How much training is needed against smart jamming?

This paper studies training-based transmissions over multiple-input multiple-output (MIMO) fading channels in the presence of jamming. Each transmission block consists of a training phase and a data transmission phase. From an information-theoretic viewpoint, we formulate a max-min problem on the energy allocation between the two phases. The legitimate user of the channel aims to design a robust energy allocation strategy which maximizes its data rate under the worst case scenario assuming that the jammer is able to optimize its jamming energy allocation between the training phase and the data transmission phase. For a fixed training length, we derive an analytical solution to the robust energy allocation. When the training length is allowed to vary, we show that a robust design of the training length is generally larger than the number of transmit antennas and approaches half of the block length at low signal to jamming and noise ratio (SJNR). Our numerical results demonstrate a potential of 20% - 40% performance gain by using the proposed robust designs in various scenarios.