In this study, the scaling laws of optimal training lengths were investigated for time-division duplexing massive multiple-input multiple-output systems. First, the generalized asymptotic achievable rate was derived by taking into account both uplink and downlink training. From the general form, the achievable rates of zero-forcing (ZF) and matched filter (MF) precoders are directly obtained by using the mean and variance of the effective channel. Then, we analyzed the rate gaps of ZF and MF with respect to uplink and downlink training, respectively. According to the analysis of rate gaps, it is shown that the achievable rates are more dominated by the uplink training than downlink training for both ZF and MF. The joint optimization problem for training lengths maximizing the spectral efficiency is formulated as a function of rate gaps. To study the scaling of optimal training lengths with the system parameters, we derived the optimal training lengths as a closed-form expression by using an approximation for the logarithm function. From the analysis, it is shown that the optimal training lengths decrease as the number of antennas increases, and increase as the coherence block length increases. In addition, the optimal training lengths increase as the transmit power increases for ZF, whereas it does not change for MF. Finally, we investigated the superior region for noncoherent detection (which means only statistical information is used for demodulation without downlink training) with the system parameters by comparing the spectral efficiency with and without downlink training.
Bibliographical noteFunding Information:
Manuscript received July 20, 2017; revised December 19, 2017 and March 31, 2018; accepted April 10, 2018. Date of publication April 17, 2018; date of current version August 13, 2018. This work was supported by the Institute for Information and Communications Technology Promotion Grant funded by the Korea government (MSIT) (2016-0-00181, Development on the core technologies of transmission, modulation, and coding with low-power and low-complexity for massive connectivity in the IoT environment). The review of this paper was coordinated by Dr. N.-D. Dao. This paper was presented in part at the IEEE International Conference on Communications, London, U.K., June 2015. (Corresponding author: Sooyong Choi.) T. Kim and K. Min are with the Samsung Electronics Company, Ltd., Suwon 16677, South Korea (e-mail:, firstname.lastname@example.org; minkyungsik@ yonsei.ac.kr).
All Science Journal Classification (ASJC) codes
- Automotive Engineering
- Aerospace Engineering
- Electrical and Electronic Engineering
- Applied Mathematics