hardware implementation of a mimo channel emulator

HARDWARE IMPLEMENTATION OF A MIMO CHANNEL EMULATOR Tran Thi Thao Nguyen, Nguyen Viet Ha, Yuhei Nagao, Leonardo Lanante, Hiroshi Ochi Dept. of Computer Science and Electronics, Kyushu Institute of Technology, Japan

E-mail addresses: tttnguyen, nagao, leonardo, [email protected], [email protected]

Abstract In this paper, we present an effective hardware implementation of channel emulator that models a wireless channel in realistic scenarios. While the currently paper provides the channel models to be used for the High Throughput Task Group IEEE 802.11 TGn, this system can be extended to incorporate other channel models, such as 802.11ac, LTE and a variety of future wireless communication models. Contrarily to commercial emulators, which are usually very expensive and not quite flexible, we have developed an FPGA-based solution that is cheap, flexible and reconfigurable. The main contribution of the paper is design and implement of the MIMO channel components including AWGN generator, Doppler, Antenna correlation, Rician fading and Interpolation on hardware exploiting FPGA-based DSP Development Kit and Synphony HLS® software from Synopsys®. Keywords: MIMO channel emulator, TGn, hardware implementation

1. Introduction The quality of the MIMO system depends on channels where the signal is transmitted from the transmitter to the receiver. Unlike wired channels are stable and predictable, radio channels are completely random and not easy to analyze. Signals are transmitted, via radio channels, hampered by buildings, mountains, trees are reflected, scattering, diffraction. These phenomena are referred to as fading. As a result, in the receiver, we collected a lot of different versions of the transmitted signal. This affects the quality of radio communication systems. Thus the master of the traditional features of the wireless channel is a basic requirement to be able to choose a suitable way including the structure of the system, the size of the components and optimize the parameters of the system. In this document we propose a set of channel models to indoor MIMO WLAN systems. The model can be used for both 2 GHz and 5 GHz frequency bands, since the experimental data and published results for both bands were used in developing the model.

The paper is organized as follows. In Section 2 we describe MIMO WLAN models. Design of MIMO channel emulator on hardware with Synopsys program is shown in Section 3. Section 4 presents the results of synthesis on FPGA board, and with Section 5 we conclude.

2. MIMO channel modeling: TGn channel models For indoor wireless channels, the typical fading effect scenario involves human-based motion. These fading effects can be described by the following Doppler power spectrum as (1). 1

S f  

 f  1  A   fd 

2

(1)

Where A is a constant, defined to set S (f) = 0.1 (a 10 dB drop) at frequency fd (thus: A=9) and fd is the Doppler spread, defined as: fd = v0/λ, with v0 representing the environmental speed (around 1.2 km/h proposed) and where λ=c/fc is the wavelength. The Doppler spectral shape determines the timedomain fading as well as the temporal correlation and fading slope behavior, and is used in Rayleigh fading simulators to produce fading waveforms with the proper time correlation. Since the S(f) function describes the power spectrum of the Doppler fading, it can be used as a spectral filter to shape the Gaussian random signals in the frequency domain, which should result, after an IFFT, in accurate time-domain waveforms of Doppler fading. For correlating the elements, we can use: T 1 1 (2) H   R RX2  H iid  R TX2  







Where RTX, RRX are transmit and receive correlation matrices and Hiid is a matrix of independent, unit variance, zero-mean, complex random variables (standard Rayleigh fading MIMO channel matrix). Computing the above complex correlation coefficients for each tap requires the power angular spectrum (PAS) and its second moment angular spread (AS), the mean AoA and AoD values, and the power of each cluster tap.

In general, the wireless MIMO channel consists of a line-of-sight (LOS) component as well as non-light-ofsight (NLOS) components. For the TGn channel models, each channel tap, matrix H is written as the sum of a constant, LOS matrix and a variable, NLOS, Rayleigh matrix.  K  1 H  P  HF  H v  K  1 K  1    e j11    K e j21  P  j31  K  1 e j41  e 

e j12

e j13

j22

j23

e e j32 e j42

e e j33 e j43

e j14   X 11   e j24  1  X 21  j34  K  1  X 31 e  j44  e   X 41

(3) X 12 X 22 X 32 X 42

X 13 X 23 X 33 X 43

X 14    X 24    X 34    X 44  

Where P is the overall power of channel, K is the Rician K-factor, e jφij are the elements for the fixed LOS matrix and Xij are correlated (between i-th receive, j-th transmit antenna) zero mean, unit variance, complex Gaussian random variable coefficients for the NLOS, Rayleigh matrix [1].

3. Overall architecture Complete MIMO channels model is presented in Figure 1. It includes AWGN generator, the Doppler generator for time-varying channels, the spatial correlation in the antenna, the Rician including LOS, NLOS in standard TGn and the interpolation to adjust the sampling rate.

Figure 2: AWGN Generator 3.2. Modeling Doppler components For indoor wireless channels, the typical fading effect scenario involves human based motion (i.e. people walking between stationary transmitter, receiver systems). These fading effects can be described as (1). Note that the number of points (or taps) should be selected to give sufficient frequency resolution to show the spectrum around the Doppler spread, fd (note that fd is around 3 Hz at 2.4 GHz, and around 6 Hz at 5.2 GHz). In TGn channel model, time variant channel is modeled by “Bell shape” power spectrum. We use the multi-stage filter of S(f) for implementation as Figure 3.

Figure 3: Time variant model

Figure 1: MIMO fading coefficient generator structure

3.3. Antenna spatial correlation modeling In TGn channel model, spatial correlation is modeled by “Kronecker MIMO channel” as (2). Because the calculation of the matrix RTX and RRX is very complexity for implementation, we used the coefficients which already calculated in Matlab. Design of spatial correlation is presented in Figure 4.

3.1. AWGN generator Wireless channel environment is a random environment. To design the AWGN generator, we used some algorithms as central limit theorem and BoxMuller [3]. In this paper, we used 12 random uniforms with different polynomial as figure 2.

Figure 4: Spatial correlation model

3.4. Rician fading model The A-F delay profile models can be separated into a fixed (constant, LOS) matrix and a variable Rayleigh matrix. In this case, there is only a part of the Rayleigh matrix since LOS component is not included. In TGn channel model, Rician fading model is designed as Figure 5.

Figure 5: Rician Fading Model 3.5. Interpolation Interpolation adjusts the original sampling rate for a sequence to a higher or slower rate. In the FPGA, the maximum clock frequency is limited about 80 [MHz]. Our target is wireless LAN standard, IEEE802.11n which bandwidth is 20 [MHz] or 40 [MHz]. Because the clock frequency is integer multiplication of its bandwidth, it is helpful for easy design. To change the sampling frequency in accordance with the sampling frequency of the system, we have to change from 1750Hz frequency (Doppler) to 125000Hz frequency (8 us). After that, we reduce the sampling frequency to 48 times (down sampling factor) to achieve the final sampling rate is 2604 Hz as shown in Figure 6.

channel coefficients and four FPGAs are used for combining the transmit signal and channel coefficients. The logic synthesis report of the prototype system is shown in Table 1. We present the results of hardware resource utilization including the adaptive logic module, registers, look up table and DSP blocks in each block and whole system. To generate the MIMO channel coefficients, which is implemented in Stratix II EP2S180F1508, the resource utilization are less than 30% of registers, 50% of ALM and 38% of DSP blocks. From these results we can conclude that the prototype system can be implemented in the target FPGAs Table 1: Hardware resource utilization Spatial MIMO Interpo Type AWGN Doppler Correl Rician Chann lation ation el Stratix II EP2S180F1508 ALUT 363 6180 1061 1211 36601 45416 Registe 477 3023 1004 1057 37247 42808 rs (0%) (2%) (0%) (0%) (25%) (28%) 306 3649 1186 1487 29552 36180 ALM (0% (5%) (1%) (2%) (41%) (50%) 21 16 37 DSP 0 (0%) 0 (0%) (21.88 (16.67 0 (0%) (38.54 blocks %) %) %) Model implementation can be validated by comparing the statistical distribution of coefficients that Fox generates to the theoretical values of these coefficients [2]. The model can generate the following plots:  Impulse response (Fig.8)  Tap magnitude cumulative distribution function (CDF) vs. theoretical Rayleigh distribution (Fig.9)  The emulated Doppler spectra vs. the spectra predicted by theory (Fig.10)  Power delay profile (PDP) vs. theoretical (Fig.11)  Spatial correlation coefficients vs. theoretical (Fig.12)

Figure 6: Adjust for sampling rate

Figure 7: Design of interpolation

4. Simulation Result The proposed architecture is designed and simulated using Synphony HLS from Synopsys. We use Synplify Premier for synthesis and implement the system on the MIMO platform @ Radrix corp. board which has five Stratix II EP2S180F1508 FPGAs and eight AD/DA converters. One FPGA is used for the generation of

Figure 8: Impulse response

5. Conclusion

Figure 9: CDF of the taps

In this paper, we have presented a flexible, reconfigurable and cost-effective solution for real-time emulation of vehicular wireless channels. Our emulator is based on FPGA technology and rapid prototyping software tools. After describing the theoretical model, we have outlined the emulator design and its basic operation. We have also detailed some of the result we have done to compare the channel coefficients with theoretical. Synthesis results have shown that the prototype system can be implemented in the target FPGAs of Stratix II EP2S180F1508.

References [1] Thomas Paul and Tokunbo Ogunfunmi, “Wireless LAN Comes of Age: Understanding the IEEE 802.11n Amendment”, IEEE Circuits and Systems Magazine, 2008. Figure 10: Doppler spectrum

[2] Vinko Erceg, Laurent Schumacher, Persefoni Kyritsi, “Indoor MIMO WLAN TGn Channel Models”, IEEE 802.11-03/940r-43, January 2004. [3] Laurent Schumacher and Bas Dijkstra, “Description of a MATLAB® implementation of the Indoor MIMO WLAN channel model proposed by the IEEE 802.11 TGn Channel Model Special Committee”, FUNDP – The University of Namur Computer Science Institute, 2005

Figure 11: The PDP characteristic of a Channel Model

[4] Persa Kyritsi, “Channel models for MIMO” (December 16, 2004) [5] Ryuta IMASHIOYA, Wahyul Amien SYAFEI, Yuhei NAGAO, Masayuki KUROSAKI, Hiroshi OCHI, “RTL Design of 1.2Gbps MIMO WLAN System and its business aspect”. [6] Synopsys, “Synphony Model Compiler User Guide”, http://solvnet.synopsys.com (March 2011) [7] White Paper 100, Spirent, “Correlation-based spatial channel modeling” (2011)

Figure 12: Spatial correlation coefficients In Figure 10, dashed red curves correspond to the reference values, whereas the blue curves are the outcome of the simulation. In the Doppler plot, the green curve represents the Welch period-gram. The red vertical lines are drawn at ± fd. The upper blue line is set at the maximum of Doppler spectrum, and lower blue line 10 dB below. Ideally, the Doppler spectrum should meet the crossing of the red and blue lines.

[8] White Paper 101, Spirent “Fading Basics”, Narrow Band, Wide Band, and Spatial Channels (2011) [9] Yong Soo Cho, Jaekwon Kim, Won Young Yang, Chung G. Kang, Chapter 1&2, “MIMO-OFDM Wireless Communications with Matlab”.