In this chapter, two different distributed CSIT setups were tackled to in-vestigate the performance that may be achieved if one foregoes sharing the channel state information fully among cooperating transmitters. The first setup arises in the context of TDD systems where CSI is gained from up-link transmission and therefore the transmitters each end up with mutually exclusive pieces of the CSI puzzle. For transmitters withNt≥2 we investi-gate extending the VSINR framework applied in the previous chapter to the MISO IC to the case of joint transmission. The second setup corresponds to transmitters being able to decode the fed back quantized CSI up to different levels of accuracy. A hierarchical quantization model for this case was pro-posed and a Bayesian formulation for the decentralized beamforming design was provided, based on team decision theory.
5.5 Conclusions 121 Upper bound, Accurate CSIT, Joint BF Distributed CSIT, Decentralized BF Lower bound, distributed CSIT, Myopic BF Lower bound, Coarse CSIT, Joint BF Knowledge at Tx1 shared, Joint BF Knowledge at Tx2 shared, Joint BF
5 10 15 20 Upper bound, Accurate CSIT, Joint BF Distributed CSIT, Decentralized BF Lower bound, distributed CSIT, Myopic BF Lower bound, Coarse CSIT, Joint BF Knowledge at Tx1 shared, Joint BF Knowledge at Tx2 shared, Joint BF
5 10 15 20
Upper bound, Accurate CSIT, Joint BF Distributed CSIT, Decentralized BF Lower bound, distributed CSIT, Myopic BF Lower bound, Coarse CSIT, Joint BF Knowledge at Tx1 shared, Joint BF Knowledge at Tx2 shared, Joint BF
Figure 5.8: Sum Rate Comparison forL1(2) =L2(1) = 2, L1(1) =L2(2) = 6 bits and different β.
122 Chapter 5 Cooperative Network MIMO with distributed CSIT
Chapter 6
Optimized data sharing in Network MIMO with finite backhaul capacity
6.1 Introduction
In this chapter, we tackle the issue of limited backhaul capacity in a co-operative multicell setup. As noted in the introductory chapters, multicell processing (multicell MIMO, network MIMO) as proposed in [10], [11] for example requires full data sharing. This subsumes high capacity backhaul links, which may not always be feasible, or even simply desirable, in certain applications. In fact, under limited backhaul rate constraints, data sharing consumes a precious fraction of the backhaul capacity which must be com-pensated by the capacity gain induced by the network MIMO channel over the classical interference channel. Imposing finite capacity constraints on the backhaul links brings with it a set of interesting research questions, in particular:
• Given the backhaul constraints, assuming thatnot alltraffic is shared across transmitters, i.e assuming a certain part remains private to each transmitter, what kind of rates can we expect to achieve? What is the capacity region of the resulting multicell channel? In fact, the
123
124 Chapter 6 Data Backhaul constrained Network MIMO multicell MIMO channel under finite backhaul no longer corresponds to a MIMO broadcast channel, nor does it correspond to the so-called interference channel.
• How useful is data sharing when backhaul constraints are present? In other words, how do the rates achieved with a data sharing-, and there-fore joint transmission enabling-scheme compare to those achieved without data sharing, when the backhaul is limited?
These questions have lead to a number of recent interesting research efforts. To cite a few, in [67] and [20], joint encoding for the downlink of a cellular system is studied under the assumption that the base stations are connected to a central unit via finite-capacity links. The authors investigate different transmission schemes and ways of using the backhaul capacity in the context of a modified version of Wyner’s channel model. One of their main conclusions is that “central encoding with oblivious cells”, whereby quantized versions of the signals to be transmitted from each base station, computed at the central unit, are sent over the backhaul links, is shown to be a very attractive option for both ease of implementation and performance, unless high data rates are required. If this is the case, the base stations need to be involved in the encoding, i.e. at least part of the backhaul link should be used for sending the messages themselves not the corresponding codewords.
In [68], an optimization framework, for an adopted backhaul usage scheme, is proposed for the downlink of a large cellular system. A so-called joint transmission configuration matrix is defined: this specifies which antennas in the system serve which group of users. The backhaul to each base station is used to either carry quantized versions of the transmit signals computed centrally similarly to the central encoding with oblivious cells scheme in [20], except that a more realistic system model is assumed, alternatively, the back-haul is used to carry uncoded binary user data. The numbers of bits per user and per antenna are optimized, such that users served by the same set of antennas are allocated the same number of bits.
In [69], a more information-theoretic approach is taken and a two-cell setup is considered in which, in addition to links between the network and each base station, a finite-capacity link connects the two multi-antenna base stations: the authors view the thus formed channel as a superposition of an interference channel and a broadcast channel. The backhaul is used to share the data to be jointly transmitted: this could be in the form of the full messages, or of quantized versions of the signals to be transmitted, depend-ing on whether the data is comdepend-ing from the network directly or shared over
6.2 System Model 125 the link between the base stations. The schemes proposed lead to noncon-vex problems which make it difficult to find the rate and power parameters that come into play, as well as to characterize the optimum beamforming vectors to use, and the suboptimal scheme of maximum ratio transmission is resorted to.
In this chapter, our contributions are as follows:
• We also consider a setup in which the backhaul is between the network and each of the base stations, and focus on how to use this given backhaul to serve the users in the system. We focus on the two-cell problem.
• We specify a transmission scheme whereby superposition coding is used to transmit signals to each user: this allows us to formulate a continuum between full message sharing between base stations (net-work MIMO) and the conventional net(net-work with single serving base stations (IC); the data rate is in fact split between two distinct forms of data to be received by the users, a private form to be sent by the
‘serving’ base alone and a common form to be transmitted via multiple bases.
• We express the corresponding rate region in terms of the backhaul constraints and the beamforming vectors used to carry the different signals.
• We reduce finding the boundary of the aforementioned region to solv-ing a set of convex optimization problems. We compare the rates achieved in such a hybrid scheme to those obtained for network MIMO and the IC and illustrate the gains related to moderate sharing levels in certain realistic situations.
• We also adapt the “central encoding with oblivious cells” in [20] to the channel model and linear precoding transmission scheme we use to enable comparison with the proposed rate splitting approach.
6.2 System Model
The system considered is shown in Figure 6.1. In this preliminary study, we focus on a two transmitter two receiver setup. We assume a noiseless back-haul link of capacityCj between the central processor (CP) or the backbone network, and transmitter j, for j = 1,2: it will be used to transmit the messages for each user. We distinguish between different types of messages:
126 Chapter 6 Data Backhaul constrained Network MIMO
• private messages will be sent from the CP to only one of the transmit-ters, and
• shared or common messages, which are sent from the CP to both transmitters, and are consequently jointly transmitted. Note that this notion of a common message is different from that commonly used in the context of interference channels for example, as they do not correspond to messages to be decoded by both receivers, but rather to messages to be sent by both transmitters.
Thus for userk, the message raterk will be split acrossrk,p and rk,c, where rk,candrk,prefer to the common and the private rates for that user, respec-tively:
rk=rk,p+rk,c. (6.1)
Assumptions Full CSIT is assumed to be available at both transmitters, since we want to focus on the cost of sharing data. Chapter 4 focuses on the problem of CSIT sharing.
Notation In what follows, ¯k = mod (k,2) + 1, k = 1,2 and is used to denote theother transmitter/receiver depending on the context.
Central
Figure 6.1: Constrained backhaul setup.