Communication-Efficient Decentralized Subspace Estimation

Machine learning techniques have been widely used in communication systems because of their superior performance. Among them, the classical machine learning algorithm Principal Component Analysis (PCA) aims to estimate the principal subspace of the received signals, and thus is also known as subspace estimation. It is often used in Direction of Arrival (DoA) tasks. Recently, the widespread deployment of networks has motivated researchers to solve the problem of subspace estimation in decentralized settings. An important concern in the design of decentralized algorithms is the communication complexity, because communication consumes much energy, while the sensors in the network are generally energy-limited. Specifically, communication complexity refers to the minimum amount of transmitted variables to obtain an estimate with an error smaller than
$\varepsilon$
. For existing algorithms, this complexity is
$O(\log ^{2}(1/\varepsilon))$
. In this paper, we improve this complexity to be
$O(\log (1/\varepsilon))$
by designing a new algorithm named Decentralized Subspace Estimation (DSE). Such improvement is achieved by using the gradient tracking technique. We theoretically analyze the influence of the network connectivity and the eigen-gap of the data on communication complexity. In addition, we use DSE to solve the DoA estimation problem. Experiments verify the effectiveness of the algorithm and the correctness of the theoretical result.