Comparison of Diversity Combining Techniques for MIMO Systems Luu Pham Tuyen Binh Dinh Operation and Maintenance Center (OMC) Vietnam Posts and Telecommunications (VNPT) Email: lptuyen@gmail.com Vo Nguyen Quoc Bao Telecom. Dept. Posts and Telecom. Inst. of Tech. (PTIT), Vietnam Email: baovnq@ptithcm.edu.vn Abstract—Several diversity combining techniques have been proposed for multiple-input multiple-output (MIMO) systems, but only isolated performance comparisons have been reported. In this paper, we aim at comparing three MIMO schemes using selection combining (SC), maximal ratio combining (MRC) and switch-and-stay combining (SSC). It is analytically demonstrated that all the systems achieve full diversity gain with different coding gain. Besides, the performance gap between SC and MRC approaches to the limit and tends to increase linearly proportional to the number of transmit antennas. In case of SSC, the loss between SSC and SC, as well as between SSC and MRC, is not bounded as increasing signal-to-noise ratio (SNR). I. I NTRODUCTION Multiple-input multiple-output (MIMO) is a wireless system that uses multiple antenna elements at both ends of a wireless communication link. For the same transmission power, MIMO technique can be used for increasing system capacity and diversity gain, i.e. reliability of a wireless link, as compared to a conventional single-input single-output (SISO) system [1]. The revolutionary idea behind MIMO technology is that contrary to SISO where fading is treated as one of the largest obstacles, fading in MIMO is viewed as an opportunity by using appropriate combining and decoding technique at the receivers. At present, MIMO has been adopted in some industry wireless standards, e.g. WiFi IEEE 802.11n, and the proposed for 3GPP Long Term Evolution/Long Term Evolution Advanced, 3GPP2 Ultra Mobile Broadband [2]. The main difficulty in MIMO practical implementation is its high complexity relative to the use of separate radio frequency (RF) chains for each employed antenna [3]. While antenna elements are usually cheap and demand simple manufacture technique, a receive RF chain normally comprising a low noise amplifier, frequency down-converters, analog-to-digital converters and several filters is a key factor which increases implementation cost significantly. Moreover, employing many RF chains, especially on mobile devices with limited size and battery capacity, results in difficult installation and/or more power consumption. The use of antenna selection (AS) technique in MIMO systems has recently gained high attention [3]–[8]. The ad- vantage of this technique is that it can mitigate the hardware complexity while retaining diversity gain offered by MIMO technique. In particular, by choosing only the best signals for decoding, the number of RF chains needed are smaller than the number of available antennas [3]–[5]. The AS technique can be applied in MIMO at the transmitters, receivers, or both, corresponding to be called as TAS (Transmitter AS), RAS (Receiver AS) or T-RAS (Transmitter-Receiver AS). Among theses, RAS is the most practical one due to its simplicity, while TAS and T-RAS require channel state information (CSI) known at the transmitters. Besides, they only work well when the channel varies slowly. In designing AS-based MIMO net- works, two common AS criteria have been proposed including maximizing system capacity and maximizing system quality. A nice overview for AS technique in MIMO system can be found in [3], [4], [9]. So far, many research works involving the performance derivation of MIMO have been reported in the literature, e.g. see [10]–[13]. However, to our best knowledge, the perfor- mance comparison of MIMO systems using maximal ratio combining (MRC), selection combining (SC) and switch-and- stay combining (SSC) in terms of diversity gain and coding gain has not been considered and demands contributions. In this paper, motivated by all of the above, we study the system performance loss of MIMO systems employing either SC or SSC instead of MRC. We also investigate the impact of the number of transmit antennas on the system performance. Some discussions in case of varying the number of receive antennas are also represented. II. SYSTEM MODEL In this paper, we consider a MIMO N × 2 system using N transmit antennas and two receive antennas, as shown in Fig. 1. The received signal vector on the ith receive antenna is written as y i =  ρ N Xh i + w i . (1) where ρ is the average signal-to-noise ratio (SNR) on each receive antenna, i ∈{1, 2} is the receive antenna index. y i and w i are L × 1 column vectors representing the received signal and AWGN noise on the ith receive antenna, respectively; X is a L × N matrix representing a transmitted space-time codeword spanning N transmit antennas and L time instants; h i =[h i1 ,h i2 ,...,h iN ] T contains the channel coefficients between N transmit antennas and the ith receive antenna. 2011 17th Asia-Pacific Conference on Communications (APCC) 2nd – 5th October 2011 | Sutera Harbour Resort, Kota Kinabalu, Sabah, Malaysia 978-1-4577-0390-4/11/$26.00 ©2011 IEEE 295