In time division duplex(TDD)beamforming systems,the base station estimates the channel state information(CSI)at transmitter based on uplink pilots and then uses it to generate the beamforming vector in the downlink transmission.Because of the constraints of the TDD frame structure and the uplink pilot overhead,there inevitably exists CSI delay and channel estimation error between CSI estimation and downlink transmission channel,which would degrade system ergodic rate.In this paper,we propose a robust ergodic rate transmission scheme,in which the uplink pilot time interval(UPTI)of an active user is adaptively adjusted according to the changing channel conditions such as Doppler frequency shift,uplink pilot signal to noise ratio(SNR),to minimize the impact of CSI delay and channel estimation error on the ergodic rate of TDD beamforming systems.In order to get the optimal UPTI,we first derive the average post-processing SNR for TDD beamforming systems with channel estimation error and CSI delay.We then obtain the optimal UPTI,which maximizes the average post-processing SNR,given the normalized pilot overhead(the number of pilot symbols per data symbol).The numerical simulation results validate that the the proposed robust ergodic rate transmission scheme not only maximizes the average post-processing SNR but also maximizes the system ergodic rate.Moreover,the scheme can adapt well to the changing channel environments compared with the current fixed UPTI scheme.Especially our research is valuable for the uplink sounding reference signal design in long term evolution advanced(LTEAdvanced)system.
This paper considers a price-based power control problem in the cognitive radio networks(CRNs).The primary user(PU) can admit secondary users(SUs) to access if their interference powers are all under the interference power constraint. In order to access the spectrum, the SUs need to pay for their interference power.The PU first decides the price for each SU to maximize its revenue. Then, each SU controls its transmit power to maximize its revenue based on a non-cooperative game. The interaction between the PU and the SUs is modeled as a Stackelberg game. Using the backward induction, a revenue function of the PU is expressed as a non-convex function of the transmit power of the SUs. To find the optimal price for the PU, we rewrite the revenue maximization problem of the PU as a monotone optimization by variable substitution. Based on the monotone optimization, a novel price-based power control algorithm is proposed. Simulation results show the convergence and the effectiveness of the proposed algorithm compared to the non-uniform pricing algorithm.
