Optimizing Training-Based Transmission Against Smart Jamming

We consider 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 study the optimal energy allocation between the two phases for both the legitimate user of the channel and the jammer. For a fixed jamming strategy, we derive a closed-form solution of the optimal transmit energy allocation for the legitimate user and show that the optimal training length is equal to the number of transmit antennas. On the other hand, if the jammer has optimized its strategy, the best choice for the training length is shown to be larger than the number of transmit antennas and approaches half of the block length at low signal-to-jamming-and-noise ratio (SJNR). From the jammer's perspective, we derive closed-form solutions of the optimal jamming energy allocation. Numerical results demonstrate 30%-50% performance gains by using optimal designs in various scenarios. We also model the energy allocation problem as a zero-sum game and prove the existence and uniqueness of the Nash equilibrium when the training length is fixed. Furthermore, we extend our analysis to the case where the channel state information (CSI) is available at the transmitter. We show that many results found for systems with no transmitter CSI are also valid for systems with full transmitter CSI.