Int. J. Electron. Commun. (AEÜ) 66 (2012) 322–331 Contents lists available at SciVerse ScienceDirect International Journal of Electronics and Communications (AEÜ) j our na l ho mepage: www.elsevier.de/a eue Modeling MIMO channels using a class of complex recurrent neural network architectures Kandarpa Kumar Sarma ∗ , Abhijit Mitra Department of Electronics and Electrical Engineering (EEE), Indian Institute of Technology Guwahati (IITG), Guwahati 781039, Assam, India a r t i c l e i n f o Article history: Received 27 April 2011 Accepted 23 August 2011 Keywords: Multi Input Multi Output Estimation Artificial Neural Network Recurrent Neural Network Self Organizing Map a b s t r a c t Artificial Neural Network (ANN) as non-parametric pattern mapping tool with suitable modification can tackle time varying nature of Multiple Input Multiple Output (MIMO) wireless set-up while carrying out channel modeling and estimation. Modified ANNs with temporal characteristics, however, suffer from configuration complexities. The Recurrent Neural Network (RNN), having better time tracking capability, provides a viable alternative with certain challenges. The RNN as Complex Time Delay Fully Recurrent Neural Network (CTDFRNN) block can be combined at the output using time averaging and Self Orga- nization Map (SOM)-based optimization, yielding a new architectural framework. The CTDFRNN based designs are explored here and several such blocks are coupled together to form a cluster which generates certain diversity aspects that improves overall performance. A Modular Network SOM (MNSOM) archi- tecture which is regarded to have certain resemblance with biological computation with an inherent reinforced modular learning, is also proposed and formulated using CTDFRNN blocks for application in MIMO channel estimation. It is found that such architectures offer considerable amount of processing time saving than the conventional stochastic estimation. © 2011 Elsevier GmbH. All rights reserved. 1. Introduction Statistical and other methods of channel estimation are capable of properly tackling the Multiple Input Multiple Output (MIMO) wireless systems [1,2]. Soft-computational approaches, however, can be appended to these available methods for providing inno- vative solutions to channel estimation. One of the viable means of such innovative channel estimation is the use of the Artificial Neural Network (ANN)s [1]. ANNs have already received attention as an optional tool for equalization and other such applications in wireless communication. Some of the relevant literature in this regard is cited in [2–7]. The most preferable aspects of the ANN in these applications have been parallelism, adaptive processing, self- organization, universal approximation and ability of tackling highly nonlinear problems. Also, as the ANN can learn complex patterns, it can act as a reliable estimator and hence can be used for modeling MIMO channels. An ANN can be specially configured to provide an estimate of the channel which may help to mitigate some of the deficiencies of multi-user transmission [2]. The advantage of these schemes is that no pilot symbol bits are required to be inserted with the MIMO transmissions which can contribute towards ∗ Corresponding author. Tel.: +91 9401454994; fax: +91 3612700031. E-mail addresses: s.kandarpa@iitg.ernet.in, kandarpaks@gmail.com (K.K. Sarma), a.mitra@iitg.ernet.in (A. Mitra). preserving bandwidth and increasing spectral efficiency. The sys- tem can also be extended to symbol recovery in Orthogonal Frequency Division Multiplexing (OFDM) scheme and user detec- tion as part of high data rate communication using MIMO-OFDM arrangement. Such systems with their ability to learn are also in a better position to use transmitter side information (TSI), channel side information (CSI) and receiver side information (RSI) for design of adaptive communication methods. Such a work dealing with static and slowly varying MIMO channels has already been reported in [8]. Another related work [9] for MIMO-OFDM channel estima- tion uses a variable step-size recursive least-squares (RLS) method for nonlinear principle component analysis (PCA) to train a two- layered ANN for the purpose. However, all these works focus mainly on the training-learning aspect of the ANN and its capacity to deal with MIMO channel estimation with practically little/no consider- ation on time-varying characteristics of the wireless channels. Till now, no recorded efforts have been observed regarding expansion of the abilities of such architectures beyond the training-testing realm which includes certain architectural challenges. These chal- lenges include: (i) ensuring stability to the system by appending a feedback path along with the usual feedforward structure of ANN, (ii) retaining only the contextual portion of the informa- tion with the above structure and (iii) properly capturing the fast time-varying nature of the channels. Keeping these challenges in consideration, one appropriate alternative to the ANN approach is the Recurrent Neural Network (RNN), which has the capacity to deal 1434-8411/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2011.08.008