CSI Dissemination for MU-MIMO Schemes Based on Outdated CSI Ansuman Adhikary * , Mari Kobayashi ‡ , Pablo Piantanida ‡ , Haralabos C. Papadopoulos † , Giuseppe Caire * * Ming-Hsieh Department of Electrical Engineering, University of Southern California, CA 90089 † Docomo Innovations Inc., Palo Alto, CA 94304 ‡ ´ Ecole Superieure d’ Electronique, SUPELEC, Gif-sur-Yvette, France Abstract— Conventional downlink MU-MIMO techniques re- quire accurate channel state information at the transmitter (CSIT) in order to realize degrees-of-freedom (DoF) gains. In practice, CSIT accuracy is limited by CSI estimation, by the delay between channel estimation and data transmission, and by the time/frequency coherence of the channel. These limitations pose significant challenges in the design and operation of efficient practical MU-MIMO systems. Recently, Maddah-Ali and Tse (MAT) have proposed a scheme achieving non-trivial degrees of freedom (DoF) gains by exploiting only strictly causal CSIT feedback, without relying on channel state prediction. The MAT scheme requires that users are provided also with the past channel states of other users. This requires not only CSI estimation and (causal) CSIT feedback from the receivers to the transmitter, but also CSI dissemination, i.e., providing the channel state of some users to some other users. In this work we focus efficient CSI dissemination for the conventional MAT scheme. We show that efficient CSI dissemination is equivalent to efficient data delivery and therefore it can be accomplished by the same MAT procedure, which delivers the necessary CSI dissemination “degrees of freedom” in the minimum number of channel uses. I. I NTRODUCTION We consider a multiple input multiple output (MIMO) Gaussian broadcast channel, corresponding to the downlink of a cellular system involving a base station (transmitter) with M antennas and K single antenna user terminals (receivers). A channel use 1 of the corresponding discrete-time complex baseband channel model is described by y = H H x + z, (1) where y =(y 1 ,...,y K ) T denotes the vector of symbols at the K receivers, z ∼ CN (0,I ) is the corresponding additive white Gaussian noise vector, x =(x 1 ,...,x M ) T is the vector of transmit symbols at the transmitter antenna array, subject to the total power constraint E[|x| 2 ] ≤ P , and H ∈ C M×K is the channel matrix, formed by i.i.d. entries ∼ CN (0, 1). We omit the channel use index when unnecessary, and use the standard “discrete-time” signal processing notation when it is needed. For example, x[n] indicates the signal vector transmitted at time slot n. In this paper, we consider the Maddah-Ali and Tse (MAT) scheme [1] for the case K = M , under the following 1 A channel use indicates the transmission of one complex signal dimen- sion on the time-frequency plane for a single-input single-output system. The number of independent complex dimensions that can be transmitted over one channel use depends on the system spatial degrees of freedom (DoF). assumptions: 1) time (or more in general, time-frequency channel uses) are divided into blocks, each block is formed by several time slots, and the channel state is constant over each block and statistically independent from block to block; 2) the receivers estimate their own channel vectors from downlink training symbols sent by the transmitter in each block; 3) the CSI estimated by each receiver is fed back in a strictly block-causal but otherwise ideal way, i.e., at block n the transmitter knows the channel estimates of all downlink channel vectors up to block n − 1; 4) the CSI is disseminated through the transmitter, by encoding CSI dissemination data in addition to information-bearing data in the downlink, i.e., no direct communication between the receivers is allowed. Under the above assumptions, we are in the presence of a block-wise memoryless Gaussian vector broadcast channel without CSIT and limited feedback. One extended channel use of this model corresponds to a block of symbols, over which the channel state is constant. A further generalization of this model would lift the restriction on explicit downlink training and allow block-wise Shannon feedback not nec- essarily restricted to the CSI only, but including a general function of the received signal. Hence, in this sense, we fix a priori a suboptimal (but highly practical) feedback coding strategy. The goal of this section is to show that, within the assumptions above, we can design a CSI training and dissem- ination strategy that minimizes the estimation/dissemination overhead, subject to the achievability of the same DoF of the original MAT scheme, i.e., subject to the requirement that the data-bearing part of the overall scheme achieves the same DoFs of the MAT scheme assuming genie-aided global CSI knowledge at the receivers and genie-aided causal global CSIT at the transmitter. We show the above result in steps. First, we consider a single session of the MAT scheme for the case M = K =3, and present the CSI training and dissemination scheme. Then, we extend the scheme to general M = K, by re- cursive dimension counting. The conventional MAT scheme, where blocks include downlink training and dissemination overhead, transmits blocks of unequal block length. This may be inconvenient in a practical implementation of a wireless communication protocol. Then, we consider a pipelined multiple-session extension of the basic MAT scheme that transmits blocks of equal length, at the cost of an increased decoding delay due to pipelining. The proof of optimality of the CSI training and dissem-