Performance analysis and algorithm design for distributed transmit beamforming

Wireless sensor networks has been one of the major research topics in recent years because of its great potential for a wide range of applications. In some application scenarios, sensor nodes intend to report the sensing data to a far-field destination, which cannot be realized by traditional transmission techniques. Due to the energy limitations and the hardware constraints of sensor nodes, distributed transmit beamforming is considered as an attractive candidate for long-range communications in such scenarios as it can reduce energy requirement of each sensor node and extend the communication range. However, unlike conventional beamforming, which is performed by a centralized antenna array, distributed beamforming is performed by a virtual antenna array composed of randomly located sensor nodes, each of which has an independent oscillator. Sensor nodes have to coordinate with each other and adjust their transmitting signals to collaboratively act as a distributed beamformer. The most crucial problem of realizing distributed beamforming is to achieve carrier phase alignment at the destination. This thesis will investigate distributed beamforming from both theoretical and practical aspects. First, the bit error ratio performance of distributed beamforming with phase errors is analyzed, which is a key metric to measure the system performance in practice. We derive two distinct expressions to approximate the error probability over Rayleigh fading channels corresponding to small numbers of nodes and large numbers of nodes respectively. The accuracy of both expressions is demonstrated by simulation results. The impact of phase errors on the system performance is examined for various numbers of nodes and different levels of transmit power. Second, a novel iterative algorithm is proposed to achieve carrier phase alignment at the destination in static channels, which only requires one-bit feedback from the destination. This algorithm is obtained by combining two novel schemes, both of which can greatly improve the convergence speed of phase alignment. The advantages in the convergence speed are obtained by exploiting the feedback information more efficiently compared to existing solutions. Third, the proposed phase alignment algorithm is modified to track time-varying channels. The modified algorithm has the ability to detect channel amplitude and phase changes that arise over time due to motion of the sensors or the destination. The algorithm can adjust key parameters adaptively according to the changes, which makes it more robust in practical implementation