Wireless Pers Commun (2014) 75:1141–1154 DOI 10.1007/s11277-013-1412-5 A Simple Analytical Design Approach to Space Time Trellis Codes Sharbari Banerjee · Monika Agrawal Published online: 20 September 2013 © Springer Science+Business Media New York 2013 Abstract The space time trellis code (STTC) is a combined design of error-control coding, modulation and transmit-receive diversity that improves data rate and error performance in a wireless channel without any loss in spectral efficiency. It can either be described by a graphical representation, or, in terms of closed analytical forms that lead to a more tractable generator matrix description. However, the main difficulty in generating best code is the long search duration which makes both trellis implementation and generator matrix description difficult, thereby, limiting the use of STTC in wireless links. Since an exhaustive search over all the matrix entries turns out to be impractical if the number of transmitter, encoder states and/or constellation size is very high, some literature provide techniques to reduce the search complexity. Some of them are sub-optimal, some are good. However, none reports any straightforward rule of thumb to design the generator matrix. In this paper, we propose two very simple rules to construct the generator matrix for designing STTC with any arbitrary number of transmit antennas and any memory-less constellation. Mathematical justification behind the rules has been presented. It has been shown that the simplicity of proposed rules reduces the code search complexity to a large extent along with a similar or better coding gain compared to those presented in previous literature. In addition, the STTCs obtained from proposed rules perform no worse than the codes given in previous literature in terms of error rate. Keywords Multiple input multiple output system · Space time coding · Space time trellis code · Generator matrix · Rank and determinant criteria · Coding gain S. Banerjee (B ) · M. Agrawal Centre for Applied Research in Electronics, Indian Institute of Technology Delhi, New Delhi 110016, India e-mail: sharba4u@gmail.com M. Agrawal e-mail: moaggarwal@yahoo.co.in 123