While the information theoretic studies corroborated the gains from MIMO systems, the possibility of exploiting these gains in practice remains a big challenge. In particular, in ad-hoc or distributed large scale wireless networks, nodes are often constrained in hardware complexity and size, which makes implementing multiple antenna systems highly impractical for many applications. For this purpose, an alternative approach for ex- ploiting the MIMO gains, through nodes cooperation, needs to be sought.
In fact, an important application for cooperation in next generation wireless networks is the formation of virtual MIMO systems through co- operation among single antenna devices. In this context, a number of single antenna devices can form virtual multiple antenna transmitters or receivers through cooperation, consequently, benefiting from the advan- tages of MIMO systems without the extra burden of having multiple an- tennas physically present on each transmitter or receiver. Thus, the basic idea of virtual MIMO is to rely on cooperation among mobile devices for benefiting from the widely acclaimed performance gains of MIMO systems. In Figure 1.3, we show an illustrative example of cooperation for virtual MIMO formation in a wireless network.
Similar to their single user MIMO counterparts discussed in the pre- vious subsection, an intensive amount of research has been dedicated to the information theoretic studies of virtual MIMO systems. For instance, the authors in [50] showed the interesting gains in terms of outage capac- ity resulting from the cooperation of two single antenna devices that are transmitting to a far away receiver in a Rayleigh fading channel. Further,
Figure 1.3: An illustrative example of a virtual MIMO system.
the work in [4, 5] considered cooperation among multiple single antenna transmitters as well as receivers in a broadcast channel. Different coop- erative scenarios were, thus, studied and the results showed the benefits of cooperation from a sum-rate perspective. It is important to also note that virtual MIMO gains are not only limited to rate gains. For example, forming virtual MIMO clusters in sensor networks can yield gains in terms of energy conservation [6].
Using a canonical coalitional game the work in [27, 28] studied fairness and cooperation gains in virtual MIMO systems. The model considered in [28] consists of a set of transmitter-receiver pairs, in a Gaussian inter- ference channel. The authors study the cooperation between the receivers under two coalitional game models: A TU model where the receivers com- municate through noise-free channels and jointly decode the received sig- nals, and an NTU model where the receivers cooperate by forming a linear multiuser detector. Further, the authors study the transmitters cooper- ation problem under perfect cooperation and partial decode and forward cooperation, while considering that the receivers have formed the grand coalition. The main interest was to study the properties of the grand coali- tions for the receivers and the transmitters. In the joint decoding game, it is shown that the game is superadditive and that the network can be seen as a single-input multiple-output (SIMO) MAC channel (when the trans- mitters do not cooperate). For this game, the authors in [27] show that
Virtual MIMO Systems
the core is non-empty and it contains all the imputations which lie on the SIMO-MAC capacity region. Further, it is proven that the Nash bargaining solution, and in particular, a proportional fair rate allocation lie in the core, and, hence, constitute suitable fair and stable allocations. For the linear multiuser detector game, the model is similar to the joint decoding game, with one major difference: Instead of jointly decoding the received signals, the receivers form linear multiuser detectors (MUD). The MUD coalitional game is inherently different from the joint decoding game since, in a MUD, the SINR ratio achieved by a user i in coalition S cannot be shared with the other users, and hence the game becomes an NTU game with the SINR representing the payoff of each player. In this NTU setting, the value v(S) of a coalition S becomes the set of SINR vectors that a coalition S can achieve. For this NTU game, the grand coalition is proven to be stable and sum-rate maximizing at high SINR regime using limiting conditions on the SINR expression.
Further, the authors consider the transmitters cooperation along with the receivers cooperation. In this case, the interference channel is mapped unto a virtual MIMO MAC channel. For maintaining a characteristic form, the authors consider a utility that captures the sum-rate under worst case interference. Using this and other assumptions, the authors show that in general the game has an empty core. Further, through [28, Th. 19], it is shown that the grand coalition is the optimal partition, from a total utility point of view. The authors conjecture that in some cases, the core can also be non-empty depending on the power and channel gains. However, no existence results for the core are provided in this game. Finally, the au- thors in [28] provide a discussion on the grand coalition and its feasibility when the transmitters employ a partial decode and forward cooperation. In summary, the work in [27, 28] provides valuable insights and results per- taining to fairness and to the cooperation gains when performing virtual MIMO systems. However, this work does not consider any cost for virtual MIMO formation (whether it be at the transmitters or receivers side) nor does it propose any strategies for forming coalitions.
Although the gains from virtual MIMO are quite well studied and es- tablished, implementing distributed cooperation algorithms that allow to exploit these advantages in a practical wireless network is challenging and desirable. In this regards, it is of interest to study a model for distributed virtual MIMO formation which accounts for both benefits and costs for co- operation. In particular, the key issues that need to be tackled in such a scenario are (among many others)
1. What are the benefits and costs from cooperation?
2. Given the benefit-cost tradeoff, which groups of users must cooper- ate?
3. How can this cooperation be performed in a distributed manner? 4. How does the cooperative behavior of the users affect the network
structure?
5. Can the network structure adapt to environmental changes such as slow mobility?
In order to answer these questions, and deploy distributed coopera- tion for virtual MIMO formation in next generation wireless networks, one needs to tackle and overcome many challenges. In this dissertation, we study the problem of virtual MIMO formation among the transmitters in the uplink of a wireless network using the analytical framework of coalition formation games. The main contributions of this work are summarized in Section 8 and the details are found in Paper B.
4
Spectrum Sensing in Cognitive Radio Networks
In this section, we introduce the basic concepts of cognitive radio networks and, then, we identify the key challenges for spectrum sensing as well as the design issues of performing joint spectrum sensing and access in cognitive networks.