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## Über dieses Buch

This Springerbreif introduces a threshold-based channel sparsification approach, and then, the sparsity is exploited for scalable channel training. Last but not least, this brief introduces two scalable cooperative signal detection algorithms in C-RANs. The authors wish to spur new research activities in the following important question: how to leverage the revolutionary architecture of C-RAN to attain unprecedented system capacity at an affordable cost and complexity.

Cloud radio access network (C-RAN) is a novel mobile network architecture that has a lot of significance in future wireless networks like 5G. the high density of remote radio heads in C-RANs leads to severe scalability issues in terms of computational and implementation complexities. This Springerbrief undertakes a comprehensive study on scalable signal processing for C-RANs, where ‘scalable’ means that the computational and implementation complexities do not grow rapidly with the network size.

This Springerbrief will be target researchers and professionals working in the Cloud Radio Access Network (C-Ran) field, as well as advanced-level students studying electrical engineering.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
Driven by the astounding development of smart phones, mobile applications and the Internet of Things (IoT), traffic demand grows exponentially in current mobile networks. Based on the recent statistics from Cisco, the global mobile data traffic has grown 18-fold over the past 5 years and is expected to increase sevenfold by 2021. Moreover, the number of mobile-connected devices, including smartphones, wearable devices, machine-to-machine modules, auto pilot cars, etc., is estimated to be 11.6 billion in 2021, which will be approximated to one and a half times of the world’s projected population at that time. The rapid proliferation of mobile devices, coupled with an abundance of new applications, will also bring a large variety of new service requirements. For instance, massive machine type communications require high connection density, videos require very high throughput per connection, auto pilot cars require low latency and ultra high reliability, augmented reality requires both high throughput and low latency, and so on.
Ying-Jun Angela Zhang, Congmin Fan, Xiaojun Yuan

### Chapter 2. System Model and Channel Sparsification

Abstract
In C-RAN, only a small fraction of the entries in the channel matrix have reasonably large amplitudes, because a user is only close to a small number of RRHs in its neighborhood, and vice versa. Thus, ignoring the small entries in the channel matrix would significantly sparsify the matrix, which can potentially lead to significant reduction in the computational complexity and channel estimation overhead. The question is to what extent can the channel matrix be sparsified without substantially compromising the system performance. In this chapter, we attempt to address this question. In particular, we propose a threshold-based channel matrix sparsification method, where the matrix entries are ignored according to the distance between the users and RRHs. We derive a closed-form expression describing the relationship between the threshold and the SINR loss due to channel spasification. The analysis serves as a convenient guideline to set the threshold subject to a tolerable SINR loss.
Ying-Jun Angela Zhang, Congmin Fan, Xiaojun Yuan

### Chapter 3. Scalable Channel Estimation

Abstract
In this chapter, we investigate the design of training sequences for time-multiplexed channel training in C-RANs. Orthogonal training sequences were shown to be optimal or nearly optimal in conventional MIMO systems, where the transmit antennas are co-located, and so are the receive antennas. However, orthogonal training design is very inefficient when applied to C-RAN, for that a C-RAN system usually covers a large number of users and RRHs. Allocating orthogonal training sequences to users leads to an unaffordable overhead to the system. As proved in the previous chapter, the signals from far-away users can be largely ignored without causing significant performance loss. Hence, rather than global orthogonality, we introduce the notion of local orthogonality, in which the training sequences of the users in the neighborhood of an RRH (i.e., the area centered around the RRH with distance below a certain threshold d 0) are required to be orthogonal to each other. The training design problem is then formulated as to find the minimum training length that preserves local orthogonality. This problem can be recast as a vertex-coloring problem, and the existing vertex-coloring algorithms can be applied to solve the problem. Further, we analyze the minimum training length as a function of the network size. Based on the theory of random geometric graph, we show that the training length is $$O(\ln K)$$ almost surely, where K is the number of users. This guarantees a scalable training-based C-RAN design, i.e., the proposed training design can be applied to a large-size C-RAN system satisfying local orthogonality at the cost of a moderate training length. Note that , on one hand, with local orthogonality, the larger the neighborhood of an RRH, the more interference from the neighboring users can be eliminated in channel estimation. Then, local orthogonality achieves a channel-estimation accuracy close to that of global orthogonality. On the other hand, a larger neighborhood area implies more channel coefficients to be estimated, thereby incurring a greater overhead to the system. As such, there is a balance to strike between the accuracy and the overhead in channel estimation. In this chapter, we study this tradeoff from the perspective of throughput maximization. We show that, with local orthogonality, the optimal d 0 for throughput maximization can be numerically determined.
Ying-Jun Angela Zhang, Congmin Fan, Xiaojun Yuan

### Chapter 4. Scalable Signal Detection: Dynamic Nested Clustering

Abstract
In Chap. 2, we proposed a threshold-based channel sparsification approach, and showed that the channel matrices can be greatly sparsified without substantially compromising the system capacity. In this chapter and the next chapter, we endeavor to design scalable algorithms for joint signal detection in the uplink of C-RAN by exploiting the high sparsity of the channel matrix. In this chapter, we propose a dynamic nested clustering (DNC) algorithm which greatly reduces the computational complexity of MMSE detection from O(N 3) to O(N a), where N is the total number of RRHs and a ∈ (1, 2] is a constant determined by the computation implementations. In the next chapter, we propose a randomized Gaussian message passing (RGMP) algorithm, which further reduces the computational complexity of MMSE detection to be linear in the number of RRHs.
Ying-Jun Angela Zhang, Congmin Fan, Xiaojun Yuan

### Chapter 5. Scalable Signal Detection: Randomized Gaussian Message Passing

Abstract
In this chapter, we convert the signal detection in a C-RAN to an inference problem over a bipartite random geometric graph. By passing messages among neighboring nodes, message passing (a.k.a. belief propagation) provides an efficient way to solve the inference problem over a sparse graph. However, the traditional message-passing algorithm does not guarantee to converge, because the corresponding bipartite random geometric graph is locally dense and contains many short loops. As a major contribution of this chapter, we propose a randomized Gaussian message passing (RGMP) algorithm to improve the convergence. The proposed RGMP algorithm demonstrates significantly better convergence performance than the conventional message passing algorithms. In addition, we generalize the RGMP algorithm to a blockwise RGMP (B-RGMP) algorithm, which allows parallel implementation. The average computation time of B-RGMP remains constant when the network size increases.
Ying-Jun Angela Zhang, Congmin Fan, Xiaojun Yuan

### Chapter 6. Conclusions and Future Work

Abstract
Featuring centralized baseband processing, cooperative radio, and real-time cloud infrastructure, C-RAN has great potential to be a predominant wireless cellular architecture in next-generation wireless systems. Aware of the prohibitively high cost caused by the high RRH density, this book focuses on designing scalable signal processing algorithms for C-RANs by exploiting the near-sparsity of channel matrices, where “scalable” means that both the overhead and computational complexity does not grow significantly with the network size.
Ying-Jun Angela Zhang, Congmin Fan, Xiaojun Yuan

### Backmatter

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