternative methods in terms of complexity and performance.

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Fixed-point simulation results are used for performance measure of inverting matrices using direct and iterative methods. As direct method the Cholesky decomposition is being used. For the iterative counterpart, the Newton's iteration has been implemented. The fixed-point implementation of matrix inversion is tested and analyzed for both cases. We compare our solutions by using some numerical examples.