On the Power Efficiency of Sensory and Ad Hoc Wireless Networks

We consider the power efficiency of a communications channel, i.e., the maximum bit rate that can be achieved per unit power (energy rate). For additive white Gaussian noise (AWGN) channels, it is well known that power efficiency is attained in the low signal-to-noise ratio (SNR) regime where capacity is proportional to the transmit power. In this paper, we first show that for a random sensory wireless network with n users (nodes) placed in a domain of fixed area, with probability converging to one as n grows, the power efficiency scales at least by a factor of sqrt n. In other words, each user in a wireless channel with n nodes can support the same communication rate as a single-user system, but by expending only 1/(sqrt n) times the energy. Then we look at a random ad hoc network with n relay nodes and r simultaneous transmitter/receiver pairs located in a domain of fixed area. We show that as long as r ≤ sqrt n, we can achieve a power efficiency that scales by a factor of sqrt n. We also give a description of how to achieve these gains

On the Capacity Region of Multi-Antenna Gaussian Broadcast Channels with Estimation Error

In this paper we consider the effect of channel estimation error on the capacity region of MIMO Gaussian broadcast channels. It is assumed that the receivers and the transmitter have (the same) estimates of the channel coefficients (i.e., the feedback channel is noiseless). We obtain an achievable rate region based on the dirty paper coding scheme. We show that this region is given by the capacity region of a dual multi-access channel with a noise covariance that depends on the transmit power. We explore this duality to give the asymptotic behavior of the sum-rate for a system with a large number of user, i.e., n rarr infin. It is shown that as long as the estimation error is of fixed (w.r.t n) variance, the sum-capacity is of order M log log n, where M is the number of antennas deployed at the transmitter. We further obtain the sum-rate loss due to the estimation error. Finally, we consider a training-based scheme for block fading MISO Gaussian broadcast channels. We find the optimum length of the training interval as well as the optimum power used for training in order to maximize the achievable sum-rate

A Practical Scheme for Wireless Network Operation

In many problems in wireline networks, it is known that achieving capacity on each link or subnetwork is optimal for the entire network operation. In this paper, we present examples of wireless networks in which decoding and achieving capacity on certain links or subnetworks gives us lower rates than other simple schemes, like forwarding. This implies that the separation of channel and network coding that holds for many classes of wireline networks does not, in general, hold for wireless networks. Next, we consider Gaussian and erasure wireless networks where nodes are permitted only two possible operations: nodes can either decode what they receive (and then re-encode and transmit the message) or simply forward it. We present a simple greedy algorithm that returns the optimal scheme from the exponential-sized set of possible schemes. This algorithm will go over each node at most once to determine its operation, and hence, is very efficient. We also present a decentralized algorithm whose performance can approach the optimum arbitrarily closely in an iterative fashion

Power bandwidth trade-off for sensory and ad-hoc wireless networks

We look at the power bandwidth trade-off in random sensory and ad-hoc wireless networks with n users and r ≤ √n simultaneous source/destination pairs. Under a specific protocol, we show that the minimum power required for maintaining an achievable scaling law of R_(sum)=Θ(f(n)) for the sum-rate in the network, scales like Θ(f(n)/√n). The required bandwidth B in this case is of order Θ(f(n)/r). It is also proved that the minimum achievable energy per information bit (E_b/N_0)min for this protocol, scales as Θ(1/√n) and in this case the spectral efficiency is nonzero and is of constant order

The capacity region of multiple input erasure broadcast channels

In this paper, we look at the capacity region of a special class of broadcast channels with multiple inputs at the transmitter and a number of receivers. The channel between an input of the transmitter and a receiver is modelled as an independent memoryless erasure channel. We assume that the signals coming from different inputs to the receiver do not interfere with each other. Also for each input, the transmitter sends the same signal through the channels outgoing from that input. This class of broadcast channels does not necessarily belong to the class of “more capable”. We will show that the capacity region of these broadcast channels is achieved by time-sharing between the receivers at each input. Finally, the implications of these results to the more general network setup are discussed

On the effect of quantization on performance at high rates

We study the effect of quantization on the performance of a scalar dynamical system in the high rate regime. We evaluate the LQ cost for two commonly used quantizers: uniform and logarithmic and provide a lower bound on performance of any centroid-based quantizer based on entropy arguments. We also consider the case when the channel drops data packets stochastically

Is broadcast plus multiaccess optimal for Gaussian wireless networks?

In this paper we show that "separation"-based approaches in wireless networks do not necessarily give good performance in terms of the capacity of the network. Therefore in optimal design of a wireless network, its total structure should be considered. In other words, achieving capacity on the subnetworks of a wireless network does not guarantee globally achieving capacity. We will illustrate this fact by considering some examples of multistage Gaussian wireless relay networks. We will consider a wireless Gaussian relay network with one stage in both fading and nonfading environment. We show that as the number of relay nodes, n, grows large, the capacity of this network scales like log n. We then show that with the "separation"-based scheme, in which the network is viewed as the concatenation of a broadcast and a multiaccess network, the achievable rate scales as log log n and as a constant for fading and nonfading environment, respectively, which is clearly suboptimal

Capacity of wireless erasure networks

In this paper, a special class of wireless networks, called wireless erasure networks, is considered. In these networks, each node is connected to a set of nodes by possibly correlated erasure channels. The network model incorporates the broadcast nature of the wireless environment by requiring each node to send the same signal on all outgoing channels. However, we assume there is no interference in reception. Such models are therefore appropriate for wireless networks where all information transmission is packetized and where some mechanism for interference avoidance is already built in. This paper looks at multicast problems over these networks. The capacity under the assumption that erasure locations on all the links of the network are provided to the destinations is obtained. It turns out that the capacity region has a nice max-flow min-cut interpretation. The definition of cut-capacity in these networks incorporates the broadcast property of the wireless medium. It is further shown that linear coding at nodes in the network suffices to achieve the capacity region. Finally, the performance of different coding schemes in these networks when no side information is available to the destinations is analyzed

On the capacity of wireless erasure networks

We determine the capacity of a certain class of wireless erasure relay networks. We first find a suitable definition for the "cut-capacity" of erasure networks with broadcast at transmission and no interference at reception. With this definition, a maxflow mincut capacity result holds for the capacity of these networks