On optimal training in massive MIMO systems with insufficient pilots

This paper studies the optimization of pilot training signals in Massive MIMO systems with insufficient pilot length. We aim at finding the optimal pilot design and pilot length that maximize the Spectral Efficiency (SE) of the system. To achieve that, we firstly derive an approximation of average achievable capacity, which is related to channel estimation error and pilot signals. Then some analysis and discussions on finding the optimal non-orthogonal pilot design are presented in order to maximize average sum SE. Since previous research on Massive MIMO systems with pilot training mainly focus on orthogonal pilots, in this paper we give a design criterion of non-orthogonal pilots, and relate the system SE as a function of pilot length. Simulation results show the gap between simulation results and our analytical results. Meanwhile, the performance of uplink SE with orthogonal and non-orthogonal pilots is shown, where for insufficient block length, non-orthogonal pilots could lead to higher SE than the orthogonal pilots. Our analysis and results suggest that choosing non-orthogonal pilots can get a better performance than orthogonal pilots in Massive MIMO systems.

[1]  Thomas L. Marzetta,et al.  Inter-Cell Interference in Noncooperative TDD Large Scale Antenna Systems , 2013, IEEE Journal on Selected Areas in Communications.

[2]  Thomas L. Marzetta,et al.  Performance of pilot reuse in multi-cell Massive MIMO , 2015, 2015 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom).

[3]  Pan Cao,et al.  Achievable Rate Performance of TDD Multi-cell Massive MIMO with Non-Orthogonal Pilots , 2016, WSA.

[4]  Thomas L. Marzetta,et al.  Pilot Contamination and Precoding in Multi-Cell TDD Systems , 2009, IEEE Transactions on Wireless Communications.

[5]  Thomas L. Marzetta,et al.  Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas , 2010, IEEE Transactions on Wireless Communications.

[6]  Yang Li,et al.  A non-asymptotic throughput for massive MIMO cellular uplink with pilot reuse , 2012, 2012 IEEE Global Communications Conference (GLOBECOM).

[7]  Qian Xu,et al.  On Design of Non-Orthogonal Pilot Signals for a Multi-Cell Massive MIMO System , 2015, IEEE Wireless Communications Letters.

[8]  Bhaskar D. Rao,et al.  The Effect of Imperfect Channel Estimation on the Performance of Maximum Ratio Combining in the Presence of Cochannel Interference , 2006, IEEE Transactions on Vehicular Technology.

[9]  Emil Björnson,et al.  Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated? , 2014, IEEE Transactions on Wireless Communications.

[10]  Timothy N. Davidson,et al.  Flexible codebook design for limited feedback downlink systems via smooth optimization on the Grassmannian manifold , 2012, 2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).

[11]  Thomas L. Marzetta,et al.  Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading , 2000, IEEE Trans. Inf. Theory.

[12]  N. J. A. Sloane,et al.  Packing Lines, Planes, etc.: Packings in Grassmannian Spaces , 1996, Exp. Math..

[13]  Peter J. Smith,et al.  Performance of Synchronized and Unsynchronized Pilots in Finite Massive MIMO Systems , 2015, IEEE Transactions on Wireless Communications.