Abstract-Multiple-input multiple- output (MIMO) and orthogonal frequency division multiplexing (OFDM) are two key techniques for broadband wireless mobile ...
Proceedings of APCC2008 copyright © 2008 IEICE 08 SB 0083
Robust Channel Estimator for MIMO-OFDM Systems with FPGA Implementation Xiaolin Hou, En Zhou, Jianping Chen, Zhan Zhang, Hidetoshi Kayama {hou, zhou, j.chen, z.zhan, kayama}@docomolabs-beijing.com.cn DoCoMo Beijing Communications Laboratories Co., Ltd Beijing, China Abstract-Multiple-input multiple- output (MIMO) and orthogonal frequency division multiplexing (OFDM) are two key techniques for broadband wireless mobile communications. In order to provide accurate channel state information (CSI) to support MIMO-OFDM transmission in doubly-selective fading channels, we propose the robust channel estimator based on twodimensional enhanced discrete-time Fourier transform interpolation (2D-EDFTI), which needs no channel statistics and can improve the channel estimation accuracy significantly. In order to validate its performance in practice, we implement it into our real-time FPGA testbed of 4-by-4 MIMO-OFDM. Also, channel estimator based on two-dimensional linear interpolation (2D-LI) is implemented for comparison. Experiments demonstrate that our proposed 2D-EDFTI channel estimator is robust to doubly-selective fading channels and its performance is always superior to 2D-LI channel estimator. Therefore, MIMOOFDM transmission by spatial multiplexing with different kinds of MIMO detector, i.e., zero-forcing (ZF) and dynamic layerordering m-path detection (DOM), can be well supported.
I.
INTRODUCTION
The rapid growth of Internet and mobile communications suggests that high-speed packet radio services will be in massive demands. Orthogonal frequency division multiplexing (OFDM) has robustness to inter-symbol-interference (ISI) and high spectrum efficiency [1], while multiple-input multipleoutput (MIMO) technology can significantly increase the capacity of wireless channel by deploying multiple transmit and receive antennas [2]. Therefore, MIMO-OFDM has been adopted as the key transmission technology for advanced wireless mobile communications including IEEE WiMAX [3] and 3GPP LTE [4]. Channel state information (CSI) is critical for the realization and performance of MIMO-OFDM systems in doubly-selective fading channels and pilot-based channel estimation [5-13] is generally used to obtain CSI in practice. Pilot pattern can be block-type, comb-type, or scattered. Generally speaking, scattered pilots will be inserted into the two dimensional timefrequency gird of MIMO-OFDM systems [3-4], which can capture the variations of doubly-selective fading channels more efficiently and different transmit antennas can be separated by orthogonal pilot subcarriers. Therefore, certain interpolation algorithms will be needed in both time-domain and frequencydomain to obtain the complete CSI. Although two-dimensional minimum mean square error interpolation (2D-MMSEI) is optimum in theory [7], accurate channel statistics are required to realize it, which are difficult to obtain in practice. Furthermore, the complexity of 2D-
MMSEI is too high for implementation. On the other hand, two-dimensional linear interpolation (2D-LI) is straightforward, but its performance may not be good enough for advanced MIMO-OFDM transmission schemes in doubly-selective fading channels. Considering the balance between accuracy and complexity, channel estimation based on two-dimensional discrete-time Fourier transform interpolation (2D-DFTI) [8-9] is a good choice. However, for burst-mode MIMO-OFDM transmission with virtual subcarriers, which is the main stream of current standardizations [3-4], its performance will degrade significantly due to the Gibbs phenomenon in both frequencydomain [10-11] and time-domain [8-9]. So we propose the channel estimator based on two-dimensional enhanced DFTI (2D-EDFTI), which can be easily implemented by concatenating frequency-domain EDFTI (FD-EDFTI) [12] with time-domain EDFTI (TD-EDFTI) [13], to eliminate the Gibbs phenomenon in both frequency-domain and timedomain, while keeping good robustness and high computational efficiency. In order to verify its performance in practice, we implement two kinds of channel estimator, i.e., 2D-LI and 2D-EDFTI, into our real-time FPGA testbed of 4-by-4 MIMO-OFDM, together with two kinds of MIMO detector, i.e., zero-forcing (ZF) and dynamic layer-ordering m-path detection (DOM) [14] to compare the performance of different combinations of channel estimator and MIMO detector. Experiments demonstrate that our proposed 2D-EDFTI channel estimator is robust to doublyselective fading channels and its performance is always superior to 2D-LI channel estimator. Therefore, both simple and exquisite MIMO detectors can be well supported. The rest of this paper is organized as follows: Section II briefly introduces the MIMO-OFDM system model. Section III describes the robust channel estimator based on 2D-EDFTI. Section IV provides the FPGA implementation and verification results and conclusions can be found in Section V. II. MIMO-OFDM SYSTEM MODEL A MIMO-OFDM system with four transmit and four receive antennas is considered in our testbed, however, the channel estimator designed in this study can be directly applied to MIMO-OFDM systems with any number of transmit and receive antennas. For spatial multiplexing, after respective pilot insertion, four parallel independent data streams are OFDM modulated and sent out with corresponding transmit antennas. The signals will experience doubly-selective fading
Proceedings of APCC2008 copyright © 2008 IEICE 08 SB 0083
in the wireless channel, i.e., frequency-selective fading caused by the multipath propagation and time-selective fading caused by the Doppler spread. For the distorted and noisy received signals, synchronization has to be first carried out to find its starting position and then OFDM demodulation can be performed. After that, doubly-selective fading channel coefficients will be obtained by channel estimation at each receive antenna and finally MIMO detection could be done to recover the four data streams. In our designed MIMO-OFDM system, OFDM symbols are organized into the frame structure of length F=32 with the index n = 0,1 ,… , F-1, as shown in Fig. 1. The transmission can be either continuous or discontinuous. The first three OFDM symbols are the preamble used for AGC and synchronization. The remaining 29 OFDM symbols include 21 data OFDM symbols for data transmission and 8 pilot OFDM symbols for channel estimation. For both the data OFDM symbol and the pilot OFDM symbol, there are virtual subcarriers (also called NULL subcarriers) reserved to ease shaping filter implementtation for spectral masking and provide guard bands to avoid interferences between adjacent systems, as illustrated in Fig. 2. There are K = U + V + 1 total subcarriers with the index k = 0, 1 ,… , K-1 in each OFDM symbol, consisting of U usable subcarriers, V virtual subcarriers, and a DC component. The received signal on the k-th subcarrier in the n-th OFDM symbol at the r-th receive antenna can be expressed as 3
Ykn, r = ∑ H kn,,rt ⋅ X kn ,t + N kn, r , r = 0,1, 2,3
(1)
t =0
where X kn ,t is the transmitted signal on the k-th subcarrier in the n-th OFDM symbol from the t-th transmit antenna; H kn,,rt is the channel frequency response (CFR) on the k-th subcarrier in the n-th OFDM symbol from the t-th transmit antenna to the rth receive antenna; N kn, r is the additive white Gaussian noise (AWGN), with zero mean and variance σ 2 , which is uncorrelated for different n, k and r. Except for the DC component and virtual subcarriers, all the other subcarriers in the data OFDM symbols are used for data transmission and all the four transmit antennas transmit simultaneously at each usable subcarrier. On the other hand, all the usable subcarriers in the pilot OFDM symbols are used for
pilot transmission, however, different transmit antenna occupies different pilot subcarriers, i.e., the four transmit antennas are orthogonally separated in the frequency domain within each pilot OFDM symbol. The corresponding pilot pattern is shown in Fig. 3, i.e., scattered pilots in the 2D time and frequency grid with equal-distances I t =4 and I f =4. To estimate the overall CFR without aliasing, both I t and I f should satisfy the Nyquist sampling theorem. III. ROBUST CHANNEL ESTIMATOR BASED ON 2D-EDFTI For the 4-by-4 MIMO-OFDM system, there are four channel estimators, each corresponding to one receive antenna. And each channel estimator should estimate four wireless channels originating from four transmit antennas. Therefore, totally 16 wireless channels should be estimated. Note that for each receive antenna the channel estimator is the same and the only difference of channel estimation for the four transmit antennas lies in the initial pilot subcarrier position pini in the pilot OFDM symbol, which takes value of 0,1,2,3, respectively. So in the following description, the receive antenna index r can be omitted. And without loss of generality, we will consider the case pini=0 first and extend to other cases later, therefore, the transmit antenna index t can also be omitted. The motivation of our proposed channel estimator based on 2D-EDFTI comes from the Gibbs phenomenon in both frequency-domain and time-domain in the traditional 2D-DFTI channel estimator, which will degrade the channel estimation accuracy significantly. The Gibbs phenomenon in frequencydomain is caused by the virtual subcarriers in the OFDM symbol and can be mitigated by FD-EDFTI [12]; while the Gibbs phenomenon in time-domain is due to the burst transmission and can be eliminated by TD-EDFTI [13]. According to the separation property of channel correlations, a 2D channel estimator can be decomposed into 2 concatenated 1D channel estimators, i.e., frequency-domain channel estimator and time-domain channel estimator, with similar performance but lower complexity. So we propose the robust channel estimator based on 2D-EDFTI by concatenating FDEDFTI with TD-EDFTI to eliminate the Gibbs phenomenon in both frequency-domain and time-domain, while keeping good
Figure 1. Frame structure.
Figure 2. Virtual subcarriers in the OFDM symbol.
Figure 3. Pilot pattern.
Proceedings of APCC2008 copyright © 2008 IEICE 08 SB 0083
robustness and high computational efficiency. Therefore, the channel estimation accuracy can be significantly improved. The implementation of 2D-EDFTI can be divided into 4 steps, where step I, II, IV correspond to FD-EDFTI and step III is TD-EDFTI. In the following text, we will briefly explain the operations in each step and the interested readers can refer to [12-13] for more details. z Step I: CFRPilot First, we perform least square (LS) estimation for the usable pilot subcarriers within each pilot OFDM symbol, i.e., H kn = H kn + N kn X kn (2) For the virtual pilot subcarrier at the DC component, simple linear interpolation is used to reconstruct the lost CFR; while for the virtual pilot subcarriers at high frequency, edge value repetition (EVR) should be deployed to shift the discontinuity points from the edge of virtual subcarriers to the center of virtual subcarriers region as illustrated in Fig. 4, thus to reduce the influence of the Gibbs phenomenon to those usable subcarriers. The initial channel estimation for both the usable pilot subcarriers and the virtual pilot subcarriers within each pilot OFDM symbol can be obtained as the Pf × Pt CFRPilot matrix, where Pf is the pilot subcarrier number within each pilot OFDM symbol and Pt is the pilot OFDM symbol number. z Step II: CIRPilot By Pf -point inverse DFT (IDFT) to each column of CFRPilot, we can get the initial channel impulse response (CIR) estimation for each pilot OFDM symbol. P −1 1 f hl n = (3) ∑ H qn⋅I f WP−f ql Pf q = 0 where WPf = exp ( − j 2π / Pf ) . Furthermore, in order to suppress the contained noises, only the properly selected samples (according to the characteristics of wireless channel) within the initial CIR estimation should be preserved to obtain the CP × Pt CIRPilot matrix, where CP is the length of cyclic prefix. z Step III: CIRData TD-EDFTI will then be used for each row of CIRPilot to obtain the CP × F CIR Data matrix h = ⎡⎣ hmn ⎤⎦ , n=0 ,… , F-1, m=0 ,… , CP-1. Here F=29, not include the preamble of AGC and synchronization. First, pilot reflection (PR, see Fig. 5) is utilized to eliminate the unequal end points of each row of CIRPilot, therefore, the time-domain Gibbs phenomenon will be mitigated later, and then DFT can be applied. After amplification and properly controlled row-wise zero insertion, CIRData
Figure 4. Edge value repetition.
Figure 5. Pilot reflection.
can be generated via row-wise IDFT. z Step IV:CFRData Finally, the remaining part of FD-EDFTI will be carried out. After properly controlled zero insertion, K-point DFT will be performed to each column of CIRData to get the K × F CFRData matrix.
H kn =
λ ⋅CP −1
∑ m=0
hmnWKmk +
K −1
∑ m = K −( )
1-λ ⋅CP
hmn− K + CPWKmk
(4)
where λ may be set by rule of thumb as λ = ( 2e − 1) 2e ,
e = 2 or 3 . As for other cases 0 < pini < I f , each column of CFRData should be circularly shifted downwards by pini samples to finish the channel estimation. The overall channel estimation procedure is given in Fig. 6, where (inverse) fast Fourier transform ((I)FFT) will be adopted in practice. IV. FPGA IMPLEMENTATION AND VERIFICATION Our 4-by-4 MIMO-OFDM testbed shown in Fig. 7 is based on the real-time FPGA implementation. The baseband modules of the transmitter and receiver are designed via Xilinx® System Generator [15] and Lyrtech® DSP/FPGA development platforms [16]. The 4-by-4 RF MIMO channel is emulated by EB® Propsim C8 channel emulator [17]. This testbed can support real-time video transmission.
Figure 6. Channel estimation based on 2D-EDFTI.
Proceedings of APCC2008 copyright © 2008 IEICE 08 SB 0083
Figure 7. 4-by-4 MIMO-OFDM testbed.
At current stage, our researches mainly focus on the receiver side including synchronization, channel estimation and MIMO detection. In this study, we only provide some testing results for the channel estimator part and the interested readers can refer to [18] and [14] for details about the synchronizer and the MIMO detector, respectively. The basic system parameters are listed in TABLE I. Note that some parameters, such as the carrier frequency and the bandwidth, are adjustable. The channel model is taken from 3GPP TR 25.996 [19] and listed in TABLE II. This 6-path channel model with different mobile speeds of 3, 30 and 120km/h will be emulated. In addition to the 2D-EDFTI channel estimator, the 2D-LI channel estimator is also implemented for performance comparison. Furthermore, two kinds of MIMO detector, i.e., ZF and DOM, are implemented. Thus we can compare the performance of different combinations of channel estimator and MIMO detector. In the typical multipath fast fading channel, i.e., doublyselective fading channel, both CIR and CFR fluctuate significantly within one frame’s duration, which is challenging for channel estimation. So for the straightforward 2D-LI
channel estimator, it is hardly to capture the channel variations accurately, therefore, cannot always support MIMO-OFDM transmission effectively and may lead to the link outage. While for our proposed 2D-EDFTI channel estimator, it still can work well in the severely doubly-selective fading channel and provide efficient support for MIMO detection. Here in Fig. 8 we provide a set of snapshots of the 16QAM constellation after ZF detection when the 2D-LI channel estimator and the 2DEDFTI channel estimator are employed, respectively, with the different velocities 3, 30 and 120 km/h. It can be easily found that the constellation with the 2D-LI channel estimator deteriorates drastically with the increasing velocity, while the constellation with the 2D-EDFTI channel estimator is still distinguishable even when the velocity is up to 120 km/h. Furthermore, we compare the uncoded bit-error-rate (BER) performance in Fig. 9 for different combinations of channel estimator and MIMO detector, i.e., 2D-LI + ZF, 2D-EDFTI + ZF, 2D-LI + DOM8 (DOM with 8 iterations) and 2D-EDFTI + DOM8. Obviously, the 2D-EDFTI channel estimator can always provide more accurate channel estimation than the 2DLI channel estimator, thus a lower BER can be achieved with the same MIMO detector. Especially, with the increasing velocity, the combination of 2D-EDFTI + ZF can even obtain a similar (30 km/h) or much better (120 km/h) BER performance
(a-1) 2D-LI, 3km/h
(b-1) 2D-EDFTI, 3km/h
(a-2) 2D-LI, 30km/h
(b-2) 2D-EDFTI, 30km/h
(a-3) 2D-LI, 120km/h
(b-3) 2D-EDFTI, 120km/h
TABLE I. SYSTEM PARAMETERS. Parameters Carrier frequency Bandwidth MIMO antenna setup Frame length Subcarrier number CP length Number of usable subcarriers Number of virtual subcarriers Modulation Schemes
Type 3GPP TR 25.996 (Case 2)
Values 2.35GHz 6.25MHz 4*4 32 OFDM Symbols 1024 96 896 128 BPSK (Pilot) 16QAM (Data)
TABLE II. CHANNEL MODEL. Path Delay (ns) Average Power (dB) 1 0 0 2 310 -1 3 710 -9 4 1090 -10 5 1730 -15 6 2510 -20
Figure 8. 16-QAM constellation after ZF detection.
Proceedings of APCC2008 copyright © 2008 IEICE 08 SB 0083
detection algorithm cannot show its advantage over the simplest ZF detection.
25.996 Case2 3km/h
0
10
BER(Uncoded 16QAM)
2D-LI+ZF 2D-EDFTI+ZF 2D-LI+DOM8 2D-EDFTI+DOM8
V. CONCLUSIONS
-1
10
-2
10
-3
10
12
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18
20 SNR(dB)
22
24
26
28
In this paper, we propose and verify the robust channel estimator based on 2D-EDFTI in the 4-by-4 MIMO-OFDM testbed with FPGA implementation. It does not require the channel statistics and has high computational efficiency. Experiments demonstrate that our proposed 2D-EDFTI channel estimator is robust to doubly-selective fading channels and its performance is always superior to the 2D-LI channel estimator. The channel estimation accuracy can be guaranteed even in the most challenging multipath fast fading wireless channel with the velocity up to 120km/h, therefore, both simple and exquisite MIMO detectors, i.e., ZF and DOM, can be well supported.
(a) 3km/h
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25.996 Case2 30km/h
0
[1]
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BER(Uncoded 16QAM)
2D-LI+ZF 2D-EDFTI+ZF 2D-LI+DOM8 2D-EDFTI+DOM8
[2] [3]
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[4] [5] [6]
-2
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[7] -3
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(b) 30km/h
[8] [9]
25.996 Case2 120km/h
0
10
[10]
BER(Uncoded 16QAM)
[11] -1
10
[12] [13] -2
10
[14]
2D-LI+ZF 2D-EDFTI+ZF 2D-LI+DOM8 2D-EDFTI+DOM8 -3
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18 SNR(dB)
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[15] [16] [17] [18]
(c) 120km/h Figure 9. Uncoded BER vs. SNR.
than the combination of 2D-LI + DOM8, which indicates that the accuracy of CSI is very important for the MIMO detection. Without accurate channel estimation, more exquisite MIMO
[19]
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