We consider a downlink cellular network where multi-antenna base stations (BSs) transmit data to single-antenna users by using one of two linear precoding methods with limited feedback: 1) maximum ratio transmission (MRT) for serving a single user or 2) zero forcing (ZF) for serving multiple users. The BS and user locations are drawn from a Poisson point process, allowing expressions for the signal-to-interference coverage probability and the ergodic spectral efficiency to be derived as a function of system parameters, such as the number of BS antennas and feedback bits, and the pathloss exponent. We find a tight lower bound on the optimum number of feedback bits to maximize the net spectral efficiency, which captures the overall system gain by considering both of downlink and uplink spectral efficiency using limited feedback. Our main finding is that, when using MRT, the optimum number of feedback bits scales linearly with the number of antennas, and logarithmically with the channel coherence time. When using ZF, the feedback scales in the same ways as MRT, but also linearly with the pathloss exponent. The derived results provide system-level insights into the preferred channel codebook size by averaging the effects of short-term fading and long-term pathloss.
There has been extensive prior work on the downlink transmission rate as a function of a finite CSI feedback rate. In toy setups where a base station (BS) serves a single user in a single cell by ignoring ICI, downlink transmission rates were characterized as a function of the codebook size and the SNR. For example, in @cite_25 @cite_29 , a channel codebook design method for a single-user transmission was proposed by using Grassmannian line packing. By employing random vector quantization (RVQ), the rate loss of a point-to-point MIMO system caused by using finite rate feedback was characterized in @cite_23 . In @cite_37 , by applying RVQ, the performance of conjugate beamforming was analyzed in a MISO system. In @cite_9 , the performance of the finite rate CSI feedback was characterized, assuming temporally correlated channel and a principle of designing a channel codebook for this particular condition was proposed. The main limitation of @cite_25 @cite_17 @cite_19 @cite_23 @cite_37 is that it assumed only a single pair of a BS and a user, in which important features of a cellular network, e.g., ICI are missing.
@cite_37 @cite_9 @cite_29 @cite_19 @cite_23 @cite_25 @cite_17
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In this paper, we consider two different models of partial channel state information at the base station transmitter (CSIT) for multiple antenna broadcast channels: 1) the shape feedback model where the normalized channel vector of each user is available at the base station and 2) the limited feedback model where each user quantizes its channel vector according to a rotated codebook that is optimal in the sense of mean squared error and feeds back the codeword index. This paper is focused on characterizing the sum rate performance of both zero-forcing dirty paper coding (ZFDPC) systems and channel inversion (CI) systems under the given two partial CSIT models. Intuitively speaking, a system with shape feedback loses the sum rate gain of adaptive power allocation. However, shape feedback still provides enough channel knowledge for ZFDPC and CI to approach their own optimal throughput in the high signal-to-noise ratio (SNR) regime. As for limited feedback, we derive sum rate bounds for both signaling schemes and link their throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for both schemes for asymptotically high SNR. In this paper, we study resource allocation in a downlink OFDMA system assuming imperfect channel state information (CSI) at the transmitter. To achieve the individual QoS of the users in OFDMA system, adaptive resource allocation is very important, and has therefore been an active area of research. However, in most of the the previous work perfect CSI at the transmitter is assumed which is rarely possible due to channel estimation error and feedback delay. In this paper, we study the effect of channel estimation error on resource allocation in a downlink OFDMA system. We assume that each user terminal estimates its channel by using an MMSE estimator and sends its CSI back to the base station through a feedback channel. We approach the problem by using convex optimization framework, provide an explicit closed form expression for the users' transmit power and then develop an optimal margin adaptive resource allocation algorithm. Our proposed algorithm minimizes the total transmit power of the system subject to constraints on users' average data rate. The algorithm has polynomial complexity and solves the problem with zero optimality gaps. Simulation results show that our algorithm highly improves the system performance in the presence of imperfect channel estimation. We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments. In this work, we propose a linear base station (BS) precoding strategy based on switched relaying (SR) processing for downlink multiuser multiple-input multiple-output (MIMO) relay systems. The BS and the MIMO relay station (RS) are both equipped with a codebook of interleaving matrices. For a given channel state information (CSI) the selection function at the BS chooses the optimum interleaving matrix from the codebook based on the maximum sum received signal-to-interference-plus-noise ratio (SINR) or sum rate to design the linear BS precoder. Prior to the payload transmission the BS sends the index corresponding to the selected interleaving matrix to the RS, where the optimum interleaving matrix is selected as the optimum relay processing matrix. The entries of the codebook are randomly generated unitary matrices. Simulation results show that the performance of the proposed techniques is significantly better than prior art in the case of perfect CSI.1