M ay 2 01 6 Coded Pilot Access : A Random Access Solution for Massive MIMO Systems

We present a novel access protocol for crowd scenarios in massive MIMO (Multiple-input multiple-output) syst ems. Crowd scenarios are characterized by a large number of users with intermittent access behavior, whereby orthogonal sch eduling is infeasible. In such scenarios, random access is a natural choice. The proposed access protocol relies on two essential proper ti s of a massive MIMO system, namely asymptotic orthogonality between user channels and asymptotic invariance of channel powers. Signal processing techniques that take advantage o f these properties allow us to view a set of contaminated pilot signals as a graph code on which iterative belief propagatio n can be performed. This makes it possible to decontaminate pi lot signals and increase the throughput of the system. Numerica l evaluations show that the proposed access protocol increas es the throughput with 36%, when having 400 antennas at the base station, compared to the conventional method of slotted ALOHA. With 1024 antennas, the throughput is increased by85%. I. I NTRODUCTION Massive MIMO (Multiple-input multiple-output) has been identified as a key technology to improve spectral efficiency of wireless communication systems and one of the main enablers of the upcoming 5th generation [1]. A massive MIMO system refers to a multi-cell multi-user system with a massive numb er of antennas at the BS that serves multiple users [2]. The number of users is much smaller than the number of BS antennas, defining an under-determined multi-user system w ith a massive number of extra spatial degrees of freedom (DoF). Exploiting those extra DoF and assuming an infinite number of antennas at the BS, the multi-user MIMO channel can be turned into an orthogonal channel and the effects of smallscale fading and thermal noise can be eliminated. However, when the number of antennas becomes massive, acquiring the channel state information (CSI) becomes a sev ere bottleneck. Downlink channel training requires a training length that is proportional to the number of antennas at the B S and is thus impractical. A solution promoted in [2] restrict s massive MIMO operations to time-division duplex (TDD) for which channel reciprocity is exploited. As the downlink and uplink channels are equal, CSI is acquired at the BS based on uplink training and then used for downlink transmission. The benefit is that the training length is proportional to the The research presented in this paper was partially supporte d by the Danish Council for Independent Research (Det Frie Forskningsråd ), grants no. DFF1335-00273 and DFF-4005-00281. Part of this work has been pe rformed in the framework of the Horizon 2020 project FANTASTIC-5G (ICT -671660), which is partly funded by the European Union. The authors wou ld like to acknowledge the contributions of their colleagues in FANTA S IC-5G. number of users, which is much smaller than the number of BS antennas. As described in [2], CSI is acquired using orthogonal pilot sequences, but, due to the shortage of orthogonal sequences , the same pilot sequences must be reused in neighboring cells , causing pilot contamination. This problem is considered as one of the major challenges in massive MIMO systems [3]. Mitigation of pilot contamination has been the focus of seve ral works recently. These include [4], where it is utilized that the desired and interfering signals can be distinguished in the channel covariance matrices, as long as the angle-of-arriv al spreads of desired and interfering signals do not overlap. A pilot sequence coordination scheme is proposed to help satisfying this condition. The work in [5] utilizes coordin ation among base stations to share downlink messages. Each BS then performs linear combinations of messages intended for users applying the same pilot sequence. This is shown to elim inate interference when the number of base station antennas goes to infinity. A multi-cell precoding technique is used in [6] with the objective of not only minimizing the mean squared error of the signals within the cell, but also minimizing the interference imposed to other cells. The pilot contamination problem has been seen as an intercell problem that arises when the users associated with two neighboring cells use the same pilot sequence. An implicit assumption associated with it is that the pilot sequences of the users associated with the same cell are perfectly scheduled , such that no intra-cell pilot contamination occurs. These assumptions fall apart when one considers very dense, crowd scenarios as envisioned in 5G wireless scenarios [7]. In suc h a setting, orthogonal scheduling of the users belonging to t he same BS becomes infeasible due to scheduling overhead. This work is motivated by the massive MIMO problem in a crowd setting, as well as the observation that the pilot con tamination problem is very much dependent on the protocol assumptionsmade in the system. Specifically, we consider a crowd scenario where the amount of users and their access behavior make it infeasible to schedule the transmissions. Instead users choose pilot sequences at random in an uncoordinated manner from a small pool shared by all users. In this way, the inter-cell pilot contamination problem becomes an intra-cell pilot contamination problem, where the BS needs to handle collisions that occur in the pilot domain. Some recen t works have considered this approach. The paper [8] features a proposal for a joint pilot and data transmission in the uplin k, where the purpose is a reliable communication by following a ergodic process. In each time slot, a user selects uniformly at random a pilot sequence and selects part of her codeword. The packet collisions are neither detected nor resolved, while over an asymptotically long time horizon, fading and effects of p ilot contamination are averaged out allowing the determination of a reliable rate for transmission. Another related work is [9 ], where the pilots are transmitted by using the random access procedure in LTE, but modified according to the specifics of pilot access. The paper proposes an approach to resolve oneshot collisions by exploiting the channel hardening proper ties of massive MIMO and enabling the terminals to detect the collision and act accordingly. The approach devised in this paper differs from [8] and [9] by having the terminals participate in a coded random access procedure [10], [11]. The terminals transmit with a predefin d probability and send a pilot in the uplink followed by the dat a part. Pilot assignment is randomized in each time slot while t e data part is repeated, which enables to use successive inter ference cancellation across the replicas of the same packet. On of the main contributions is the way successive interferenc e is implemented, as it relies on two features specific to massive MIMO: (1) asymptotic orthogonality between user channels; and (2) asymptotic invariance of the power received from a user over a short time interval. Furthermore, we also propos e t have flexible switching from uplink to downlink transmissio n on a time slot basis for the users that are not affected by pilo t collision. A preliminary version of this work has appeared in [12]. The present version provides a thorough elaboration on the andor tree analysis of the degree distribution of the random acces s code. Differently from [12], this work considers a channel c ode at the physical layer, which exists in most practical system , and is shown to greatly influence the design and performance of the random access code. II. SYSTEM MODEL In this work we denote scalars in lower case, vectors in bold lower case and matrices in bold upper case. A superscript ‘ T ’ denotes the transpose, a superscript ‘ ∗’ denotes the complex conjugate and a superscript ‘ H ’ denotes the conjugate transpose. We consider a random access system consisting of a single base station withM antennas andK users, each one with a single antenna, see Fig. 1. Communication is performed by using slotted time, where each time slot consists of an uplink pilot phase and a data phase (either uplink or downlink), see Fig. 2. In each time slot, each user is active with probability pa. There areτ orthogonal pilot sequences {s}, each consisting of τ symbolss = [s(1) s(2) . s(τ)]. An active user selects a pilot sequence randomly from the τ available pilot sequences. Note that multiple users may choose the same pilot sequence. See Fig. 3 for an example of a random pilot schedule withτ = 2 andK = 3. The channel between the k’th user and the BS during the n’th time slot is denotedhnk = [hnk(1) hnk(2) . hnk(M)] T , where s2