Achievable Rate of a Space-Time Encoded Holographic MIMO

The existing works on holographic MIMO are mainly based on the time encoding (TE) scheme. Since the continuous aperture of holographic MIMO is able to capture both the temporal and the spatial variation of electromagnetic waves, we propose a space-time encoding (STE) scheme, which relies on the orthogonal basis function representation of the spatial-temporal EM waves. From the perspective of electromagnetic information theory, we derive the achievable information rate of the STE scheme in the narrowband communication systems and prove that the STE scheme achieves a higher information rate than the TE scheme. Firstly, We build the transmission model of the STE scheme based on electromagnetic information theory and investigate the characteristics of the model, including the blocklength of codewords and the signal-to- noise ratio. Specifically, the blocklength is determined through proving the eigenvalue distribution of the space-time-wavenumber-frequency limited operator and the signal-to-noise ratio is obtained based on proposed noise model. Then we derive the achievable information rate of both the STE scheme and the TE scheme by employing the finite blocklength information theory. Closed-form approximations of the rates are further derived, based on which we prove the conclusion that the STE scheme achieves a higher information rate than the TE scheme while utilizing the same spatial and temporal resources. Numerical results verify the accuracy of the approximations and indicate that the STE scheme improves the information rate by 7.96% over the TE scheme.