Impacts of three‐dimensional array over channel estimation for cell‐free massive MIMO considering spatially correlated channels

Recently, a promising technology known as the cell‐free (CF) massive multiple‐input multiple‐output (M‐MIMO) network has emerged as an alternative wireless communication network that offers numerous advantages to wireless communication systems. During this work, we address the uplink (UL) pilot‐based channel estimation (CE) and spectral efficiency (SE) for a CF M‐MIMO network considering spatially correlated channels. The CE and SE are computed respectively, using the Bayesian minimum mean square error (MMSE) estimator and MMSE combining vector. Moreover, we investigate the SE metric and CE procedure for correlated and uncorrelated channels, where in the correlated case, we employ the Gaussian local multi‐scattering (GLMS) model to describe the spatial correlation (SC). Furthermore, since the array geometry influence the SC, we deal with a CF M‐MIMO network wherein each access point (AP) is outfitted either with a uniform linear array (ULA), a uniform circular array (UCA), or a uniform cylindrical array (UCLA). Inspired by the GLMS for the ULA arrangement, we propose the GLMS model for a CF M‐MIMO network where each AP is equipped with a UCA arrangement. In other words, we propose and compute the expression of the channel co‐variance matrix (CM) that describes the SC in a CF M‐MIMO network where each AP is equipped with the UCA arrangement. Additionally, using the Kronecker product of the CM generated through the UCA arrangement and the CM generated through the ULA arrangement, we propose the GLMS model for a CF M‐MIMO network generated through the UCLA arrangement. Our theoretical expressions are validated and reinforced using numerical results, where we evaluate the system performance using the normalized mean square error metric and bits of information per second per hertz (i.e., bit/s/Hz$$ bit/s/ Hz $$). This work dealt with uplink pilot‐based channel estimation (CE) procedure and spectral efficiency (SE) for a CF M‐MIMO network considering spatially correlated channels, where the CE and SE are computed using the Bayesian minimum mean square error (MMSE) estimator and MMSE combining vector, respectively. Moreover, we investigate the CE and SE for correlated and uncorrelated channels, where for correlated channels scenario, we describe the spatial correlation using the Gaussian local multi‐scattering (GLMS) model. Inspired by the GLMS for the ULA arrangement, we propose the GLMS model for a CF M‐MIMO network where each AP is equipped with a UCA arrangem