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This paper addresses the problem of estimating the frequencies, amplitudes and phases of the n sinusoidal components of a possibly biased multi-sinusoidal signal. The proposed adaptive observer allows the direct adaptation of the frequency estimates with a relatively low dynamic order 3n + 1 (3n for an unbiased signal). The stability analysis proves the global exponential convergence of the estimation error and the robustness to additive norm-bounded measurement perturbations.

A novel generalized polarization-space modulation (GPSM) is proposed for polarized multiple-input multiple-output (MIMO) systems with a limit number of radio frequency (RF) chains. In the spatial domain, multiple dual-polarized (DP) transmit antennas are activated, and then combinations of those indices are used to convey information. While in the polarization domain, depending on the random input bits, only one polarization state is selected for each active DP transmit antenna to transmit information following the rule of the polarized shift keying. At the receiver, the maximum likelihood detector is employed as a benchmark to detect information bits being used to select the polarization state and activated DP antennas. In the detector, imperfect channel state information (CSI) is taken into account. Two less computationally complex detectors, i.e., a linear detector and a sphere decoding (SD) detector are proposed to relieve the computational burden. Sacrificing the average bit error probability (ABEP) performance, the proposed linear detector can reduce the computational complexity significantly. The proposed SD detector can achieve the optimum ABEP performance, while reducing computational complexity by reducing the search space. A closed-form union upper bound (UUB) on the ABEP of the GPSM system with imperfect CSI at the receiver is analytically derived and validated through simulations. From the UUB, a loose asymptotic bound on the ABEP, which sheds light on deriving the diversity gain and the coding gain, is derived. Numerical results show that the signal-to-noise ratio loss caused by increasing the number of transmit antennas is less than 3 dB while the spectral efficiency is increased by 7 b/z/Hz. Therefore, the GPSM can be a promising candidate of down link massive MIMO systems to achieve a high spectral efficiency with a limit number of RF chains.