Optimized time splitting to maximize the lower bound of rate with channel estimation in an interference alignment based network

In this paper, for an interference alignment (IA) based network, a time splitting scheme for transmitting training and data symbols is optimized. The time allocated for transmitting training symbol will affect the precision of channel estimation (CE) and thus the achievable rate as well as the duration for data symbol transmission. With the least square (LS) and relaxed minimum mean square error (RMMSE) CE algorithm, the lower bounds of achievable rate are carefully derived, respectively. Then we formulate an optimization problem to maximize the lower bounds of achievable rate by optimizing the time splitting factor (TSF). The existence of optimum is first proved. Then, regarding the complexity of solution, Taylor expansion is adopted to find the approximated optimal TSF. Numerical results are presented to show the optimal TSF can achieve larger lower bound of achievable rate over other fixed TSFs due to its adaptivity to the channel characteristics and its statistics of CE errors. Numerical results also validate that the approximation just brings out some small and acceptable errors on the system rate. In addition, RMMSE CE algorithm shows better performance than LS CE because RMMSE considers noise statistics as modification.