This work identifies the fundamental limits of cache-aided coded multicasting in the presence of the well-known worst-user' bottleneck. This stems from the presence of receiving users with uneven channel capacities, which often forces the rate of transmission of each multicasting message to be reduced to that of the slowest user. This bottleneck, which can be detrimental in general wireless broadcast settings, motivates the analysis of coded caching over a standard Single-Input-Single-Output (SISO) Broadcast Channel (BC) with K cache-aided receivers, each with a generally different channel capacity. For this setting, we design a communication algorithm that is based on superposition coding that capitalizes on the realization that the user with the worst channel may not be the real bottleneck of communication. We then proceed to provide a converse that shows the algorithm to be near optimal, identifying the fundamental limits of this setting within a multiplicative factor of 4. Interestingly, the result reveals that, even if several users are experiencing channels with reduced capacity, the system can achieve the same optimal delivery time that would be achievable if all users enjoyed maximal capacity.
Recently, significant effort has been made toward understanding the behavior of coded caching in the finite Signal-to-Noise Ratio (SNR) regime with realistic (and thus often uneven) channel qualities. In this direction, the work in @cite_23 showed that a single-stream coded caching message beamformed by an appropriate transmit vector can outperform some existing multi-stream coded caching methods in the low-SNR regime, while references @cite_14 @cite_9 (see also @cite_19 ) revealed the importance of jointly considering caching with multicast beamformer design. Moreover, the work in @cite_17 studied the connection between rate and subpacketization in the multi-antenna environment, accounting for the unevenness naturally brought about by fading.
@cite_14 @cite_9 @cite_19 @cite_23 @cite_17
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We study downlink beamforming in a single-cell network with a multi-antenna base station (BS) serving cache-enabled users. For a given common rate of the files in the system, we first formulate the minimum transmit power with beamforming at the BS as a non-convex optimization problem. This corresponds to a multiple multicast problem, to which a stationary solution can be efficiently obtained through successive convex approximation (SCA). It is observed that the complexity of the problem grows exponentially with the number of subfiles delivered to each user in each time slot, which itself grows exponentially with the number of users in the system. Therefore, we introduce a low-complexity alternative through time-sharing that limits the number of subfiles that can be received by a user in each time slot. It is shown through numerical simulations that, the reduced-complexity beamforming scheme has minimal performance gap compared to transmitting all the subfiles jointly, and outperforms the state-of-the-art low-complexity scheme at all SNR and rate values with sufficient spatial degrees of freedom, and in the high SNR high rate regime when the number of spatial degrees of freedom is limited. A single cell downlink scenario is considered where a multiple-antenna base station delivers contents to multiple cache-enabled user terminals. Using the ideas from multi-server coded caching (CC) scheme developed for wired networks, a joint design of CC and general multicast beamforming is proposed to benefit from spatial multiplexing gain, improved interference management and the global CC gain, simultaneously. Utilizing the multiantenna multicasting opportunities provided by the CC technique, the proposed method is shown to perform well over the entire SNR region, including the low SNR regime, unlike the existing schemes based on zero forcing (ZF). Instead of nulling the interference at users not requiring a specific coded message, general multicast beamforming strategies are employed, optimally balancing the detrimental impact of both noise and inter-stream interference from coded messages transmitted in parallel. The proposed scheme is shown to provide the same degrees-of-freedom at high SNR as the state-of-art methods and, in general, to perform significantly better than several base-line schemes including, the joint ZF and CC, max-min fair multicasting with CC, and basic unicasting with multiuser beamforming. Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple-input multiple-output (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector; both are hard to realize. In this article, a quantized maximum signal-to-noise ratio (SNR) beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter. By using the distribution of the optimal beamforming vector in independent and identically distributed Rayleigh fading matrix channels, the codebook design problem is solved and related to the problem of Grassmannian line packing. The proposed design criterion is flexible enough to allow for side constraints on the codebook vectors. Bounds on the codebook size are derived to guarantee full diversity order. Results on the density of Grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or SNR loss. Monte Carlo simulations are presented that compare the probability of error for different quantization strategies. We consider the content delivery problem in a fading multi-input single-output channel with cache-aided users. We are interested in the scalability of the equivalent content delivery rate when the number of users, @math , is large. Analytical results show that, using coded caching and wireless multicasting, without channel state information at the transmitter, linear scaling of the content delivery rate with respect to @math can be achieved in some different ways. First, if the multicast transmission spans over @math independent sub-channels, e.g., in quasi-static fading if @math , and in block fading or multi-carrier systems if @math , linear scaling can be obtained, when the product of the number of transmit antennas and the number of sub-channels scales logarithmically with @math . Second, even with a fixed number of antennas, we can achieve the linear scaling with a threshold-based user selection requiring only one-bit feedbacks from the users. When CSIT is available, we propose a mixed strategy that combines spatial multiplexing and multicasting. Numerical results show that, by optimizing the power split between spatial multiplexing and multicasting, we can achieve a significant gain of the content delivery rate with moderate cache size.