The performance of cellular networks is typically limited by inter-cell interference. In particular, users close to the cell boundaries suffer from strong interference. Network multiple-input multiple-output (MIMO) can reduce such inter-cell interference through coherent cooperation between base stations via advanced backhaul links to jointly transmit signals in the downlink and jointly detect signals in the uplink. This has fundamental limitations but cooperation can still yield signiﬁcant higher spectral efﬁciencies and coverage probabilities compared to the case where interference is ignored. Consequently, there has been a great deal of interest in network MIMO over the past decade. The main challenges in the implementation of network MIMO are the need for a substantial backhaul overhead, high deployment costs, and a sufﬁciently capable central processing unit. In particular, pre-coded signals and channel state information (CSI) need to be shared among the base stations. Recently, cell-free massive MIMO has been introduced as a practical and useful embodiment of the network MIMO concept. In our research,
we consider the cell-free massive MIMO downlink where a very large number of distributed multiple-antenna access points (APs) serve many single-antenna users in the same time-frequency resource. A simple (distributed) conjugate beamforming scheme is applied at each AP via the use of local channel state information (CSI). This CSI is acquired through time-division duplex operation and the reception of uplink training signals transmitted by the users. We derive a closed-form expression for the spectral efﬁciency taking into account the effects of channel estimation errors and power control. This closed-form result enables us to analyse the effects of backhaul power consumption, the number of APs, and the number of antennas per AP on the total energy efﬁciency, as well as, to design an optimal power allocation algorithm. This algorithm aims at maximizing the total energy efﬁciency, subject to a per-user spectral efﬁciency constraint and a per-AP power constraint. Compared with the equal power control, our proposed power allocation scheme can double the total energy efﬁciency, especially for large numbers of APs. Moreover, under a requirement of good quality-of-service for all users, cell-free massive MIMO outperforms the collocated counterpart in terms of energy efﬁciency.
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