We analyze the achievable rate of the uplink of a single-cell multi-user distributed massive multiple-input-multipleoutput (MIMO) system. Each user is equipped with single antenna and the base station (BS) is equipped with a large number of distributed antennas. We derive an analytical expression for the asymptotic ergodic achievable rate of the system under zero-forcing (ZF) detector. In particular, we consider circular antenna array, where the distributed BS antennas are located evenly on a circle, and derive an analytical expression and closed-form bounds for the achievable rate of an arbitrarily located user. Subsequently, closed-form bounds on the average achievable rate per user are obtained under the assumption that the users are uniformly located. Based on the bounds, we can understand the behavior of the system rate with respect to different parameters and find the optimal location of the circular BS antenna array that maximizes the average rate. Numerical results are provided to assess our analytical results and examine the impact of the number and the location of the BS antennas, the transmit power, and the path-loss exponent on system performance. Simulations on multi-cell networks are also demonstrated. Our work shows that circularly distributed massive MIMO system largely outperforms centralized massive MIMO system.Index Terms-Massive MIMO, distributed MIMO, achievable rate analysis, antenna location optimization. 3 tr(Z) is its trace. The symbol I M denotes the M ×M identity matrix, while 0 M,N denotes the M × N matrix whose entries are zeros. The symbol E denotes the statistical expectation operation. The symbol · F denotes Frobenius norm of a matrix or a vector. The function log 2 (·) is the base-2 logarithm and ln(·) is the natural logarithm.
II. SYSTEM MODEL AND ASYMPTOTIC ACHIEVABLE RATE ANALYSIS
A. Multi-User Distributed Massive MIMO System ModelWe consider a single-cell multi-user distributed massive MIMO system. In this system, there is one BS equipped with M antennas which are spatially distributed [32], [33]. The number of antennas M is assumed to be large, e.g., a few hundreds. This is different to the multi-user centralized MIMO system [16]-[27], where the BS antennas are centralized and spatially co-located. Compared with centralized MIMO systems, distributed MIMO systems provide macro-diversity and have enhanced network coverage and capacity, due to their open and flexible infrastructure [6], [8], [29]. This is also different to systems with distributed BSs, in which several BSs with multiple antennas cooperate with each other to jointly transmit or receive the information; and each BS has its own power constraint [37], [38]. We assume that the distributed BS antennas are connected with high capacity backhaul (e.g., optical fiber channels) and have ideal cooperation with each other. There are K users, each equipped with single antenna. We assume that M K, which is necessary in achieving high spectral efficiency in massive MIMO systems [16], [21].Denote the channel coefficient between ...