| The explosive demand on wireless access has motivated the fast-growing re-searches on seeking new techniques that are high throughput, energy efficient and more flexible. In general, fading and interference are two major obstacles for realiz-ing practical wireless communication. Of all the current techniques, spatial diversity is arguably the most promising tool for reliable communication in the presence of fading and interference. Traditionally, multiple-input and multiple-output (MIMO) technique is the primary method for realizing spatial diversity by mounting multiple antennas both at the transmitter and the receiver. According to the practical sys-tem configuration, while it may be possible for the base station to install multiple antennas, it is prohibitively expensive for most mobile terminals to do so due to size, complexity and cost limitations. Then one possible way to reap the spatial diversity beyond these limitations is through cooperation.Cooperative communication technique, where spatially separated nodes are al-lowed to work collaboratively to form a virtual MIMO system, serves as an appealing alternative to the conventional MIMO techniques for its great potential. The basic idea is quite intuitive, where the information sent by the source can be overheard by the distributed relay nodes. By allowing cooperation among relay nodes, the destination can receive multiple replicas of the original information, which signifi-cantly improves the reliability and the energy efficiency of the network. To reveal the performance limits of such systems, extensive information-theoretic analysis arc carried out under different cooperation schemes. While the information-theoretic analysis can be used to assess different cooperative architectures, it may not be able to reflect the performance achieved by actual transmission systems, since in practical environment, realizing these potential gains may give rise to unbounded complexity and latency. As a result, designing cooperative communication systems by taking practical constraints into consideration is a great challenge and of great significance for engineering implementation.Collaborative bcamforming is a new emerging scheme of cooperative commu-nication where synchronized relay nodes can work collaboratively to form a beam with the help of AF protocol. The beam is guided towards the intended receiver to enhance the received signal, suppress the undesired interference and increase the diversity order. To achieve collaborative beamforming, CSI is generally needed both at the transmitter and at the receiver. However, the wireless media is inher-ently random that subjects to time/frequency/space selectivity. Hence, obtaining the perfect CSI is a great challenge. It is normally assumed that CSI at the re-ceiver side can be acquired by the training sequences. CSI at the transmitter side can be obtained through feedback from receiver (e.g., in sufficiently slow varying channel) or by exploiting the uplink-downlink reciprocity (whenever possible, e.g., in time division duplex system), therefore it is much more difficult. With respect to the different assumptions on the degrees of the CSI, the existing techniques can be roughly divided into two categories:1) techniques with no CSI at transmitter (e.g., Space-Time Coding), and2) techniques with full CSI at the transmitter (e.g., Beamforming). However, rather than being too pessimistic or optimistic, it is more realistic to assume the knowledge of CSI is imperfect (or partial). Hence, for the system with no CSI at the transmitter, we can use the partial CSI to improve the system performance. On the other hand, for the techniques requiring full CSI at the transmitter, we can take the impcrfectness into consideration and make it robust to the mismatch of the CSI.As mentioned above, the CSI mismatch is inevitable in practical wireless com-munication environment, how to make the system robust to parameter mismatch is a big challenge. What makes things more complicated is that, there arc multiple sources of uncertainties, such as low training SNR, quantization, limited feedback bits, and feedback delay. Base on the different hypothesis on the distribution of the CSI mismatches, there are two main robust design criteria:1) worst-case analysis technique and2) probability constrained optimization approach. In general, the worst-case analysis design can provide guaranteed robustness against bounded CSI uncertainties without knowing their probability distribution. However, this design tends to be over conservative since worst-case rarely occurs and it thus leads to unnecessary performance loss. Besides, the assumption of bounded CSI is some-what impractical regarding the training process of obtaining the CSI. To overcome these shortcomings, stochastic model can be employed to characterize the mismatch in CSI. The QoS constraint can be allocated into the predefined confidence inter-val instead of setting to constant value. Yet, the latter design criterion needs the knowledge of the distribution of the CSI mismatch and is much more complicated compared to the former one. The main design objective of both criteria is to make it less conservative for given uncertainty model. Historically, these problems often resorted to some convex optimization approaches. The original optimization prob-lem is usually non-convex, however, after some manipulation on the optimization variables, objective function as well as the constraint, it can be converted into con-vex form. It is widely recognized that, once the problem is formulated into convex form, it can be effectively solved even if closed-form solution may not exist (e.g., by Interior-Point-Method).Moreover, most of the existing researches on collaborative beamforming are based on two-hop relay model. We consider a new three-hop multi-relay beamform-ing network where joint optimization on two clusters of relay nodes are carried out. In general, the main contributions of our work can be summarized as follows:1. In the outage probability constrained downlink collaborative beamforming net-work, we consider the CSI of the second-hop is imperfect with Gaussian un-certainties and the equivalent condition for the QoS constraint is derived. As the original optimization problem is non-convex, by carrying out relaxation on the constraint, a convex optimization based sub-optimal solution is pro-posed. Then a near-optimal solution is also presented with the help of an one-dimension search and convex optimization.2. We consider the transmitter-receiver collaborative-relay beamforming in a three-hop relay network. We find that the original optimization problem is non-convex and thus intractable for conventional optimization methods. In-spired by the development on heuristic optimization method, we employ a simulated annealing based method to find the stochastic optimal solution. Nevertheless, heuristic algorithms are computational demanding and are cur-rently impractical for real-time application. Then an efficient closed-form sub-optimal solution is also proposed.3. The robust peer-to-peer collaborative-relay beamforming with ellipsoidal CSI uncertainties is proposed, where the CSIs of both the first-and second-hop are imperfect. The upper-bound for the transmit power and the equivalent condition for the worst-case QoS constraint are derived. Subsequently, the optimization problem is resorted to an semi-definite programming with the re-laxation on the optimization variable thus can be optimally solved by interior-point-method. |
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