Physical layer secrecy for MISO channel with quantized feedback

摘要

This paper studies the beamforming design of a multiple-input single-output system with eavesdropping, when a quantized channel feedback is available. We consider two basic cases a) the beamforming vector belongs to the quantization codebook and b) the beamforming design is not limited to the quantization codebook. For the first case, we design two beamforming schemes that incorporate a feedback channel from the eavesdropper, which provides the direction of its physical channel or the direction of its null-space. For the case where the codebook constraint is relaxed, we design an optimal beamformer that requires feedback from both receivers as well as a scheme that transmits towards the quantized null-space of the eavesdropper's channel. The ergodic secrecy rate is derived in closed-form and we show that all schemes suffer from a secrecy rate floor for a constant-size feedback. Simplified asymptotic expressions are proposed and the scaling laws of the feedback, which ensure constant secrecy losses, are provided.