Short-Packet Communications with Multiple Antennas: Transmit Diversity, Spatial Multiplexing, and Channel Estimation Overhead

We present finite-blocklength upper and lower bounds on the maximum coding rate achievable over a multiple-antenna Rayleigh block-fading channel under the assumption that neither the transmitter nor the receiver have a priori knowledge of the channel realizations. Numerical evidence suggests that the bounds delimit tightly the maximum coding rate already for short blocklengths (packets of 168 channel uses). The bounds allow us to estimate the number of transmit antennas and the degree of time-frequency diversity that trade off optimally the rate gains resulting from an increase in the number of independent time-frequency-spatial diversity branches against the corresponding increase in channel estimation overhead. This work was supported in part by the Swedish Research Council under grant 2012-4571, by the National Science Foundation CAREER award under grant agreement CCF-12-53205, by the European Communitys Sevenths Framework Programme FP7/20072013 under Grant 333680, by the Ministerio de Economa y Competitividad of Spain under Grant TEC2013-41718-R, by Consoliderlngenio 2010 CSD2008-00010 COMONSENS, and by the Comunidad de Madrid under Grant S2013/ICE-2845. The simulations were performed in part on resources at Chalmers Centre for Computational Science and Engineering (C3SE) provided by the Swedish National Infrastructure for Computing (SNIC). The material of this paper was presented in part at the 2012 IEEE Information Theory Workshop, Lausanne, Switzerland, and in part at the 2014 IEEE International Symposium on Wireless Communication Systems, Barcelona, Spain. G. Durisi and W. Yang are with the Department of Signals and Systems, Chalmers University of Technology, 41296, Gothenburg, Sweden (e-mail: {durisi,ywei}@chalmers.se). T. Koch is with the Signal Theory and Communications Department, Universidad Carlos III de Madrid, 28911, Leganés, Spain (e-mail: [email protected]). J. Östman is with the Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China (email: [email protected]) Y. Polyanskiy is with the Department of Electrical Engineering and Computer Science, MIT, Cambridge, MA, 02139 USA (e-mail: [email protected]). December 22, 2014 DRAFT