Interchannel Interference Analysis of OFDM in a Mobile Environment* Mark Russell and Gordon I;. Stuber School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, Georgia 30332-0250 Abstract - Othogonal frequency division multiplexing w i t h a suitably chosen guard interval is a n effective means of eliminating intersymbol interference for high-rate transmission over fading dispersive channels. T i m e variations of t h e channel, however, lead t o a loss of subchannel orthogonality, resulting i n interchannel interference (ICI). T h i s article examines t h e effects of IC1 t h r o u g h analysis a n d simulation, i n t h e context of a system design for digital video broadcasting t o mobile receivers. It is shown t h a t IC1 can b e modeled as a n additive Gaussian r a n d o m process t h a t leads t o a n error floor which can be determined analytically as a function of the Doppler frequency. A n t e n n a diversity a n d trellis coding are t h e n examined as methods for reducing t h i s error floor. I INTRODUCTION Orthogonal frequency division multiplexing (OFDM) is an effective technique for mitigating the effects of delay spread introduced by the mobile radio channel. OFDM uses a discrete Fourier transform (DFT) to multiplex blocks of d a t a symbols over subchannels which are spectrally overlapping yet orthogonal in time. OFDM yields high spectral efficiency and reduces the effects of intersymbo1 interference (ISI) by making the block period much larger than the delay spread of the channel. The second point is especially advantageous for high bit rate applications, such as digital video broadcasting (DVB), where the channel impulse response can extend over many symbol periods. The loss of subchannel orthogonality due to interference between d a t a blocks (ISI) can be eliminated by adding a guard interval of length greater than the maximum delay spread of the channel. For a fading channel, however, time variations also lead to a loss of subchannel orthogonality, known as interchanne1 interference (ICI). If not compensated for, IC1 will result in an error floor that increases with Doppler frequency. If the time-varying impulse response of the chan~~ *This research was supported by the Multimedia Systems R & D Division, Hitachi, Ltd. 0-7803-2742-XI95 $4.00 0 1995 IEEE ne1 can be estimated accurately, it is possible to reduce IC1 through equalization. In [3], Cimini used pilot tone assisted estimation and linear equalization before the demodulating DFT. It is also possible to use training symbol assisted estimation [7], and equalization after the DFT. Irrespective of the method, the equalizer will introduce both noise enhancement, which is especially undesirable when coding is used, and increased complexity. Furthermore, for wideband applications such as DVB, significant capacity must be sacrificed to estimate the channel with the accuracy required for effective IC1 reduction. Thus the desirability of IC1 equalization will depend on the acceptability of the unequalized error floor. For a given Doppler frequency and block length, the extent to which the channel can vary during a block period decreases with increasing symbol rate. Thus, for the high rates associated with broadcasting of HDTV, systems in the literature often assume the channel does not change significady over a block period and ignore IC1 [6, 91. At the same time, the sensitivity to errors of low bit rate HDTV decoders necessitates a bit error rate (BER) on the order of lo-’, which can make even small amounts of IC1 unacceptable. This problem is further exacerbated when considering the Doppler frequencies which result from mobile reception in vehicles such as trains and buses. The purpose of this article is to analyze the degradatiop due to ICI, illustrating the performance limitations it generates. This will be done in the context of a DVB system for transmission of HDTV. The system model is defined in Sect. 11. In Sect. 111, the origin and statistics of the IC1 are analyzed and the performance of an uncoded system is discussed. The possible performaiice improvements resulting from antenna diversity are examined in Sect. IV, and from trellis-coded modulation (TCM) in Sect. V. Some concluding remarks are given in Sect. VI. I1 SYSTEMMODEL The discrete-time baseband equivalent model of the system under coi.sideration is shown in Fig. 1. The input dat,a b, consists of source coded HDTV video plus audio 820 Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on March 30, 2009 at 10:45 from IEEE Xplore. Restrictions apply. b, Symbol - Generator Serial/ an Parallel 7I~ tap # x 1 delay ( p ) 0.0 frac. Dower 0.19 L I :zIl1 2 3 4 5 6 0.2 0.38 0.5 0.24 1.6 2.3 0.09 0.06 5.0 0.04 Table 1: 6-tap typical urban channel model, [4]. where Figure 1: System model for video broadcast system using OFDM. (4) 1 ) The symbol detector makes decisions on the transmitted data. Since mobile reception of DVB is of interest, performance is examined as a function of Doppler frequency. and control bits. Using state-of-the-art video source coding, an input rate of 20 Mbps can be achieved [SI. In order t o use the 6 MHz bandwidth T V channels in North America, the symbol generator outputs symbols a, at a rate 1/T = 5 Msps. These symbols are assumed independent, identically distributed, and possibly coded. The serial-to-parallel converter transfers blocks of symbols t o the OFDM modulator, which uses an N-point I F F T t o modulate them onto the subchannels. A guard interval of length G is then added to give a transmitted sequence corresponding t o samples a t t = ICT, of 1 x: = c N-l a,exp (j?) I11 IC1 ANALYSIS It is possible to model IC1 as additive interference by rewriting (3) as 21 = vial C I , (5) + is a multiplicative noise term and O < t < N S G - 1, M-1 n=O where & = & ( l+ g),xk is the output sequence of the IFFT, X i = X(k)Nis the sequence with guard interval, and ( k ) is~ the residue of IC modulo N . The channel is modeled as a wide sense stationary, uncorrelated scattering, Rayleigh fading channel with niaximum delay MT,. This was simulated using the 6-tap tapped-delay-line model defined in Table 1, which represents typical values for an urban environment as given in [4].T h e received sequence has the form n f l m=O is the random IC1 term. Note that when hm,k = h, (no time variations during block period), H m ( n - I) = h,6,1, where 6,i is the Kronecker delta function, and CI = 0. For N sufficiently large, the central limit theorem can be invoked and the IC1 modeled as a Gaussian random process. Since a, and H,(n - 1) are independent random variables and E[an] = 0, E [ q ] = 0, where E[ . ] is the expectation operator. For uncorrelated scattering and E[u,u;,] = E,~,,I, where E, is the symbol energy, the autocorrelation of ci can be written M-1 Ri = hm,kXi-, 2anm (1) 5 IC 5 -I- - 1j m=O M-1 where hm,k is the value of the channel impulse response a t position m and instant t. The demodulator removes the guard interval according t o Rk = R&(k-,)N, 0 k N-1, and performs a D F T on the resulting sequence. The guard interval is set to lops, resulting in no IS1 for the typical urban environments assumed here. Thus X i - , for IC < m corresponds to a value in the guard interval, allowing for independent analysis of the d a t a blocks. The demodulated sequence can be written as n$l,l+r m=O < < = u,H,(n-l)exp n=O If we further assume E[lh,,k12] = 1 and isotropic scattering, the autocorrelation becomes E, E[c~c;+,.] = E,& - ~2 27nm (-jT) o 5 1s N-1, m=O (3) N-1 N-1 JO(2afDTs(k - k’)) k=O , . [ex, (j?) N-1 M-1 ZI E I H m ( n - I ) H L ( n - I - r ) ] . (8) E[c~c;+,]= E, k=O + (1 -6,)exp ( 2;r)] j- (9) where fo is the maximum Doppler frequency and Jo(.) is the zero-order Bessel function of the first kind. Note 821 Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on March 30, 2009 at 10:45 from IEEE Xplore. Restrictions apply. 66.0 ~ N=1024 _ _ _ _ N=512 55.0 N=256 - 45.0 !!i ar v) 35.0 // 25 .O 15.0 50 f,T ( x 10-7 150 100 ,f 200 250 )O (H4 Figure 2: Signal-to-interference ratio due t o ICI. Figure 3: Error floor due t o IC1 for 16-QAM. that, due t o the symmetry of the summations over k , the autocorrelation is not influenced by the positioning of the guard interval. For symbol-by-symbol detection, it is sufficient to examine the IC1 variance, which can be simplified t o give impulse response. In practice, it may be preferable t o decrease complexity by sending pilot symbols and accepting an IC1 corrupted version of 171. Fig. 3 illustrates t h a t the choice of N represents a trade-off between loss in capacity due t o the guard interval and IC1 degradation. For N E {256,512,1024} and G = 1 0 p s / T s , the percentage of capacity lost is {16.8%, 8.9%, 4.7%}, respectively. Irrespective of N , however, even for small values of f D , a n error floor below lo-' cannot be achieved for a fading channel without additional effort. Since fading compensation is desirable in and of itself, it is of interest t o analyze the effects of fading compensation on IC1 performance. T h e next two sections will examine the ability of two common techniques, antenna diversity and trellis-coded modulation, t o provide IC1 performance improvement. N-I where the fact t h a t Jo( .) is a n even function has been used. Note t h a t the degradation due t o IC1 is only a function of E,, N , T,, and fo, and is independent of the signal constellation. Fig. 2 shows the ratio of symbol energy to IC1 power, denoted SIR, as a function of f D T for several values of N . For uncoded transmission of the 4 bits/symbol required for the DVB system, 16-QAM modulation is used. The symbol error rate (SER) will be used instead of the BER t o simplify the analysis. T h e SER for 16-QAM is [8] where yS is the instantaneous signal-to-noise ratio (SXR) per symbol. T h e SER averaged over the Rayleigh fading is found by integrating (11) over the SNR distribution 1 P(Ysj = T e x P ( - T s / y , j , Ys Ys > 0, (12) where rsis the average SNR. This was done numerically and, for large SNR, the result is SER M 6.48/Ys. Substituting the SIR for y8 gives the error floor due t o ICI, which is shown in Fig. 3. Simulation results are also given to confirm the analysis. This result assumes perfect knowledge of ~ l which , can be derived by estimating the channel IV ANTENNADIVERSITY Antenna diversity is an effective means of reducing the degrading effects of a fading channel, as well as being 'compatible with coding. I t is thus of interest t o examine the ability of antenna diversity t o reduce the effects of ICI. There are a variety of signal combining methods which offer a trade-off between performance and complexity [SI. In terms of IC1 performance, however, the less complex, power-based combining techniques such as selection diversity will offer no improvement. This is because IC1 is not a function of signal power, but rather the rate a t which the channel varies. T h u s this section will consider maximum ratio combining (MRC). It will be assumed that the received signals a t the various antennas are mutually uncorrelated. MRC uses knowledge of the channel state information (CSI) and the fact that the CSI is uncorrelated with the noise to improve the received SNR. For the OFDM system 822 Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on March 30, 2009 at 10:45 from IEEE Xplore. Restrictions apply. of the analog TV channel is either 7 or 8 MHz. However, for a 6 MHz bandwidth, the increase in bit rate due t o RS coding would necessitate an increase in signal constellation size in order t o maintain the extra bandwidth needed t o absorb the guard interval, pilot symbols, adjacent channel protection, and NTSC co-channel interference rejection. Thus only TCM will be considered. The symbol generator of Fig. 1 is now considered to also contain a TCM encoder, while the symbol detector contains a Viterbi decoder. It is assumed that interleaving, which for OFDM can be done in both frequency and time, is sufficient such that successive symbols are independently 10" I 0" a, c d IOJ j ,0'5 L IO4 (I) 10-7 1 Io'B 10" 50 100 150 200 250 1 a a a i ] faded. NumerLal terleaving is also sufficient to provide successive samples whose IC1 terms are uncorrelated. 300 fo (W Figure 4: Error floor due t o IC1 for 16-&AM and antenna diversity with MRC. using D antennas, the combining will be performed after the demodulating F F T , thus requiring D front-ends and D OFDM demodulators. The resulting decision variable is D 2,= 1v;12al + vp'cp. (13) d= 1 MRC will improve IC1 performance in the same way as it improves noise performance as described in [8] if 17; and c;" are uncorrelated. The prescence of the data a, in CI provides this decorrelation. The SER performance of 16&AM can be calculated by replacing the SNR distribution of (12) with where I/e is the average SNR per diversity channel. The IC1 performance can be calculated by substituting the SIR for 'ye, which is shown in Fig. 4 for N E {512,1024} and D E { 1 , 2 , 3 , 4 } . It can be seen that the diversity gain resulting from MRC can provide an acceptable error floor over a wide range of Doppler frequencies. Note that, since the rate of increase in IC1 power decreases with Doppler frequency, values of D > 2 offer a significant extension of the range of fo over which a SER of lo-' can be achieved. V TRELLIS-CODED MODULATION Channel coding is another technique for improving performance on a fading channel. Due to the bandwidth constraints imposed on DVB, the bandwidth efficiency of TCM makes it a sensible candidate. Some papers have suggested reducing the requirements on the TCM code by concatenating an outer Reed-Solomon (RS) code. This is a reasonable suggestion for Europe, where the bandwidth V-A &AM Coding For the Rayleigh channel, the error rate decreases exponentially with the minimum error event length I, and linearly with the product distance of the error events. Thus ,I is the most important design parameter. As shown in [5] for rate R / ( R 1) coding, as n increases the value of I , achievable for a given constraint length v decreases. In fact, for rate 4/5 coding v = 9 is required to achieve 1, = 3. This is important because the complexity of the assumed Viterbi decoder increases exponentially with v. Improved performance can be achieved by using rate d / ( d 1) coding with PAM modulation independently on the in-phase (I) and quadrature (Q) channels [a], where R' = n/2. For R = 4,this gives rate 2/3 coding on the I and Q channels, for which ,I = 3 can be achieved with v = 4 . The resulting overall constellation is 64-&AM. The codes chosen are given in [2] and were designed for 8-PSK on the Rayleigh channel. -+ + V-B Performance Bounds Since ideal CSI is assumed, the SER for the hybrid, two-dimensional coding scheme can be determined from that of the one-dimensional %PAM coding scheme via SER2d = 1 - ( I - S E R I ~ ) ~ . (15) An upper bound on performance was obtained using the Chernoff bound on the error event probability and a truncated union bound on the overall error probability [a]. Since the codes are uniform, the code spectrum can be determined by comparing error events versus the all zero code word and using the error weight profile for 8-PAM. The Chernoff bound is then calculated for each error event and multiplied by the number of symbol errors corresponding to that error event. Finally, an approximation on the union bound for the overall error probability is found by summing the SER probabilities due to error 823 Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on March 30, 2009 at 10:45 from IEEE Xplore. Restrictions apply. I 10-$’8 ,f d ’ ’ 50 I’ 100 ’ 150 f, I 1 200 I I 250 1 300 (W Figure 5: IC1 error floor using TCM, f, N = 1024. + events which have length 5 I, 3. A lower bound on the error probability can be determined by calculating the exact error probability due t o the most likely error event, as described in [l]. The bounds on IC1 error floor for v E {3,5,7} are given in Fig. 5 for N = 1024 and Fig. 6 for N = 512. Simulation results are also given to confirm the bounds. T h e codes illustrated here have lower bounds that include only a single error event of length .,I Thus the lower bound becomes tighter much more rapidly for these codes than for codes having multiple error events of length 1., These results show that using T C M coding independently on the I and Q channels is an effective method of reducing the effects of ICI. Furthermore, for the low error rates required for DVB, moving to larger values of v offers significantly more gain than for applications where the error rate constraints are less strict. VI (H4 Figure 6: IC1 error floor using T C M , N = 512. considered in this paper, it is reasonable that a combination of diversity and T C M would provide even further performance improvement. REFERENCES [l] E. Biglieri and P.J. McLane, “Uniform distance and error probability properties for TCM schemes,” IEEE Trans. Commun., vol. 39, No. 1, pp. 41-52, Jan. 1991. [2] A. Brajal and A. Chouly, “Optimal trellis-coded 8-PSK and 4-AM modulations for the Rayleigh channel,” Proc. ICC ’94, pp. 28-33, New Orleans, Dec. 1994. [3] L.J. Cimini, Jr., “Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing,” IEEE Trans. Commun., vol. COM-33, pp. 665-675, July 1985. [4] COST 207 Management Committee, “COST 207: digital land mobile radio communications,” Commission of the European Communities, Luxembourg 1989. CONCLUSIONS [5] J. Du, Y. Kamio, H. Sasaoka, and B. Vucetic, “Tcellis- coded M-QAM for efficient data transmission over land mobile radio channels,” Proc. PIMRC ’93, pp. C1.6.1C1.6.5, Yokohama, Sept. 1993. T h e interchannel interference resulting from the use of OFDM over a Rayleigh fading channel has been analyzed in the context of a system for transmission of HDTV to mobile receivers. It was shown that IC1 leads to an error floor dependent on the number of subchannels and the fading rate. For the error rates in the range of lo-’ required by state-of-the-art video source decoders, IC1 alone can lead to an unacceptable error rate. Antenna diversity and trellis-coded modulation were examined as methods of reducing the error floor. Antenna diversity with maximum ratio combining was found to provide acceptable performance over a wide range of Doppler frequencies. This was also found to be the case for T C M . T h e performance improvement using rate 2/3 coding independently on the I and Q channels versus 2dimensional rate 4/5 coding was discussed. Although not [6] J.F. Helard and B. Le Floch, “Trellis coded orthogonal frequency division multiplexing for digital video transmission,” Proc. GLOBECOM ’91, pp. 785-91, Phoenix, Dec. 1991. [7] P. Hoeher, “ T C M on frequency-selective land-mobile fading channels,” Proc. of Fifth Tzrrenia International Workshop, pp. 317-28, Tirrenia, Sept. 1991. [SI J.G. Proakis, Digital Communications, McGraw-Hill: New York, 1983. [9] M . Sablatash, “Transmission of all-digital advanced television: state of the art and future directions,” IEEE Trans. Broudcasting, vol. 40, pp. 102-121, June 1994. 824 Authorized licensed use limited to: Georgia Institute of Technology. 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