A Generic Validation Framework for Wideband MIMO Channel Models Yu Zhang *† , Jianhua Zhang † , Guangyi Liu ‡ , Xinying Gao † and Ping Zhang * * Key Lab. of Universal Wireless Communications (Beijing Univ. of Posts and Telecom.), Ministry of Education Email: zhangyu@mail.wtilabs.cn, pzhang@bupt.edu.cn † Wireless Technology Innovation Institute, Beijing Univ. of Posts and Telecom., P.O. Box #92, China, 100876 Email: jhzhang@bupt.edu.cn, gaoxinying@mail.wtilabs.cn ‡ Research Institute of China Mobile, Beijing, China, 100053 Email: liuguangyi@chinamobile.com Abstract—In this paper, a generic framework for validating wideband MIMO channel models based on channel measurement results is proposed. The framework is formulated as a series of continuous functions (metrics) and a definition of distance of continuous function space (degree of approximation). The metrics characterize the MIMO channel from different perspectives, and the distance provides a quantiative measure of the degree of approximation for the specified model. Several fundamental metrics which reflect the spatial multiplexing gain, diversity capa- bility, time and frequency variability, are derived for exploring the frequency-selective fading property. Based on an extensive measurement campaign at 5.25 GHz, the propagation channel is reconstructed by a WINNER-like model. The metrics are calculated from both the model generated channel realizations and the measured impulse response as a demonstration. The proposed framework can be applied to compare different channel models and to evaluate the simplified version of channel models. I. I NTRODUCTION Multiple-Input Multiple-Output (MIMO) systems are promising candidate for future wireless communication sys- tems. Wideband wireless transmission is also required to sup- port the growing need for higher data rate access demanded by future mobile applications and services. It is well known that channel model has a crucial impact on the design, simulation, and deployment of new communication systems. Therefore, the realistic wideband MIMO channel model is an important prerequisite. In general, deterministic channel models may lose some generality because it focus on regenerate the physical propagation charateristics as accurately as possible. At the meanwhile, the statistical models may describe the realistic radio environment behavior by introducing many random variables which lead to a heavy computational complexity. As a consequence, it is a common sense that a “good” channel model is a tradeoff among reality, generality and com- plexity. This raises question like “How to define the goodness of a MIMO channel model?” Many researches on this topic have been reported. In [1], some different metrics has been This work was supported in part by the National 863 High Technology Re- search and Development Program of China under Grant No. 2006AA01Z258, and by the 111 Project under Grant No. B07005, and by Research Institute of China Mobile. proposed to compare narrow band analytical MIMO channel models including the Kronecker model [2], the Weichselberger model [3], and the virtual channel representation [4]. Spatial- temporal correlation properties of the 3GPP Spatial Channel Model (SCM) [5] and the Kronecker model are compared in [6]. Properties of three geometry based stochastic models: SCM, SCME [7], and WINNER channel models [8], [9] are compared and summarized in [10]. The above comparisons of channel models can be divided into three categories: a) analytical model validation based on measurements; b) theo- retical analysis on properties of analytical model and physical model; and c) comparison on architecture of physical models. The validation of the measurement-based physical models has not been reported yet. The main contribution of this paper is the generic validation framework for wideband MIMO channel models based on measurement results. Some useful metrics are also developed to provide different aspect of views on the wideband MIMO channel model. The proposed framework and metrics are verified with the measurement results. The outline of the remaining of the paper is as follows. The channel model validation framework is explained in Sec. II. Derivation of various metrics for the wideband MIMO channel validation is presented in Sec. III. The measurement campaign which the result is used for demonstrating the framework and channel reconstruction is described in Sec. IV. The comparison analysis and conclusion are showned in Sec. V and Sec. VI, respectively. The following notations will be used throughout this paper: (·) H stands for matrix Hermitian transposition; (·) * stands for complex conjugation; ‖·‖ F denotes the Frobenius norm; E x {·} denotes the expectation operator over x; R - stands for the set of all non-negative real numbers. II. MEASUREMENT- BASED VALIDATION FRAMEWORK FOR CHANNEL MODELS A. Signal Model Considering an N R × N T MIMO channel with bandwidth B, we denote the channel impulse response (CIR) at time t to 978-1-4244-1645-5/08/$25.00 ©2008 IEEE 330