46 CHAPTER 3 REDUCTIO OF ITERCARRIER ITERFERECE 3.1 ITERCARRIER ITERFERECE I OFDM SYSTEMS OFDM is a spectray efficient uticarrier oduation technique and it handes frequency seective channes we when cobined with error correction coding. Athough OFDM has proved itsef as a powerfu oduation technique, it has its own chaenges such as, inter-sybo interference and intercarrier interference. Both are dua of each other occurring at different doains; one in tie-doain and the other in frequency-doain. In OFDM systes, the entire channe is divided into narrowband subcarriers and the high-rate data are transitted siutaneousy parae through the subcarriers. Since the sybo duration is ties onger than the singe carrier systes, the inter-sybo interference is reduced by ties in OFDM systes. As the subcarriers are orthogona, the spectru of each carrier has a nu at the center frequency of each of the other subcarriers in the syste. This resuts no interference between the carriers and aow the to be spaced as cose as theoreticay possibe. However, in high obiity environent carrier frequency offset introduced in OFDM systes due to Dopper Effect, or frequency differences between oca osciators at the transitter and receiver. With this frequency offset, the orthogonaity aong a OFDM subcarriers is ost and intercarrier interference is generated, siuated by Moose (1994) and Poet et a (1995). So intercarrier interference is the ajor setbac in OFDM and it needs to be taen into account when designing the systes.
47 3.1.1 State of Orthogonaity Matheaticay, two vectors are orthogona if, when utipied together and averaged over tie, the resut is zero. In other words, two vectors perpendicuar to each other are orthogona and their dot product is equa to zero. Frequency Figure 3.1 Orthogonay spaced carriers In counications, orthogonaity eans two signas are uncorreated or independent over a sybo interva. When two signas are orthogona, buiding a receiver that responds to one whie copetey rejecting the other is possibe. In OFDM, cross ta aong the subcarriers is prevented by the orthogonaity principe, that is, each subcarrier ust be spaced at intervas of 1/Ts, where Ts is the sybo duration for each subcarrier. As ong as orthogonaity is aintained, recovering the individua subcarrier s signas despite their overapping spectrus is sti possibe. Figure 3.1 shows the OFDM signa spectru with four subcarriers (=4).
48 Obviousy the spectra of the subcarriers are not separated but overap and the orthogona carriers are spaced in frequency by integer utipes of 1/Ts. 3.1.2 Effects of Carrier Frequency Offset Frequency Figure 3.2 Effects of Carrier Frequency Offset: Reduced Apitude and ICI The carrier frequency offset has two destructive effects on OFDM systes. The first is the reduction of the apitude of the desired subcarrier and the second is the introduction of ICI, shown in Figure 3.2. The reduction of the apitude happens because of the desired subcarrier is not saped at the pea of the sinc function of the FFT, since the sinc functions are shifted. Aso, the ICI is caused due to orthogonaity is ost between the neighboring subcarriers. Severa ethods have been proposed in the iterature to itigate the frequency-offset probe and to reduce ICI in OFDM systes.
49 3.1.3 Causes of Intercarrier Interference ICI is often odeed as Gaussian noise which affects both channe estiation, and detection of the OFDM sybos, presented by Cheon and Hong (2002) and anayzed by Sathananthan and Teabura (2001). Soe of the OFDM ipairents resebing carrier frequency synchronization errors, anayzed by Arstrong (1999), tie varying channe, investigated by Russe and Stuber (1995) and phase noise presented by Arada (2002) causes ICI in the OFDM systes. Siiary frequency offset and Dopper spread are aso reason for ICI, observed by Chen et a (1998). 3.2 PRESET ICI REDUCTIO TECHIQUES The ost extended ICI reduction ethods are frequency-doain equaization, tie-doain windowing, ICI sef-canceation and the puse shaping technique. 3.2.1 Frequency-Doain Equaization Frequency doain equaization can be used to reove the effect of distortions causing ICI. In 1993, Ahn and Lee investigated the frequency doain equaization ethod to reove the fading distortion in an OFDM signa where a frequency non-seective, tie varying channe is considered. Once the coefficients of the equaizer are found, inear or decision feedbac equaizers are used in frequency doain. Since ICI is different for each OFDM sybo, the pattern of ICI for each OFDM sybo needs to be cacuated. ICI is estiated through the insertion of frequency doain piot sybos in each sybo. Figure 3.3 shows the deonstration of piot sybo inserted aong two sub-bocs. In 2000, Chang and Powers proposed a noninear adaptive fiter in frequency doain to reduce ICI.
50 Figure 3.3 Dispersed pattern of piot in OFDM data sybo 3.2.2 Tie-Doain Windowing Tie doain windowing is used to reduce the sensitivity to inear distortions and frequency errors (ICI). Window ay be reaized with the raised cosine or other ind of function that fufis the yquist criterion. Raised cosine window is used to reduce the ICI effects. However, this intuitive window is shown to be sub-optiu and a cosed soution for optiu window coefficients is derived by Muer (2001). Apitude Frequency Figure 3.4 Raised cosine window with different ro-off factors A condition for orthogonaity of windowing schees in ters of the DFT of the windowing function is derived by Arstrong (1999). A window which reduces the side obes and preserves the orthogonaity is caed yquist
51 window. In 1996, Muschai proposed an adaptive yquist window is used to reduce the apitude of the fiter side obes depending on the ro-off factor. To reduce the sensitivity to frequency errors, usefu part of the signa and unused part of the guard period is shaped with the yquist window function. Windowing reduces overa Signa-to-noise Ratio (SR) copared with OFDM without windowing. A the windows incude Hanning, yquist, and Kaiser etc, give soe reduction in the sensitivity to frequency offset. Figure.3.4. shows the side obe agnitudes of the frequency response of raised cosine window for different ro-off factors. 3.2.3 Sef-Canceation Schee Sef-Canceation ethod is studied ost aong other ICI reduction ethods. This ethod is investigated by Arstrong et a (1998) and Sathananthan and Teabura (2001). It is aso caed as Poynoia Canceation Coding (PCC) or (haf-rate) repetition coding. The ain idea in sef-canceation is to oduate one data sybo onto a group of subcarriers with predefined weighting coefficients to iniize the average carrier to interference ratio (CIR). Due to the repetition coding, the bandwidth efficiency of the ICI sef-canceation schee is reduced by haf. 3.2.4 M-ZPSK Moduation This ethod was introduced by Sathananthan and Teabura (2002) and it can be used to reduce both PAPR and ICI. M-ZPSK eans M- point zero-padded PSK, which incudes a signa point of zero apitude in the consteation as oduation schee. The M-ZPSK schee is ess sensitive to frequency offset errors than conventiona schees. The frequency of the bit pattern of og M 2 bits in an input sybo can be counted. And the ost iey bit pattern is apped to a signa consteation of zero apitude. This increases the nuber of vanishing ters in the output of frequency seective
52 channe and thus reduces the ICI effects ore. However, transission of side inforation is necessary to et the receiver which apping is used. 3.2.5 Correative Coding Correative coding is another ethod used to copress the ICI caused by channe frequency errors shown in Figure 3.5. In this coding new sybos are deterined fro od sybos using the correation poynoia F (D) = 1-D. The expression for carrier to interference ratio (CIR) with correative coding is derived and copared with the conventiona OFDM, presented by Zhao and Haggan (1998). Without any oss in the bandwidth 3.5dB iproveent in CIR eve is gained with this ethod for Binary Phase Shift Keying (BPSK). Figure 3.5 A possibe different signa consteation for 4-ZPSK
53 3.2.6 Tone Reservation Tone reservation is another ethod which is aso adopted fro PAPR reduction technique, proposed by Sathananthan and Teabura (2001). It is based on adding a sybo dependent tie doain signa to the origina OFDM sybo to reduce ICI. The transitter does not send data on a sa subset of carriers, which are used to insert the optiized tones. 3.3 PROPOSED ICI REDUCTIO METHODOLOGY In this heading, a genera phase factor optiization agorith is proposed to reduce ICI caused by carrier frequency offset. The proposed phase factor optiization agorith shorty described that, axiu interference to signa ratio (MISR) notion is used to easure the resuting ICI presented in the OFDM systes and it is diinished by fractiona spread sequence (FSS) approach. In FSS, each boc of subcarriers is utipied by a constant phase factor and these phase factors are optiized to iniize the MISR, which resuts the reduction of ICI effect in OFDM systes. The cuuative distribution function (CDF) and copeentary cuuative distribution function (CCDF) are chosen to evauate the MISR of the OFDM signa. The CCDF is the distribution function of MISR. Given the reference eve of MISRo, the probabiity of the MISR higher, it can be expressed as, Pr ( MISR > MISRo ) = 1- ( 1- e MISRo ), MISRo > 0 where is the nuber of carriers. 3.3.1 OFDM Syste with Frequency Offset An OFDM transission sybo with point copex oduation sequence,
54 x n K j2 n / 1 X e (3.1) K where n=0,1,2,, 1 and 2+1.There is 2+1copex sinusoids which have been oduated with 2+1 copex oduation vaues (X K ). The copex enveope of the received sequence, after passing through the bandpass channe can be expressed as, y n 1 K K X H e j2 n / w n (3.2) where H is the transfer function of the channe at the frequency of the th subcarrier, is the noraized frequency offset defined as a ratio between the frequency offset and the subcarrier spacing and w n is the Additive White Gaussian oise (AWG). The deoduation process with FFT is affected by frequency offset. Y 1 n 0 y n e j2 n / (3.3) The th eeent of FFT sequence consists of three coponents; Y X H sin j 1 / e sin I W (3.4) Y 1 X S X S W 0 0, (3.5) The first coponent is the oduation vaue X odified by the channe transfer function. This coponent experiences an apitude reduction and phase shift due to the frequency offset. The second ter is the
55 ICI caused by the frequency offset and the third one is the copex Gaussian noise sape. AWG is not taen into account for further derivations. The ICI caused by the frequency offset is given by, I 1 X 0, sin j 1 / e e sin j / (3.6) 1 I X S for 0 1 (3.7) 0, where S sin sin j e 1 / e j / (3.8) Here, S - represents the ICI coefficients between the th and th subcarrier. The ICI depends on the noraized frequency offset, and the distance between th and th subcarriers (-). For zero frequency offset the ICI coefficient S K reduces to the unit ipuse sequence. 3.3.2 Maxiu Interference to Signa Ratio (MISR) written as, The received signa sape for th subcarrier after FFT can be Y 1 X S 0 X S (3.9) 0, The Maxiu Interference to Signa Ratio is defined as, MISR 0 ax I 1 2 X S 0 2 (3.10)
56 Fro the equation (3.10), MISR is the functions of both X and and it specifies the worst case ICI on any subcarrier. By iniizing the MISR the effect of ICI can be reduced. 3.3.3 Fractiona Spread Sequence (FSS) Anaysis Mode Figure 3.6 Proposed ICI reduction ode In FSS, the input data boc is partitioned into disjoint subbocs or custers which are cobined to iniize the peas. Here the data frae is partitioned into M disjoint subbocs which are represented by a vector, X=[X 1, X 2,, X M ]. Assue a subbocs are equa in size and it consists of a set of subcarriers. Then the weighted cobination of M bocs is given by, X M a X 1 (3.11) where (a, = 1, 2,, M) are weighting factors, The IFFT of X are caed Fractiona Spread Sequence (FSS). The phase factors are chosen to iniize the peas and it is to be transitted to the receiver as side inforation, concuded by Muer et a (1997) & Ciini and Soenberger (2000). Therefore, the receiver ust now the generation process of the transitted OFDM signa. 3.3.4 ICI Reduction Using FSS Approach The data fraes are partitioned into M disjoint subbocs and each subboc is zero padded to ae its ength. X = (x 0, x -1 ) now each
57 subboc is utipied by a weighting factor a. Thus, I, FSS M 1 1 0, a X S (3.12) where X is the data sybo in the newy fored th subboc. Hence the equation (3.12) can be rewritten as, I, FSS M 1 a I, I 0, 1 X S (3.13) where I is the interference on th subcarrier of boc. Thus, the tota ICI is the weighted su of ICI fro each subboc. Therefore, the ICI can be reduced by optiizing the phase sequence a = (a 1,a 2,, a M ). To reduce the copexity of the optiization process, ony binary phase factors are considered (ie. a = ±1). When a 1 = 1 there are (M - 1) binary variabes to be optiized. Finay the optia MISR can be found as, MISR optia a, in, a 0 ax 1 M X S I 1, 2 0 FSS 2 (3.14) 3.3.5 Siuation Resuts Matab siuations are perfored by using 128 subcarriers with binary phase shift eying (BPSK) oduation. For = 128, the MISR exceeds - 4 db for ony 1 out 10 4 of a OFDM bocs. Therefore, consider MISR as a rando variabe and dependent on data frae. Figure 3.7 shows that MISR as a function of for = 0.1. Figure 3.8 shows MISR for M = 8. In FSS approach, MISR exceeds -6 db for ony 1 out 10 4 of a OFDM bocs whereas that of nora OFDM MSIR exceeds -4dB. Figure 3.9 shows how the perforance varies with M.
58 Figure 3.7 MISR of ora OFDM Syste with = 0.1 Figure 3.8 MISR of an OFDM Syste with = 0.1 and M = 8
59 Figure 3.9 Variation of MISR with M for = 0.1 There are 2dB reductions in MISR over nora OFDM with M = 8. Optiized phase sequence requires 2 M-1 coputations of MISR. When M is arge, MISR reduction is arge. However, the coputationa copexity depends on M. 3.3.6 Suary The error perforance of OFDM systes with ICI anayzed by the proposed ethod and this ethod is very precise and independent of any paraeter. The introduction of MISR to quantify ICI effects is aso shown to be very usefu in designing ICI reduction schees at the transitter. The siuation resuts show that the MISR reduction at the transitter effectivey transates into iproveent in error perforance. The ain drawbac of this ethod is the optiization of phase factor, which in turn the copexity of this optiization process.