A cloud radio access network (Cloud-RAN) is a network architecture that holds the promise of meeting the explosive growth of mobile data traffic. In this architecture, all the baseband signal processing is shifted to a single baseband unit (BBU) pool, which enables efficient resource allocation and interference management. Meanwhile, conventional powerful base stations can be replaced by low-cost low-power remote radio heads (RRHs), producing a green and low-cost infrastructure. However, as all the RRHs need to be connected to the BBU pool through optical transport links, the transport network power consumption becomes significant. In this paper, we propose a new framework to design a green Cloud-RAN, which is formulated as a joint RRH selection and power minimization beamforming problem. To efficiently solve this problem, we first propose a greedy selection algorithm, which is shown to provide near- optimal performance. To further reduce the complexity, a novel group sparse beamforming method is proposed by inducing the group-sparsity of beamformers using the weighted @math -norm minimization, where the group sparsity pattern indicates those RRHs that can be switched off. Simulation results will show that the proposed algorithms significantly reduce the network power consumption and demonstrate the importance of considering the transport link power consumption.
A main design tool applied in this paper is optimization with the group sparsity induced norm. With the recent theoretical breakthrough in compressed sensing @cite_11 @cite_20 , the sparsity patterns in different applications in signal processing and communications have been exploited for more efficient system design, e.g., for pilot aided sparse channel estimation @cite_1 . The sparsity inducing norms have been widely applied in high-dimensional statistics, signal processing, and machine learning in the last decade @cite_31 . The @math -norm regularization has been successfully applied in compressed sensing @cite_11 @cite_20 . More recently, mixed @math -norms are widely investigated in the case where some variables forming a group will be selected or removed simultaneously, where the mixed @math -norm @cite_27 and mixed @math -norm @cite_13 are two commonly used ones to induce group sparsity for their computational and analytical convenience.
@cite_1 @cite_27 @cite_31 @cite_13 @cite_20 @cite_11
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It has been known for a while that l1-norm relaxation can in certain cases solve an under-determined system of linear equations. Recently, E. Candes ("Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Information Theory, vol. 52, no. 12, pp. 489-509, Dec. 2006) and D. Donoho ("High-dimensional centrally symmetric polytopes with neighborlines proportional to dimension," Disc. Comput. Geometry, vol. 35, no. 4, pp. 617-652, 2006) proved (in a large dimensional and statistical context) that if the number of equations (measurements in the compressed sensing terminology) in the system is proportional to the length of the unknown vector then there is a sparsity (number of nonzero elements of the unknown vector) also proportional to the length of the unknown vector such that l1-norm relaxation succeeds in solving the system. In this paper, in a large dimensional and statistical context, we determine sharp lower bounds on the values of allowable sparsity for any given number (proportional to the length of the unknown vector) of equations for the case of the so-called block-sparse unknown vectors considered in "On the reconstruction of block-sparse signals with an optimal number of measurements," (M. , IEEE Trans, Signal Processing, submitted for publication. In a number of signal processing applications, problem formulations based on the l 1 norm as a sparsity inducing signal prior lead to simple algorithms with good performance. However, l 1 norm is not flexible enough to handle certain signal structures that are represented using a few groups of coefficients. Formulations that make use of mixed norms provide an alternative that can handle such signals by forcing sparsity on a group level and allowing non-sparse distributions within the groups. However, conventional mixed norms allow only non-overlapping groups - a restriction that leads to characteristics unlikely for natural signals. In this paper, we investigate mixed norms with overlapping groups. We consider a simple denoising formulation that gives a convex optimization problem and provide an algorithm that solves the problem. We use the algorithm to evaluate the performance of mixed norms with overlapping groups as signal priors. Sparse regression often uses l p norm priors (with p < 2). This paper demonstrates that the introduction of mixed-norms in such contexts allows one to go one step beyond in signal models, and promote some different, structured, forms of sparsity. It is shown that the particular case of the l1,2 and l2,1 norms leads to new group shrinkage operators. Mixed norm priors are shown to be particularly efficient in a generalized basis pursuit denoising approach, and are also used in a context of morphological component analysis. A suitable version of the Block Coordinate Relaxation algorithm is derived for the latter. The group-shrinkage operators are then modified to overcome some limitations of the mixed-norms. The proposed group shrinkage operators are tested on simulated signals in specific situations, to illustrate and compare their different behaviors. Results on real data are also used to illustrate the relevance of the approach. SUMMARY Group sparsity is one of the important signal priors for regularization of inverse problems. Sparsity with group structure is encountered in numerous applications. However, despite the abundance of sparsity-based adaptive algorithms, attempts at group sparse adaptive methods are very scarce. In this paper, we introduce novel recursive least squares (RLS) adaptive algorithms regularized via penalty functions, which promote group sparsity. We present a new analytic approximation for lp,0 norm to utilize it as a group sparse regularizer. Simulation results confirm the improved performance of the new group sparse algorithms over regular and sparse RLS algorithms when group sparse structure is present. Copyright © 2013 John Wiley & Sons, Ltd.