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We consider the problem of differentiated rate scheduling for the downlink (i.e., multi-antenna broadcast channel), in the sense that the rates required by different users must satisfy certain constraints on their ratios. When full channel state information (CSI) is available at the transmitter and receivers, the problem can be readily solved using dirty paper coding (DPC) and the application of convex optimization techniques on the dual problem which is the multiple access channel (MAC). Since in many practical application full CSI may not be feasible and computational complexity prohibitive when the number of users is large, we focus on other simple schemes that require very little CSI: time-division opportunistic (TO) beamforming where in different time slots (of different lengths) the transmitter performs opportunistic beamforming to the users requiring the same rate, and weighted opportunistic (WO) beamforming where the random beams are assigned to those users having the largest weighted SINR. For single antenna systems we also look at the capacity-achieving superposition coding (SC) scheme. In all cases, we determine explicit schedules to guarantee the rate constraints and show that, in the limit of large number of users, the throughput loss compared to the unconstrained throughput (sum-rate capacity) tends to zero. We further provide bounds on the rate of convergence of the sum-rates of these schemes to the sum-rate capacity. Finally, we provide simulation results of the performance of different scheduling schemes considered in the paper.

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.

The throughput of a multiple-antenna broadcast channel highly depends on the channel state information (CSI) at the transmitter side. However, due to the time variant nature of wireless channels, having perfect knowledge of the under- lying links appears to be a questionable assumption, especially when the number of users and/or antennas increases. Although it can become computationally prohibitive in practice, theoretically any point on the capacity region of a Gaussian broadcast channel is achievable using dirty paper coding (DPC) if full CSI is available. The aforementioned drawbacks of DPC have motivated the development of simpler transmission strategies that re- quire little CSI and yet can deliver a large portion of the capacity. One such scheme is opportunistic beam-forming that is shown to be able to achieve the same throughput scaling as that of DPC for the regime of large number of users. In this paper we investigate the performance of opportunistic beamforming when the perfect channel state information is not available; i.e., the channel estimation is erroneous. We will show that in order to maximize the throughput (sum rate capacity), the transmitter needs to back off the rate than what is suggested by the estimated channel state. We obtain the optimal back off and show that by using this modified opportunistic scheme, the same multiuser gain can be achieved.

Broadcast (or point to multipoint) communication has attracted a lot of research recently. In this paper, we consider the group broadcast channel where the users' pool is divided into groups, each of which is interested in common information. Such a situation occurs for example in digital audio and video broadcast where the users are divided into various groups according to the shows they are interested in. The paper obtains upper and lower bounds for the sum rate capacity in the large number of users regime and quantifies the effect of spatial correlation on the system capacity. The paper also studies the scaling of the system capacity when the number of users and antennas grow simultaneously. It is shown that in order to achieve a constant rate per user, the number of transmit antennas should scale at least logarithmically in the number of users.

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.

We consider the throughput of a MIMO Gaussian broadcast channel with two generalizing assumptions: (1) differentiated quality of service, in the sense that the rates required by different users must satisfy certain rational constraints, and (2) imperfect channel side information (CSI), where we assume that the estimate of the underlying channel has some error with known distribution. Theoretically, with full and perfect CSI in hand, dirty paper coding (DPC) can achieve any point on the capacity region, including the non-symmetrical boundary points. However, the full CSI requirement and the computational complexity of DPC motivates the development of simpler schemes which require little feedback from the users and can obtain a large portion of the capacity of the channel. In this paper we will look at the throughput and rate ratio achieved by schemes based on the idea of opportunistic beam-forming and employing a rate back-off mechanism in order to maximize the throughput in the case of imperfect CSI. We will determine the optimal scheduling parameters and will show the order optimality of these schemes in the regime of large number of users.

In this paper, we consider a fading broadcast channel where users have different rate demands. In particular, we assume users are divided into M groups, each group of which requires the same rate, and where the ratio of the rates of the groups are given. The transmitter would like to maximize the throughput (sum of the rates to all users) while maintaining the rational rate constraints. In general, this problem appears to be computationally intractable since the ergodic capacity region is described as the convex hull of (an infinite) set of rates. In this paper, we therefore, focus on the asymptotic regime of many users (large n) where explicit results can be found. In particular, we propose three scheduling schemes to provide the rational rate constraints namely, weighted opportunistic (WO), time division opportunistic (TO), and superposition coding (SC). The WO scheduling is a generalization of the opportunistic scheduling in which we transmit to only the user that has the maximum weighted signal to noise ratio (SNR). In TO, each group has its own time slot in which the transmitter chooses the user with the best SNR from the corresponding group. Superposition coding is the one that achieves the capacity region. For each scheduling we give explicit scheme to guarantee the rational rate constraints. We also analyze the throughput loss due to rate constraints for different schemes. In particular, we show that the throughput loss compared to the maximum throughput (i.e., the sum rate capacity without any rate constraints) tends to zero for large n, and finally, we analyze the convergence rate of all the schemes.

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.

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 AWGN channels, it is well known that power efficiency is attained in the low SNR regime where capacity is proportional to the transmit power. In this paper we show that for a sensory wireless network with n nodes, or for an ad-hoc wireless network with n users and up to /spl radic/n transmit/receive pairs, the power efficiency scales at least by a factor of /spl radic/n. In other words, each user in a wireless channel with n nodes can support the same communications rate as a single user system, but by expending only 1/(/spl radic/n) the energy. We also give a description of how to achieve these gains.