Ehsan Karamad

Optimizing placements of backhaul hubs and orientations of antennas in small cell networks

While small cells (SCs) are an important feature of emerging network architectures, providing backhaul to SCs is a challenging problem. Non-line-of-sight (NLOS) wireless backhaul networks provide a cost effective approach in urban areas where providing a wired- or fiber-based backhaul is difficult. An important problem in designing such networks is to optimize the position of backhaul hubs in a way that all SCs are properly serviced. However, this is a NP-complete problem requiring suboptimal, but effective, solutions. In this work, we will propose a novel suboptimal algorithm, based on dynamic programming, to solve the NP-hard problem of hub placement in backhaul networks. We will further consider an extended problem of optimizing both the placement of hubs and the orientation of the hub antennas. Our design methodology is backed up with numerical examples using deterministic channel prediction tools which leads to a robust and smart design of the backhaul network.

Quantization and Bit Allocation for Channel State Feedback in Relay-Assisted Wireless Networks

This paper investigates quantization of channel state information (CSI) and bit allocation across wireless links in a multi-source, single-relay cooperative cellular network. Our goal is to minimize the loss in performance, measured as the achievable sum rate, due to limited-rate quantization of CSI. We develop both a channel quantization scheme and allocation of limited feedback bits to the various wireless links. We assume that the quantized CSI is reported to a central node responsible for optimal resource allocation. We first derive tight lower and upper bounds on the difference in rates between the perfect CSI and quantized CSI scenarios. These bounds are then used to derive an effective quantizer for arbitrary channel distributions. Next, we use these bounds to optimize the allocation of bits across the links subject to a budget on total available quantization bits. In particular, we show that the optimal bit allocation algorithm allocates more bits to those links in the network that contribute the most to the sum-rate. Finally, the paper investigates the choice of the central node; we show that this choice plays a significant role in CSI bits required to achieve a target performance level.

Distributed power control subject to channel and interference estimation errors

Perfect estimation of receiver interference power is a fundamental assumption in most distributed power control algorithms. Newer techniques in managing interference through transmit power control rely on local observations of channel information where the obtained information is assumed to be error-free. In this paper, we investigate the performance degradation in distributed power control algorithms due to estimation errors. We present some bounds on the resulted transmit power and signal to interference and noise ratio (SINR) errors due to imperfect estimations. Specifically, we find that for interference-limited scenarios, there is a potential SINR loss of up to 3-dB even for tiny errors in channel state information.

Scalable and Efficient Power Control Algorithms for Wireless Networks

Efficient optimization techniques are important to manage interference in emerging dense wireless networks. Here, we address interference management through power control as a general utility maximization problem. For the class of utility functions that are concave in the logarithm of the optimization variables, we propose a power control algorithm based on fixed-point iterations. The iterations converge to the globally optimal power vector. One key benefit is that, for a network with N transmitters and a centralized implementation of the power control algorithm, the computational complexity per iteration of the algorithm is O(N2). When implemented in a distributed fashion and allowing for a signaling complexity of N messages per iteration, the computation complexity is reduced to O(N). We show that the proposed centralized and distributed versions of the algorithm converge to the optimal power vector at a linear rate. Our numerical results suggest that in most instances, the algorithm takes fewer than ten iterations to converge, even fewer if the initialization is close to the optimal power vector. The proposed algorithm is, therefore, very efficient for power control in slowly fading channels. Furthermore, unlike previous works in the literature, the proposed algorithm does not require the objective function to be separable into a sum of individual utilities. As an example, we present results for power control in a two-hop decode-and-forward cooperative relay network and illustrate the performance gains due to interference management.

Channel quantization and bit allocation in multi-source multi-relay cooperative networks

This paper investigates quantization of the channel state information (CSI) in a cooperative cellular network. This CSI, delivered to some central node, is to be used to allocate resources in order to maximize the sum-rate in a multi-source network assisted by multiple relays. We start by deriving tight bounds on the performance loss due to quantization and then, through minimizing these bounds, we propose an efficient quantization and bit allocation technique. To this end, we present the bound on the overall performance loss as the sum of individual terms where each term represents the loss caused by the quantization of the CSI for an individual link. Then we show that each of these terms can be written as the product of two important components: the standard quantization error, and the link coefficient which is only a function of the large scale fading parameters. The quantization error is similar for all links and leads to the optimal quantization problem. Then using a simple bound on the quantization error, and also considering the link coefficients, we allocate bits to quantize each link. Further, we discuss the candidates in the network to play the role of the central node. A numerical example shows that the overall sum-rate (overall CSI demand), is significantly increased (decreased) through bit allocation.

Fractional cooperation and the max-min rate in a multi-source cooperative network

We maximize the minimum rate among sources in a multi-source, multi-relay, single destination cooperative network. The relays use the decode-and-forward protocol while all transmissions use orthogonal frequency division multiplexing. The key to our approach is fractional cooperation: there may be fewer relays than sources and not all source subcarriers are relayed. Optimal matching of the sources subcarriers with those of the relays is a combinatorial problem with exponential complexity. We develop an upper bound on the max-min rate and present an algorithm with a close to optimum performance. Furthermore, our simulation results show that for certain number of sources in a network, accounting for the overhead due to relaying, there is an optimal number of relays maximizing the max-min rate. This number is in general less than the number of sources.

Optimizing limited channel state information in wireless cooperative networks

Over the last decade, the development of resource allocation algorithms for cooperative communication networks has focused on optimal, or acceptable suboptimal, solutions assuming full knowledge of channel state information (CSI) in the network. This assumption is, unfortunately, unlikely to be satisfied in practice. Here we turn our attention to the effects of limited CSI on the performance of a cooperative network. We show that the performance gap between the fully centralized approaches and fully distributed algorithms falls exponentially with the number of CSI bits per link available at the central node. We use this to show that, for a large class of objective functions, a close-to-optimal solution is achievable with limited CSI. We also show that proper allocation of the CSI bits to different links in the network is a crucial issue. We propose a simple upper bound on the performance gap and a bit allocation algorithm that minimizes the upper bound. Our numerical results confirm that through optimal bit allocation considerable savings in CSI bits is achieved.

Performance loss minimization in cooperative networks based on quantized channel feedback

In wireless networks, having channel state information (CSI) at some central node is essential for most resource allocation problems. We turn our attention to the uplink transmission in a cellular network where the cell users are assisted by a single relay; our goal is to maximize sum rate over the users. Understanding that assuming perfect CSI is a purely theoretical construct, we investigate the scenario where only quantized CSI (QCSI) is available at a central node. Here we design quantization levels which minimize the performance loss in terms of loss in sum rate due to quantization in the network. Next, assuming a finite capacity for the CSI feedback link, we argue that the performance loss may be further reduced through proper bit allocation, i.e., quantization of different links with different precision. We further show that for any given network, there is always savings in terms of CSI bits required as long as optimal bit allocation is deployed. Finally, we propose a lower bound on performance loss achieved through optimal bit allocation.

Resource allocation to achieve cross-layer metrics in cooperative networks

We consider a network utility maximization (NUM) framework to allocate resources in a cooperative network comprising multiple sources, dedicated relays and a single destination. The allocation is designed to ensure the average queue length at each source is below a chosen demand. The optimization is over power allocation at all nodes, relay selection and relaying strategy. We formulate the NUM problem and propose a solution to achieve the optimal allocation scheme. The two main contributions here are the formulation including queue length and an efficient solution that has only linear complexity in the number of source nodes. Furthermore, unlike previous works, it avoids a brute-force search over rates.

Optimal rates for decode-and-forward cooperative networks with partial CSI

Centralized algorithms for relay selection and power allocation in cooperative networks have been widely considered in the literature. As effective as the proposed algorithms are, the complexity of centralized implementation and feedback required to communicate the required channel state information makes these solutions impractical. Here we investigate, in terms of the achievable rates for the nodes, relaying and power allocation for cooperative networks and consider the effects of partial channel state information. We first consider 1-bit knowledge of relevant channels followed by the multi-bit case. We also consider the case of multiple sources wherein relay resources must be sub-divided amongst the sources.