# A Flexible FPGA-Based Channel Emulator for Non-Stationary MIMO Fading Channels
2 The Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space, College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China; [EMAIL_ADDRESS] (Correspondence: [EMAIL_ADDRESS] 2 The Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space, College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China; [EMAIL_ADDRESS] 2 The Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space, College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China; zhongwz@nuaa. There are very limited non-stationary channel emulators reported in the literatures [19; 20; 21; 22; 23; 24; 25; 26; 27]. A hardware emulator for the discrete-time triply selective fading channel was developed in [19]. The channel coefficients were calculated by software dynamically, which cannot support real-time updating. The authors in [20; 21] proposed an improved sum-of-sinusoid (SoS) method to generate channel fading, and implemented it into a \(2\times 2\) non-stationary MIMO channel emulator. A \(4\times 4\) MIMO channel emulator was designed in [22], but the authors did not give the details of implementation. In [23; 24], two specific MIMO channel emulators for high speed WLAN 802.ac and LTE-A channels were developed, respectively. In [25], the authors divided the non-stationary channel into several stationary channel segments and adopted the traditional stationary channel emulation method. The authors in [26] designed a channel emulator based on software defined radios (SDR) platform, but the emulator can only be applied to vehicular communications. To the best of our knowledge, the aforementioned channel emulators still adopted traditional stationary channel models and considered the non-stationary aspect by updating parameters periodically. However, we have found that the output fading phases of this kind of method are not accurate, which leads to the output Doppler power spectrum density (DPSD) not fitting well with the theoretical ones [28]. To overcome this shortcoming, an improved 3D non-stationary geometry-based stochastic model (GBSM) was proposed in [27] and implemented in a \(2\times 2\) MIMO channel emulator. However, the developed hardware was only suitable for the corresponding channel model and the structure was not general and flexible. This paper proposes a discrete non-stationary channel model with accurate channel fading and phase. The channel parameters such as power, delay, and Doppler frequency are all time-variant in order to take the non-stationarity into account. Furthermore, a flexible hardware architecture is proposed and implemented in a single FPGA chip. Finally, we validate the correctness of the proposed channel model as well as the hardware emulator. The major contributions are summarized as follows. * Based on the improved GBSM with the accurate channel fading phase and Doppler frequency in [27], this paper proposes a discrete non-stationary MIMO channel model, which is suitable to implement on the FPGA-based hardware platforms. Meanwhile, a flexible hardware architecture tailored for the proposed model is developed, in which the channel size and parameters can easily be reconfigured. * An improved emulation method of channel fading, namely, sum-of-frequency-modulated-signals (SoFM), is employed to guarantee the accurate channel fading and phase. In addition, the architectures of other key modules, i.e., the delay module, fading generation module, and interpolator module, are developed and implemented on a single Xilinx XC7 VX690T FPGA. * For the developed channel emulator, the output statistical properties, i.e., the probability density function (PDF), cross-correlation function (CCF), and DPSD are tested and verified by the theoretical results. The power delay profile (PDP) is also validated by the measurement data. The rest of this paper is organized as follows. In Section 2, a discrete non-stationary MIMO channel model is briefly introduced.