We consider the multihop broadcasting problem for @math nodes placed uniformly at random in a disk and investigate the number of hops required to transmit a signal from the central node to all other nodes under three communication models: Unit-Disk-Graph (UDG), Signal-to-Noise-Ratio (SNR), and the wave superposition model of multiple input single output (MISO). In the MISO model, informed nodes cooperate to produce a stronger superposed signal. We do not consider the problem of transmitting a full message nor do we consider interference. In each round, the informed senders try to deliver to other nodes the required signal strength such that the received signal can be distinguished from the noise. We assume sufficiently high node density @math . In the unit-disk graph model, broadcasting needs @math rounds. In the other models, we use an Expanding Disk Broadcasting Algorithm, where in a round only triggered nodes within a certain distance from the initiator node contribute to the broadcasting operation. This algorithm achieves a broadcast in only @math rounds in the SNR-model. Adapted to the MISO model, it broadcasts within @math rounds. All bounds are asymptotically tight and hold with high probability, i.e. @math .
For the MIMO model in @cite_6 and @cite_36 the authors give a recursive construction, which allows a capacity of @math for @math senders using MIMO communication. However, in @cite_20 , an upper bound of @math has been proved. This seeming contradiction has been addressed in @cite_22 , where they address the question whether distributed MIMO provides significant capacity gain over traditional multi-hop in large ad hoc networks with @math source-destination pairs randomly distributed over an area A. It turns out that the capacity depends on the ratio @math , it describes the spatial degree of freedom. If it is larger than @math it allows @math degrees of freedom @cite_6 , if it is less than @math the bound of @cite_20 holds. For all regimes optimal constructions are provided in these papers. While in @cite_6 path loss exponents @math are considered, for @math the regularity of the node placement must be taken into account @cite_36 .
@cite_36 @cite_20 @cite_22 @cite_6
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Multiple-input-multiple-output (MIMO) communication systems can provide large capacity gains over traditional single-input-single-output (SISO) systems and are expected to be a core technology of next generation wireless systems. Often, these capacity gains are achievable only with some form of adaptive transmission. In this paper, we study the capacity loss (defined as the rate loss in bits s Hz) of the MIMO wireless system when the covariance matrix of the transmitted signal vector is designed using a low rate feedback channel. For the MIMO channel, we find a bound on the ergodic capacity loss when random codebooks, generated from the uniform distribution on the complex unit sphere, are used to convey the second order statistics of the transmitted signal from the receiver to the transmitter. In this case, we find a closed-form expression for the ergodic capacity loss as a function of the number of bits fed back at each channel realization. These results show that the capacity loss decreases at least as O(2 sup -B (2MMt-2) ) where B is the number of feedback bits, M sub t is the number of transmit antennas, and M=min M sub r ,M sub t where M sub r is the number of receive antennas. In the high SNR regime, we present a new bound on the capacity loss that is tighter than the previously derived bound and show that the capacity loss decreases exponentially as a function of the number of feedback bits. We consider a large distributed MIMO system where wireless users with single transmit and receive antenna cooperate in clusters to form distributed transmit and receive antenna arrays. We characterize how the capacity of the distributed MIMO transmission scales with the number of cooperating users, the area of the clusters and the separation between them, in a line-of-sight propagation environment. We use this result to answer the following question: can distributed MIMO provide significant capacity gain over traditional multi-hop in large ad hoc networks with n source-destination pairs randomly distributed over an area A? Two diametrically opposite answers [24] and [26] have emerged in the current literature. We show that neither of these two results are universal and their validity depends on V the relation between the number of users n and √A λ, which we identify as the spatial degrees of freedom in the network. λ is the carrier wavelength. When √A λ ≥ n, there are n degrees of freedom in the network and distributed MIMO with hierarchical cooperation can achieve a capacity scaling linearly in n as in [24], while capacity of multihop scales only as √n. On the other hand, when √A λ ≤ √n as in [26], there are only √n degrees of freedom in the network and they can be readily achieved by multihop. Our results also reveal a third regime where √n ≤ √A λ ≤ n. Here, the number of degrees of freedom are smaller than n but larger than what can be achieved by multi-hop. We construct scaling optimal architectures for this intermediate regime. Large multiple-input multiple-output (MIMO) networks promise high energy efficiency, i.e., much less power is required to achieve the same capacity compared to the conventional MIMO networks if perfect channel state information (CSI) is available at the transmitter. However, in such networks, huge overhead is required to obtain full CSI especially for Frequency-Division Duplex (FDD) systems. To reduce overhead, we propose a downlink antenna selection scheme, which selects S antennas from M > S transmit antennas based on the large scale fading to serve K ≤ S users in large distributed MIMO networks employing regularized zero-forcing (RZF) precoding. In particular, we study the joint optimization of antenna selection, regularization factor, and power allocation to maximize the average weighted sum-rate. This is a mixed combinatorial and non-convex problem whose objective and constraints have no closed-form expressions. We apply random matrix theory to derive asymptotically accurate expressions for the objective and constraints. As such, the joint optimization problem is decomposed into subproblems, each of which is solved by an efficient algorithm. In addition, we derive structural solutions for some special cases and show that the capacity of very large distributed MIMO networks scales as O(KlogM) when M→∞ with K, S fixed. Simulations show that the proposed scheme achieves significant performance gain over various baselines. In this paper, the capacity of airborne multiple-input-multiple-output (MIMO) wireless communication systems with arbitrary alignments of linear transmit and receive antenna arrays is systematically analyzed and the maximum achievable capacity is determined. Based on a general three-dimensional (3D) airborne MIMO communication model, we are able to approximate the airborne MIMO capacity as a function of the transmit and receive antenna array geometry in the 3D space. The capacity approximation is asymptotically tight as the distance between the transmit and receive antenna arrays large compared to their size. Based on the asymptotically tight capacity approximation, we derive an upper bound as well as a lower bound of the airborne MIMO capacity. Interestingly, both the upper and lower bounds are achievable. We also derive a necessary and sufficient condition for airborne MIMO communication systems to achieve the capacity upper bound for any given 3D transceiver antenna array geometry. The necessary and sufficient condition allows us to properly select the system parameters and design airborne MIMO communication systems that reach the best possible performance in terms of system capacity. We prove that when the distance between the transmit and receive antenna arrays is within a certain range, there exists a set of system parameter values (e.g. antenna element separation) for which the capacity of the MIMO communication system achieves the theoretical upper bound and this capacity value is larger than the average capacity of the corresponding conventional MIMO communication system under Rayleigh fading. Finally, we prove that the airborne MIMO capacity converges to the capacity lower bound when the distance between the transmit and receive antenna arrays goes to infinity. Extensive numerical studies included in this paper illustrate and validate our theoretical developments.