On the Impact of Quantized Channel Direction Feedback in Multiple-Antenna Wiretap Channels

In this work, we examine the impact of quantized channel direction feedback on the achievable secrecy rate of multiple-antenna wiretap channels. To guarantee secrecy without knowledge of the eavesdropper's channel, we consider the transmission scheme proposed by Goel and Negi where artificial noise (AN) is imposed in the null space of the legitimate receiver's channel to disrupt the eavesdropper's reception. When perfect knowledge of the legitimate receiver's channel direction information (CDI) is available at the transmitter, the secrecy rate can be made arbitrarily large by increasing the transmission power. However, perfect CDI is difficult to achieve in practice due to rate-limitations on the feedback channel. When only quantized CDI is available at the transmitter, the AN that is only intended to disrupt the eavesdropper's reception may leak into the legitimate receiver's channel, causing significant loss in secrecy rate. In fact, we show that the achievable secrecy rate under quantized CDI is bounded by a constant even as the transmission power increases. To guarantee a constant rate loss compared to the perfect CDI case, we show that the number of feedback bits must scale at least logarithmically with the transmission power. These theoretical claims are verified by computer simulations.