An analogue overlaying scheme based on phase rotations

We introduce a scheme for overlaying an analogue phase signal on digitally modulated symbol sequences. The scheme applies phase rotations to generic PSK or QAM constellations that are rotationally invariant by multiples of an angle, and uses phase signatures to spread the phase signal over a block of symbols in order to resolve any ambiguity in the rotated constellations. A near maximum-likelihood estimator for reconstructing the analog signal is derived as well as conditions for the design of the signature sequences. The proposed scheme may be used as an alternative to quantisation and digital transmission in control channels of mobile or WLAN standards, where one or more phase references have to be provided to the terminals and where other existing digitally-modulated control information can serve as host. Analysis and simulations show that the analogue overlaying scheme can offer better performance than a digital scheme with the same spectral efficiency for the host signal, in terms of both mean square error of the reconstructed phase information and bit error rate of the underlying digital stream.