Carrier Frequency Offset with I/Q Imbalance Analysis of Fifth Generation WiFi

Lalitha H, Reema Sharma Department of Electronic and Communication

The Oxford College of Engineering, Bangalore, India lalithahmohan@gmail.com

Navin Kumar Department of Telecommunication

CMR Institute of Technology, Bangalore, India navinkumar@ieee.org

Abstract The performance of the Orthogonal Frequency Division Multiplexing (OFDM) based systems degrades especially being sensitive to carrier frequency offset (CFO) and inphase and quadrature (I/Q) imbalance which destroys orthogonality between subcarriers. The IEEE 802.11ac (fifth generation) wireless local area network (WLAN) standard uses OFDM equally spaced subcarriers to transmit data, and the number of subcarriers signal depend on the bandwidth. In this paper, we investigate the system behaviour considering CFO and I/Q imbalance impairments. Our studies focus on two important non data aided algorithms. The results of analysis are presented for different subcarriers in combination with modulation and throughput.

Keywords – OFDM; carrier offset; I/Q imbalancing; 802.11ac.

I. INTRODUCTION

The IEEE 802.11ac is a new addition to the 802.11 family of standards operating in 5 GHz [1]. It is the fifth generation Wi-Fi networking standard, and an extension of standard IEEE 802.11n. It offers capabilities to that of gigabit ethernet and is backward compatible to 11a/b/g/n devices. Therefore supports fast, high quality video streaming and nearly instantaneous data synching to the notebooks, tablets and mobile phones. The 802.11ac supports an astonishing maximum raw data rate in excess of 1Gbps by making use of number of enhancements such as channel bonding wherein the bandwidth is increased to that of 80MHz, 160MHz and even non-adjacent 80+80MHz which doubles the data rate with doubling the channel bandwidth. While the 802.11n standard supported only 20MHz and 40MHz channels.

It makes use of advanced multiple input multiple output (MIMO) techniques such as 8 spatial streams in both single-user and multi-user modes. The multi user MIMO (MU MIMO) allows simultaneous transmission of different user streams in the same channel at the same time. Whereas 802.11n supports a maximum of only 4 spatial streams and there was no support for MU MIMO. In addition 802.11ac standard supports enhancement such as standard beamforming implementation that enables interoperability and increases the coverage area while beamforming was optional in 802.11n standard.

Thus IEEE 802.11ac offers to deliver very high throughput (VHT) for high definition video streaming multimedia devices,

high capacity and improved coverage area of all the existing Wi-Fi Standards [2].

The standard 802.11ac uses OFDM technology to cope with severe varying channel conditions and narrowband interference. In OFDM the subcarriers are overlapped to offer high spectral efficiency [3]. Also, it uses the Fourier Fast Transform (FFT) and its inverse, FFT (IFFT) to efficiently create multiple orthogonal subcarriers using a single radio. The number of used data carriers varies with the bandwidth. For example, 52 data carriers are used with 20MHz bandwidth and 108 data carriers with 40MHz bandwidth and the number of spatial streams vary from 1 to 4 as in the case of 802.11n. The 802.11ac standard pushes further and accommodates a data carriers of 234 at 80MHz and twice i.e. 2x234 at 160MHz, supporting a spatial streams of 5 to 8 [2]. In addition of support of all the OFDM modulation schemes of 802.11n, the standard 802.11ac offers denser modulation scheme such as 256 QAM which enables 33% increase in throughput compared to 64QAM.

OFDM technology requires a high level of accuracy in frequency synchronization between the receiver and transmitter. In other words, any deviation causes the subcarriers to no longer be orthogonal, resulting in intercarrier interference (ICI) and cross-talk between adjacent subcarriers. OFDM is very sensitive to the carrier frequency o set (CFO) that is introduced by the down conversion process. CFO can destroy the orthogonality between sub-carriers. So, it becomes necessary for the OFDM systems to estimate the CFO. Also, I/Q imbalance is one of the main non idealities in the receiver front end which arises when a front-end component doesn’t respect the power balance or the orthogonality between the I and Q branch.

CFO estimation is an important criterion for the better performance and success of 802.11ac. CFO estimation for OFDM systems had been studied and analyzed and various algorithms based on both the blind estimation and pilot based estimation have been proposed in literatures. In this paper we analyze various non data aided algorithms for the CFO with I/Q imbalance for the new standard 802.11ac. Our main interest is to investigate CFO with I/Q imbalance characteristics for 802.11ac standard and then feasibility to improve the performance of the

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algorithm. The device promises for very high throughput which can be used for high definition video over wireless connection, rapid upload and download of files, video/media content distribution. Therefore, we analyzed for channel conditions such as additive white Gaussian noise. The simulation results are shown for two of the FFT sizes of 64 and 128 for single stream with Quadrature phase shift keying (QPSK) modulation, a mandatory requirement in the IEEE 802.11ac.

The rest of the paper is organized as follows. Section II presents recent related work in brief while section III describes the mathematical model for CFO and I/Q Imbalance estimation in OFDM systems. Section IV discusses the estimation algorithm and implementation methods for CFO in the presence of I/Q imbalance. Simulation results are discussed in section V and finally section VI concludes the paper.

II. RECENT RELATED WORK

This section presents some of the recent works related to impairment studies in respect of CFO and I/Q imbalance of OFDM system. Although, no such study is found particularly for this new standard 802.11ac which is yet to be finalized, but there are significant papers in general. Algorithms based on pilot carrier and blind carrier have been discussed in length. For example, authors in [4] present a high-performance/low-complexity blind carrier offset estimation algorithm. They exploited the intrinsic structure information of OFDM signals. They claim to have achieved an accuracy of a super resolution subspace method, for example; MUSIC, without involving computationally intensive subspace decompositions.

Authors in [5] proposed a method based on a training symbol specifically designed to have a steep rolloff timing metric. The proposed timing metric also provided a robust sync detection capability. They also incorporated in the system the channel estimation scheme based on the designed training symbol in order to give both fine-timing and frequency-offset estimates.

A joint maximum likelihood (ML) symbol-time and carrier frequency offset estimator is discussed in [6]. Authors used the redundant information contained within the cyclic prefix (CP) to estimate without pilot carrier. They concluded that the frequency estimator can be used in a tracking mode while the time estimator can be used in acquisition mode. J. Tubbax et. Al. in [7] analyzed the joint I/Q-CFO estimation/compensation and proposed a low-cost, highly effective compensation technique. They concluded that for the large I/Q imbalance and large CFO, the degradation remain below 0.5dB on an average as compared to the reference case without I/Q imbalance or frequency offset. Therefore low-

cost, low-complexity OFDM receiver would be designed. Blind estimator for joint estimation of CFO, DC offset (DCO) and I/Q imbalance in OFDM systems with direct-conversion receiver (DCR) was discussed in [8]. They presented a blind estimator based on eigen-decomposition estimator (EDE) of signal correlation matrix which does not depend on specific preamble or pilots. The estimation algorithms employed by EDE are based on two basic ideas. First, DCO and I/Q imbalance in received signal can be completely removed by weighted linear combination of received signal itself, its complex conjugate and an arbitrary dc signal. DCO and I/Q imbalance can be estimated from the weighting factors of the combination. Second, after DCO mitigation, existing CFO estimation algorithms for OFDM systems without DCO and I/Q imbalance can be directly applied. Joint exploration of the two ideas gives rise to EDE.

In [9], authors proposed a novel algorithm for blind CFO estimation without training sequence. They exploited the mirror spectrum induced by I/Q imbalance for CFO estimation. To minimize the overhead for the efficient bandwidth utilization, we considered non data aided algorithm in this paper.

III. SIGNAL MODEL OF OFDM SYSTEM

A. Model of CFO Estimator without I/Q Imbalancing

The discrete version of OFDM suitable to develop mathematical model and based on inverse discrete Fourier transform (IDFT) in the transmission chain and discrete Fourier transform (DFT) in the receiver chain is shown in Fig. 1. The IFFT and FFT are the fast algorithm pair of IDFT and DFT. An OFDM system of bandwidth B Hz, comprising N subcarriers1; the frequency spacing can be given by f = B/N. The received signal is initially down converted and sampled with sampling frequency of B Hz. We consider Fc the carrier frequency and f0 denote the frequency offset CFO. Initially the guard interval is removed from the received samples before further processing, Once the guard is removed, we obtain the samples of an OFDM symbol which was sent through the transmitter and can be expressed as:

, (1) where , (2) , (3) . (4)

1N subcarriers include real subcarriers which carry data and virtual subcarriers which do not carry any

data.

Fig. 1. : OFDM System Model with single stream

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where y represents the received vector samples in one OFDM symbol, x is the transmitted vector and w is the noise vector.

represents the nth sample in the received vector. Similarly for the xn and wn.

The transmitted signal from the transmitter through the channel is given by the equation:

(5) where

E( ) = diag([ ]), (6) H = diag([ ]), (7) (8) ‘ ’ denotes the CFO normalized to the frequency space between adjacent subcarriers and M is the number of real subcarriers. U represents the part of N-dimensional Inverse discrete Fourier transform matrix corresponding to the M real subcarriers.

denotes the frequency domain channel response of the kth subcarrier and the represents the data carried respectively.

The Basic Estimator in [7] performs the non data aided CFO estimation by taking advantage of the inherent orthogonality present among different OFDM subcarriers i.e. exploiting the fact that U and V are orthogonal to each other, where V is the complementary part of U within N dimensional IFFT matrix. The matrices U and V represent the subspaces of the real subcarriers and the virtual subcarriers, respectively. Shifting the carrier frequency of the received signal and determining the inner product of will approach a minimum value when the frequency shift is equal to the CFO introduced because only the noise part remains [2]:

(9) where superscript H is the Hermitian operation. E(f)y represents the shifting of the carrier frequency of the received signal by f Hz ,when the shift in the signal exactly matches the CFO introduced then the inner product is zero because only the noise part will remain.

Hence select the frequency shift whose norm of the inner product between achieves a minimum value as the estimated CFO value.

B. Model of OFDM system with I/Q Imbalance

In OFDM systems where the I/Q imbalance impairment exists along with the CFO, the received symbol samples are represented as: , (10) where , (11)

where the amplitude imbalance and the phase mismatch are the parameters induced by the I/Q imbalance [3] and given below in equations (12) and (13) respectively; is the complex conjugate. (12) (13) I/Q Imbalance exists in the received signal except if =0 and

=0, or equivalently =1 and =0.

IV. CFO ESTIMATOR IN PRESENCE OF I/Q IMBALANCE

In the New Estimator, we consider the received signal and its complex conjugate and perform the inner product with , then we obtain the equations (14) and (15) respectively, i.e. , (14) (15) From the equations (14) and (15), we see that the inner product will no longer attain a minimum value even though the frequency shift is equal to the CFO. This is due to the presence of I/Q imbalance. Hence the basic estimator cannot be used directly. Whereas the ratio of the two inner product will approach a constant i.e. , when the frequency shift is equal to the CFO. Based upon above information, we can formulate a new CFO and I/Q estimation algorithm. For this, let us define: (16) (17)

(18)

where division is carried out every sample wise and resulting Q is a vector, c is a column vector of all ones

. Based on the above equations, we propose the I/Q estimator and CFO estimator as: (19)

(20) respectively, where (Q) is the mean of the Q vector.

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V. PERFORMANCE ANALYSIS, RESULTS AND DISCUSSION

In this section, we compare the performance of the basic estimator in [9] with the new estimator proposed. The simulation parameters are given in the Table 1.

The Fig. 2 and Fig. 3 shows the mean square error (MSE) of CFO estimation without I/Q imbalance using both the basic estimator and with the new estimator for FFT size of 64 and 128 respectively. The Fig.4 and Fig.5 shows the performance of both the estimators in the presence of the I/Q Imbalance.’*’ indicates the estimates obtained by the basic estimator in [9],’ ’ is the estimates obtained with the new estimator proposed in this paper in all the plots.

From the observations of the Fig.2 and Fig.3 which plots the simulation results of both the estimators without considering the effects of I/Q imbalance. It can be concluded that the basic estimator performs better than the new estimator as we are considering both the received signal and its conjugate version and in the absence of the I/Q imbalance, it enlarges the noise during estimation. In the Fig.4 and Fig.5, the performance of both the

estimators in the presence of the I/Q Imbalance is shown. The new estimator performance is poor in both the FFT sizes as compared to the basic estimator initially at the low SNR regions

TABLE-1 SIMULATION PARAMETERS

Parameters Values

FFT size 64/128

No. of data subcarriers 52/108

Modulation QPSK

Amplitude imbalance 1 dB

Phase imbalance 50

Fig.5: CFO Estimation with I/Q Imbalance for FFT size of 128

Fig.3: CFO Estimation without I/Q Imbalance for FFT size of 128

Fig.4: CFO Estimation with I/Q Imbalance for FFT size of 64

Fig.2: CFO Estimation without I/Q Imbalance for FFT size of 64

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due to the assumption that ratio of the two inner products approach will have large error due to the noise. It can be seen that the new estimator’s performance is significantly better in the high SNR regions and the improvements is better with higher bandwidth as can be seen in the Fig. 5. However, the basic estimator remains constant even at higher SNR since it does not take into account the effects of I/Q imbalance. It can be concluded from the simulation results that the new estimator performs better than the basic estimator especially in the presence of I/Q Imbalance.

I. CONCLUSION

Non data aided estimation for CFO with I/Q imbalance algorithms have the advantage of reducing the overhead. Such algorithm can be implemented in WiFi systems particularly for 5th Generation 802.11ac which has elaborate training sequences that can be avoided for efficient use of bandwidth. The investigation and the simulation results show that the performance of the new proposed estimator is better especially in the presence of I/Q imbalance.

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[2] IEEE 802, “Specification Framework for TGac,” Institute of Electronic and Electrical Engineers, IEEE 802.11-09/0992r21, 2011. [Online]. Available: https://mentor.ieee.org/802.11/dcn/09/11-09-0992-21-00ac-proposed-specification-framework-for-tgac.doc

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