In this paper, a novel analytical blind single-input single-output (SISO) identification algorithm is presented, based on the noncircular second-order statistics of the output. It is shown that statistics of order higher than two are not mandatory to restore identifiability. Our approach is valid, for instance, when the channel is excited by phase shift keying (PSK) inputs. It is shown that the channel taps need to satisfy a polynomial system of degree 2 and that identification amounts to solving the system. We describe the algorithm that is able to solve this particular system entirely analytically, thus avoiding local minima. Computer results eventually show the robustness with respect to noise and to channel length overdetermination. Identifiability issues are also addressed.
A polynomial criterion is proposed to perform blind source separation, extending previous works to MIMO systems. The criterion is proved to be asymptotically MAP-equivalent in presence of PSK sources. An efficient minimization algorithm dedicated to polynomial criteria is then developed, improving on the fixed-step stochastic gradient previously utilized in this framework.
Channel equalization and identification appear as key issues in improving wireless communications. It is known that the linearization of the GMSK modulation (used in the European standard GSM) leads to a continuous phase OQPSK which can be considered as a Minimum Shift Keying (MSK) modulation. Thus methods of equalization and identification when the channel is input by MSK modulated signals is worth to look at. Most algorithms consider MSK signals as two independent white binary PAM staggered signals; this is not the case in our approach. Here, MSK signals are seen, after sampling at baud rate, as colored complex discrete signals. Even if this view of MSK modulation is quite simple, it has never been utilized with the purpose ofblind equalization. The particular statistics ofsuch signals are studied, yielding an original closed-form analytical solution to blind equalization, both in the monovariate case (SISO or SIMO) and in the source separation problem (MIMO) . Simulations show a good behavior of the algorithms in terms of Bit Error Rate (BER) as a function of SNR, both in the case of blind equalization and source separation.
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