Spectral Efficiency Analysis for Grant-Free Random Access Cell-Free Massive MIMO with Ricean Fading

The spectral efficiency in cell-free massive MIMO with grant-free random access under Ricean fading, utilizing a linear maximal-ratio combining detector, is the focus of this paper. Firstly, explicit expressions for the effective signal-to-interference-plus-noise ratio (SINR) are introduced, using the least squares (LS) and minimum mean squared error (MMSE) estimation methods, valid for varying Ricean K-factor and for varying numbers of access point antennas M. Furthermore, we drive the asymptotic SINR expressions under extreme conditions of infinite Ricean K-factor, infinite M, and the appropriate scaling of the users’ power. The corresponding analysis shows that as M approaches infinity, the sum uplink rate converges to $\log _{2} M$, regardless of the Ricean K-factor. Particularly, in the case of LS estimation, reducing each user’s transmit power by $1 / \sqrt{M}$ maintains the rate, converging to a definitive value irrespective of the Ricean K-factor. In the case of MMSE estimation, power is able to be scaled down by $1 / \sqrt{M}$ to achieve it when Ricean K-factor is zero, whereas the power of nonzero Ricean K-factor necessitates a reduction by $1 / M$. Finally, simulations confirm all theoretical outcomes.