# OFDM Mobile Systems

### Joint Equalization and ICI Suppression for OFDM Mobile Systems

### Abstract—

Orthogonal Frequency Division Multiplexing (OFDM) is robust against frequency selective fading due to the increase of the symbol duration. However, it suffers from Inter-Carrier Interference (ICI) due to rapid time variation of fading channel and Carrier Frequency Offset (CFO) which degrades the performance. This becomes more severe as in multipath fading channels is present. Therefore, to have an acceptable reception quality, there is a need for ICI mitigation within one OFDM symbol. In this paper, we address the problem of OFDM transmission over a frequency-selective channel with CFO. A Nnovel joint equalization and ICI suppression technique is devised to combat the CFO effects. We first derive a Model for ICI while sampling the received signal at the receiver which isusing a convolutional model. Then we introduce an optimal method which uses Adaptive Viterbi Algorithm for both equalization and ICI suppression. Simulation results show that this method can collect result in significant gain in ans of ICI-impaired OFDM system, since it is optimal by means of ML and improve the performance with an affordable complexity; and can benefit from common methods of ICI mitigation.

### Index Terms—

Carrier Frequency Offset (CFO), Equalization, Inter-Carrier Interference (ICI), Orthogonal Frequency Division Multiplexing (OFDM), Viterbi Algorithm.

### I. INTRODUCTION

THE wireless communication industry has experienced rapid growth in recent years, and digital cellular systems are currently designed to provide high data rates at high terminal speeds. High data rates give rise to Inter Symbol Interference (ISI) due to so-called multipath fading. Such an ISI channel is called frequency-selective. On the other hand, due to terminal mobility and/or receiver frequency offset the received signal is subject to frequency shifts (Doppler shifts). Doppler shift induces time-selectivity characteristics. In addition to the channel effects, the analog front-end may suffer from carrier frequency offset. These analog front-end imperfections then result in an additional and significant degradation in system performance, especially in multi-carrier based transmission techniques [1].

Orthogonal frequency division multiplexing (OFDM) is one of the multi-carrier modulation (MCM) techniques that transmit signals through multiple carriers. These carriers (subcarriers) have different frequencies and they are orthogonal to each other. OFDM handles frequency selective fading resulting from delay spread by expanding the symbol duration [2]–[5]. By adding a guard interval to the beginning of each OFDM symbol, the effect of delay spread (provided that there is perfect synchronization) would appear as a multiplication multiplicative factor in the frequency domain for a time-invariant channel. Adding the guard interval will also prevent inter-OFDM symbol-interference. This feature allows for higher data rates and has resulted in the selection of OFDM as a standard for digital audio broadcasting (DAB [6]), digital video broadcasting (DVB [7]), and wireless local area networks (802.11a).

In the case of OFDM transmission, the channel time-variation over an OFDM symbol period destroys the orthogonality between subcarriers and hence induces inter-carrier interference (ICI), i.e. the energy of a particular subcarrier is leaked to neighboring subcarriers. There are two factors that cause the ICI, namely frequency offset and time variation. As discussed in [8], some kinds of time variations of channelsfls can be modeled as a white Gaussian random noise when N is large enough, while other time variations can be modeled as frequency offsets, such as Doppler shift. Only frequency-offset is discussed in this paper. ICI problem would become more complicated when the multipath fading is present.

It can be assumed that most of the wireless receivers cannot make perfect frequency synchronization. In fact, practical oscillators for synchronization are usually unstable, which introduce frequency offset. Although this small offset is negligible in traditional communication systems, it is a severe problem in the OFDM systems. In most situations, the oscillator frequency offset varies from 20 ppm (Parts Per Million) to 100 ppm. Provided an OFDM system operates at 5 GHz, the maximum offset would be 100 KHz to 500 KHz (20-100 ppm.). However, the subcarriers frequency spacing is only 312.5 KHz. Hence; the frequency offset could not be ignored; hence as a result many existing schemes were proposed to attack CFO-Induced ICI problem [9].

Some approaches are based on CFO estimation and compensation, which makes use of pilot sequences, virtual carriers or blind signal processing techniques at the price of sacrificing some bandwidth as stated in [10]-[12].

Some others are based on the windowing technique in either time domain or frequency domain at transmitter, such as Nyquist and Hanning windowing [13]-[14].

The third one is called ICI self-cancellation, where the repeated bits are transmitted to mitigate inter-carrier interference [9]. Another ICI self- cancellation scheme is proposed recently in [15]. In these methods only half or less of bandwidth is used for information transmission since involving with encoded redundancy.

In this paper, first a brief overview of OFDM transmission over time-invariant channel is studied. Then we derive a convolutional Model model for ICI due to CFO at receiver. Based on this Modelmodel, we develop an optimala scheme for joint equalization and ICI suppression which is based on using Viterbi Algorithm algorithm for ICI mitigation. In our proposed method, the Viterbi Algorithm algorithm is also adapted to channel coefficients for equalization. At end via computer simulations we show that the new method can improve the performance.

### II. SYSTEM MODEL

Multi-carrier systems can either be simulated in the time domain or more computationally efficient, in the frequency domain. Preconditions for the frequency domain implementation are the absence of ISI and ICI, the frequency nonselective fading per subcarrier, and the time-invariance during one OFDM symbol. An Iindoor wireless channel approximately fulfills these preconditions.

### A. OFDM Transmitter

A communication system with multi-carrier modulation transmits complex-valued source symbols in parallel on subcarriers. The source symbols may, for instance, be obtained after source and channel coding, interleaving, and symbol mapping. The complex-valued source symbols transmitted with equal power, represented by the vector.

(1)

The source symbol duration of the serial data symbols results after serial-to-parallel conversion in the OFDM symbol duration. The principle of OFDM is to modulate the substreams on subcarriers with a spacing of., In order to achieve orthogonality between the signals on the subcarriers, presuming a rectangular pulse shaping. The subcarrier frequencies are located at

(2)

A key advantage of using OFDM is that multi-carrier modulation can be implemented in the discrete domain by using an IDFT, or a more computationally efficient IFFT. The sampled sequence, is the IFFT of the source symbol sequence,. The block diagram of an OFDM system based on an IFFT and FFT is illustrated in 1. This sequence with cyclic extended guard interval is passed through a multipath fading channel. The OFDM symbol duration after adding GI is .

### B. Channel

An important design goal for a multi-carrier transmission scheme based on OFDM in a mobile radio channel is that the channel can be considered as time-invariant during one OFDM symbol and that fading per subchannel can be considered as flat. When ISI and ICI can be neglected, the multi-carrier transmission system can be viewed as a discrete time and frequency transmission system with a set of parallel Gaussian channels with different complex-valued attenuations as shown in 2.

The discrete channel transfer function adapted to multi-carrier signals results in

(3)

where the continuous channel transfer function is sampled in time at OFDM symbol rate and in frequency at subcarrier spacing . A symbol transmitted on subchannel of the OFDM symbol is multiplied by the resulting fading amplitude and rotated by a random phase. The phase is uniformly distributed in the interval.

In the case that the multipath channel contains a Line Of Sight (LOS) or dominant component in addition to the randomly moving scatterers, the distribution of is Rician e and the channel is called "a Ricean Rician fading channel". In the absence of LOS or a dominant component, the channel is called "a Rayleigh fading channel" Since the distribution of is Rayleigh.

The channel matrix is of diagonal type in the absence of ISI and ICI. The diagonal components of are the complex-valued flat fading coefficients assigned to the subchannels.

These channel models are based on the assumption that the fading on adjacent data symbols after inverse OFDM and de-interleaving can be considered as uncorrelated. The resulting complex-valued channel fading coefficient is thus generated independently for each subcarrier and OFDM symbol.

### C. OFDM Receiver

The output of the channel is sampled at rate. Since ISI is only present in the first samples of the received sequence, these samples are removed before multi-carrier demodulation due to guard interval. The ISI-free part of the received samples, , is multi-carrier demodulated by inverse OFDM exploiting an FFT, . The output of the FFT is the multi-carrier demodulated vector.

Since ICI can be avoided due to the guard interval, each subchannel can be considered separately. Furthermore, when assuming that the fading on each subchannel is flat and ISI is removed, a received vector is obtained from the frequency domain representation according to

(5)

where represents the additive noise. The variance of the noise on the th subchannel is given by.

### III. ICI MODEL

In OFDM transmission, Frequency offset induces inter-carrier interference, i.e. the energy of a particular subcarrier is leaked to neighboring subcarriers. Since each subcarrier is affected by other subcarriers the ICI can be modeled as convolutional pattern.

If denotes the output vector of channel before ICI insertion and denotes the value at frequency, after sampling at receiver, CFO causes subcarriers not to be orthogonal any more which asis illustrated in 3. The ICI which is added to each subcarrier can be represented by the matrix.

(6)

Thus The vector description of is

(7)

where represents additive Noise after adding ICI. For simplicity we assume the uniform ICI pattern for all subcarriers, which results in

(8)

The most important method to restore the input vector for convolutional patterns is represented by the maximum likelihood (ML) Viterbi Aalgorithm which is optimal.

In [16], it is showed shown that the most of the symbol energy is distributed on a few subcarriers, and the ICI power on a subcarrier mainly comes from several neighboring subcarriers and effect of other subcarriers is negligible and can be assumed as an additive Noise. For this reason the complexity of Viterbi Algorithm algorithm is reduced. Suppose If the ICI is just from adjacent subcarriers

### IV. JOINT EQUALIZATION AND ICI SUPPRESSION

According to (5), the out output of the multipath channel before adding ICI is. After adding ICI, the outputfirst enters the Viterbi Algorithm algorithm for ICI suppression and then enters the equalizer to compensate the effects of multipath channel.

Suppose the channel estimation is well down performed at the receiver. The ICI insertion pattern can modify so that Viterbi Algorithm algorithm handles both ICI suppression and equalization by an adaptive metrics. We can rewrite (5) in this wayas:

(10)

Assume the signal is passed through an ideal channel and then at receiver, ICI represented byis added to it because of CFO. Due to (10), each subcarrier is affected by adjacent subcarriers with different coefficients. These coefficients are change due to channel variations and so the ICI suppression method must be adapted by the channel variations.

### V. USING ADAPTIVE VITERBI ALGORITHEM

We propose Viterbi Algorithm for both equalization and ICI suppression. But since the channel coefficients are enter the model, so the convolutional coefficients are no longer constant and vary from one subcarrier to another and therefore the metrics used for Viterbi Algorithm algorithm are adapted to channel coefficients. That's This is the reason for the namewhy we call this method as "Adaptive Viterbi Algorithm".

Supposedenotes the alphabet size of inputand denotes the number of memory stages in the convolutional pattern. Then the number of states in trellis diagram is and the number of transactions in each phase is.

The model which we considered for ICI in 4, has memory stages. The size of input alphabet depends on the constellation that the symbols are chosen from. For example in BPSK modulation, and in 64QAM it is 64.

### VI. SIMULATION

In this section we provide simulation results of the proposed method for two cases. We simulate an OFDM system in a discrete frequency domain environment. Our goal is to calculate BER when ICI is mitigated and compare it to that of the “no mitigation” case. For this reason we draw the BER versus SNR for these two cases.

In first case, BPSK symbols are modulated on andsubcarriers and transmit over Time-Invariant Rayleigh Fading channel with AWGN noise. At receiver, we assume that each subcarrier is affected by adjacent subcarries withand also. The effect of other subcarriers is assumed as a Gaussian noise with variance; hence we define the variance of noise in each sample after adding ICI as.

It can be seen from 6 that how proposed method reduces the error rate considerably for both number of subcarriers. Whendecreases, the graph shows a slightly better performance. This is due to the smaller size of OFDM symbols and so fewer errors occurred during ML detection in Viterbi Algorithmalgorithm. For comparison, the case of no ICI mitigation with Zero Forcing equalizer is also shown in this graph.

In the second case, we assume the same transmitter with subcarriers and ICI model with and. Our goal is to calculate BER when SNR increases and compare the efficiency of the method to mitigate ICI when the amount of ICI is increased.

### VII. CONCLUSION

We propose a new modeling scheme for ICI insertion due to imperfection of oscillators namely CFO. We introduce a novel method for joint ICI suppression and equalization in OFDM transition which uses Viterbi Algorithm algorithm and so it isas an optimal solution. Since its metrics are not constant and change due to channel variations, Viterbi metrics change from one symbol to another and so it is calledwhich results in an Adaptive Viterbi Algorithm.

### VIII. REFERENCES

[1] Barhumi, I., Transaction over time and frequency selective mobile wireless channels, Department of Electronic, Katholieke University Leuven, Sept. 2005.

[2] Fazel, K. and Kaiser, S., Multi-carrier and spread spectrum systems, Wiley, 2003.

[3] Schulze, H. and Luders, C., Theory and applications of OFDM and CDMA, Wiley, 2005.

[4] Hara, S. and Prasad, R., Multicarrier techniques for 4G mobile communications, Artech House, 2003.

[5] Goldsmith, A., Wireless communications, Cambridge University Press, 2005.

[6] Floch, B. Le, Hallbert-Lasalle, R. and Castellain, D., “Digital audio broadcasting to mobile receivers”, IEEE Trans. Consum. Electron, vol. 35, pp. 493–503, Aug. 1989.

[7] Sari, H., Karam, G. and Janclaude, J., “Transmission techniques for digital TV broadcasting,” IEEE Commun. Mag., vol. 36, pp. 100–109, Feb.1995.

[8] Russell, M. and Stuber, G.L., “Inter-channel interference analysis of OFDM in a mobile environment”, IEEE 45th Vehicular Technology Conference, Vol. 2, pp. 820–824, 1995.

[ 9] Xiao, Y., Orthogonal frequency division multiplexing modulation and inter-carrier interference cancellation, Department of Electrical and Computer Engineering, Louisiana State University, May 2003.

[10] Liu, H. and Tureli, U., “A high-efficiency carrier estimator for OFDM communications”, IEEE Communications Letters, vol. 2 Issue: 4, pp. 104 –106, Apr. 1998.

[11] Chen, B. and Wang, H., “Maximum likelihood estimation of OFDM carrier frequency offset” IEEE International Conference on Commun. (ICC 2002), vol. 1, pp. 49 -53, 2002.

[12] Jian L., Guoqing L. and Giannakis, G.B., “Carrier frequency offset estimation for OFDM-based WLANs”, IEEE Signal Processing Letters, vol. 8 Issue: 3, pp. 80 –82, Mar. 2001.

[ 13] Armstrong, J., “Analysis of new and existing methods of reducing inter-carrier interference due to carrier frequency offset in OFDM”, IEEE Transactions on Communications, Vol. 47, pp. 365-369, 1999.

[14] Muller-Weinfurtner, S.H., “Optimum Nyquist windowing in OFDM receivers”, IEEE Transactions on Commun., vol. 49 Issue: 3, pp. 417 –420, Mar. 2001.

[15] Li, Y.G., Winters, J.H. and Sollenberger, N.R., “MIMO-OFDM for wireless communications: signal detection with enhanced channel estimation”, IEEE Transactions on Commun, vol. 50 Issue: 9, pp. 1471 –1477, Sep. 2002.

[16] Cai, X. and Giannakis, G.B., “Low-complexity ICI suppression for OFDM over time-and frequency-selective Rayleigh fading channels”, Proc. Asilomar Conf. Signals, Syst. Comput., vol.2, pp.1822–1826, Nov. 2002.