AbstractÑWe consider a downlink of a cellular communication system with a multi-antenna base station (BS). A regularized zero forcing (RZF) precoder is employed at the BS to manage the inter-user interference. Using methods from random matrix theory, we derive an asymptotic approximation for the achievable ergodic sum rate, taking into account the randomness from both fading and random user locations. The obtained deterministic approximation describes well the behavior of Þnite-sized systems and enables computationally efÞcient optimization of the RZF precoder matrix.
I. PRELUDEMultiple-input multiple-output (MIMO) transmission can signiÞcantly increase the performance of a communication system [1] and is therefore seen as a potential building block for future mobile communications. Nowadays, multiple antennas are widely deployed at base stations (BSs) in current cellular systems, which makes MIMO a particularly attractive solution. Multi-user multiple-input single-output (MISO) broadcast setting, where a multi-antenna BS communicates to a set of single-antenna mobile terminals (MTs) through the downlink channel, provides an efÞcient means to deal with such limiting factors as correlation and line-of-sight components [2]. At the same time, such an approach suffers from inter-user interference. It is the mitigation of the latter that motivates the use of spatial precoding at the BS.It is known that the sum capacity of Gaussian broadcast vector channels can be achieved by the so-called dirty-paper coding (DPC) scheme [3], [4]. This precoding scheme is, however, computationally infeasible in current real-world systems. Regularized zero forcing (RZF) precoding serves as a more plausible alternative with close to optimal performance [5]. Due to the particular structure of the corresponding precoder matrix, this scheme turns out to be suitable for analysis using methods from large-dimensional random matrix theory [6]. The setup has been extensively studied in [7], [6, Ch. 14]. The analysis is further generalizable, e.g.,t ot h em u l t i -c e l l setting [8] and to broadcasting with conÞdential messages [9].Usually, the analysis of MIMO channels is done based on the assumption of deterministic user placement. This is, however, rarely the case in practice. The MTs are typically freely moving, randomly changing the underlying network topology, which, in turn, inßuences the performance of the system. To account for random user locations in the uplink scenario, [10] proposes to combine the random-matrix analysis with the methods of stochastic geometry [11]. Namely, the positions of the MTs are assumed to be sampled from an independent spatial point process and the corresponding performance metricisaveraged over its distribution. The one-dimensional analysis of the uplink multi-user MIMO system performed in [10] is later extended to two-and three-dimensional cell planning in [12] and non-Gaussian channel inputs in [13]. This letter aims at extending the aforementioned analysis to the downlink scenario.F o rt h a tw ed e r ...