CHAPTER 3 ADAPTIVE MODULATION TECHNIQUE WITH CFO CORRECTION FOR OFDM SYSTEMS

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1 44 CHAPTER 3 ADAPTIVE MODULATION TECHNIQUE WITH CFO CORRECTION FOR OFDM SYSTEMS 3.1 INTRODUCTION A unique feature of the OFDM communication scheme is that, due to the IFFT at the transmitter and the FFT at the receiver, the frequency selective fading channel is converted into flat fading channels. However the OFDM approach can suffer from CFO (Leke and Cioffi 1998). The effects of CFO has been analyzed quite extensively in Beek et al (1997) and Jungwon Lee et al (006). Carrier Frequency error in the transmission due to synchronization errors and Doppler shift results in loss of orthogonality between the subcarriers. There are two deleterious effects caused by CFO, one is degradation of SNR and the second is introducing ICI (Ma et al 003). Due to this SNR degradation, the performance of BER is poor. The orthogonality among OFDM subcarriers are destroyed because of CFO. It causes the leakage of FFT, and eventually leads to common phase error (CPE) and ICI among subcarriers. Also a CFO of only 1 - % of the subcarrier spacing results in the effective SNR being limited to 0 db (Santhanam and Tellambura 001, Martin and Hermann 007). In OFDM scheme, some subcarriers may undergo a deep fading. Adaptive modulation technique can be employed to mitigate the deep fading effect if the CSI is available at the transmitter (Keller and Hanzo 000, Chung and Goldsmith 001, Yue Rong et al 006). Conventionally CSI is estimated

2 45 from average signal to noise ratio of received OFDM signals. The performance of adaptive modulation technique depends on the accurate estimation of CSI. But in practice the CFO will make the estimated CSI to deviate from the actual CSI. This imperfect estimated CSI will reduce the spectral efficiency greatly. Hence accurate estimation technique and correction techniques are very much essential. As an attempt, in this thesis the effect of CFO, estimation of CFO and correction techniques are analysed and a novel adaptive modulation technique to maximize the spectral efficiency of the OFDM system has been proposed. The BER is used as the criterion to evaluate the system performance. With the assumption that the feedback channel is perfect, adaptive modulation selection (AMS) is used to exploit the feedback CSI and the results are compared with non adaptive modulation (fixed modulations) systems. This thesis analyzes the impact of CFO on the performance of AMS for OFDM systems. Although AMS scheme has better performance when the CFO is very low, it behaves worse, when the CFO is large. In the proposed method, the CFO is estimated using MLE which is followed by correction of CFO and then estimation of CSI for adaptive modulation selection. 3. SYSTEM MODEL OF PROPOSED OFDM SYSTEM OFDM partitions the incoming data stream into N low rate parallel substreams, as shown in the baseband equivalent model of Figure 3.1. In order to obtain the time domain signals it modulates a set of subcarriers using IFFT. A CP is then added to the time domain signal to eliminate ISI caused by channel multipath fading and enables simple channel equalization at the receiver. The IFFT is performed on the transmitted symbol X ( k ), k=0, 1, N-1, to produce the time domain samples x ( n) of the m-th OFDM symbol (Chung and Goldsmith 001): m m

3 46 1 N 1 j k( n N ) / N, for 0 n N N 1 g g X ( k) e N m x ( n) k 0 m 0 otherwise (3.1) where N and N g are the number of data samples and CP samples, respectively. The OFDM symbol x ( n) is passed through a Rayleigh fading m channel hm ( n) and is affected by AWGN W(n). When the oscillator of the receiver is perfectly matched to the carrier of the received signal, a carrier frequency offset and a phase offset will not appear. Then the received signal can be represented as follows: y [ n ] h [ n ] * x [ n ] w ( n ) (3.) m m m where * is the convolution operator. The insertion of guard intervals renders the received carriers orthogonal on the N point symbol interval. However the demodulation process, which is implemented with a DFT, is affected by CFO. The CFO will appear when the oscillator of the receiver is not perfectly matched to the carrier of the received signal (Jung won Lee et al 006). After removing the CP and taking the N point DFT at the receiver, (k+r) th subcarrier signal of the m th symbol can be expressed as Y ( k r) X ( k ) H ( k ) C (0) m m m m N 1 X ( k l) H ( k l) C ( l) Z ( k r) m m m m l 1 l 0 (3.3)

4 47 where sin j ( N 1) / N j ( l r ) / N Cm ( l) e e N sin( ( l r ) / N ) (3.4) From equation (3.3), it can be seen that the received signal is attenuated by the factor offset which is defined as C sin m (0) N sin( / N ) fnt, where is normalized frequency. In equation (3.3) the second term is the ICI caused by the frequency offset. Third term Z ( k r) denotes the AWGN noise with zero mean and variance. m Input Data. Adaptive Mod S/P IDFT. Cyclic prefix. P/S h ( ) m n CSI Estimation j f [ nm( NNg )] T e X Output Data Adaptive De- Mod P/S. DFT. Remove Cyclic prefix. S/P + y ( ) m n w( n ) CFO estimation & correction Figure 3.1 Block diagram of proposed OFDM system using adaptive modulation with CFO correction The effect of ICI in OFDM systems is mitigated by statistically estimating the frequency offset and canceling this frequency offset at the receiver. In this technique, an OFDM symbol stream of N symbols is replicated. These symbols are then modulated using a N-point IFFT. At the

5 48 receiver, to get the sequence Y 1k the first set of N symbols are demodulated using an N-point FFT, and the second set is demodulated with another N- point FFT to yield the sequence Y k. The frequency offset is the phase difference between Y 1k and Y k, that is, Y j k Y1 ke (Beek et al 1997). The ML estimate of the normalized frequency offset is given by K Im * Y Y 1 k 1k tan 1 k K K Re Y Y * k 1 k k K (3.5) This ML estimate is a conditionally unbiased estimate of the frequency offset and will be computed using the received data (Moose 1994). Once the frequency offset is known, the ICI distortion in the data symbols can be reduced by multiplying received symbols with a complex conjugate of the frequency shift. 3.3 ADAPTIVE MODULATION SELECTION Adaptive modulation is a powerful technique for maximizing the data throughput of subcarriers allocated to a user. Adaptive modulation involves measuring the SNR of each subcarrier in the transmission, then selecting a modulation scheme that will maximize the spectral efficiency, while maintaining an acceptable BER (Keller and Hanzo 000, Chung and Goldsmith 001). The AMS scheme is based on the following idea. When a certain subcarrier is corrupted by fading channels, a constellation with smaller dimension and higher transmitted power can be assigned to this particular carrier, while constellation of large dimensions and less transmitted power can be assigned to the subcarriers whose channel gain is high. The modulation

6 49 scheme was chosen from the set of Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), 16-level Quadrature Amplitude Modulation (16-QAM), 64-level Quadrature Amplitude Modulation (64- QAM), as well as No Transmission, for which no signal was transmitted. Each scheme provides a trade off between spectral efficiency and the BER (Keller and Hanzo 000). This adaptive modulation has greater performance than conventional non adaptive modulation technique. The spectral efficiency can be maximized by choosing the highest data rate modulation scheme that will give an acceptable BER. In systems that use a fixed modulation scheme, the modulation scheme must be designed to provide an acceptable BER under the worst channel conditions. This results in the usage of using BPSK or QPSK most systems. However, these modulation schemes give a poor spectral efficiency (1 - bps/hz) and results in an excess link margin most of the time. Using adaptive modulation, the remote stations can use a much higher data rate modulation scheme when the radio channel is good. Thus as a remote station approaches the base station, the modulation can be increased from 1 bps/hz (BPSK) up to 4-8 bps/hz (16-QAM 56- QAM), significantly increasing the spectral efficiency of the overall system. Adaptive modulation scheme can effectively control the BER of the transmission, as subcarriers that have a poor SNR can be allocated a low modulation scheme such as BPSK or none at all, rather than causing large amounts of errors with a fixed modulation scheme. This significantly reduces the need for Forward Error Correction(FEC). In order to keep the system complexity low, the modulation scheme is not varied on a subcarrier-by-subcarrier basis, instead the total OFDM bandwidth of total subcarriers is split into blocks of adjacent subcarriers, referred to as subbands. The same modulation scheme is employed for all subcarriers of the same subband. This substantially simplifies the task of modem mode signaling.

7 ADAPTIVE MODULATION FOR OFDM SYSTEMS The instantaneous data rate is defined as s( ) / T (bps), where s s( ) log [ M ( )] (bits/symbol), T s is the symbol period, γ is the instantaneous average SNR and M is the constellation size. Assuming Nyquist data pulse B = 1/T s, then the spectral efficiency of the discrete rate adaptation is given by (Chung and Goldsmith 001) R N -1 i 1 s p ( ) B d i i 0 i bps/hz (3.6) For the discrete rate case, the rate region boundaries -1 i define i 0 the range of γ values over which different constellations are transmitted. More clearly, the different constellation sizes correspond to a set of discrete rates N s 1 which are allocated respectively to each fading region [ i, i 1] (0 i i i 0 N 1). When the instantaneous SNR γ falls within a given fading region, the associated signal constellation is transmitted. N This thesis investigates the spectral efficiency under a constrained average BER requirement with the assumption that M-QAM is employed for each subcarrier, and β [m, k] bits/symbol are sent for the k th subcarrier in the m th block.. According to algorithm in Chung and Goldsmith (001), given the channel frequency response H [n, k], the instantaneous BER can be approximated as 1. 6 H [ m, k ] p [ m, k ] 0. e x p e [ m, k ] 1 (3.7)

8 51 In the following sections, non adaptive modulation where the constellation size is fixed irrespective of channel, ideal adaptive modulation where the perfect CSI information is available at the transmitter and the proposed adaptive modulation techniques have been presented and their performances have been analyzed Non Adaptive Modulation for OFDM Systems In the case of non adaptive modulation, where β [m, k] =β is a constant for all n and k. Since H[m, k] is a complex Gaussian random variable and all H[m,k] have identical distributions, the overall average BER becomes (Yue Rong et al 006) 1.6 p E { P [ m, k ]} e H [ m, k ] e (3.8) In the non adaptive modulation, the spectral efficiency is derived by inverting the equation (3.8). The maximum number of bits that can be transmitted for the given target BER (P target ) constraint is 1.6 lo g P t a rg e t (3.9) The spectral efficiency (number of bits per second per Hz) is equal to β, under the assumption that the symbol interval is the reciprocal of the sub channel and bandwidth. Here the spectral efficiency is fixed throughout the transmission.

9 Ideal Adaptive Modulation for OFDM Systems There is no possibility to maximize the spectral efficiency with respect to the channel conditions in non adaptive modulation, because the constellation size is fixed throughout the transmission. Hence an adaptive modulation technique has been adapted in recent OFDM systems, but it requires the CSI. For adaptive OFDM, different modulation schemes are used for different subchannels. In adaptive modulation, the perfect knowledge of the receiver channel information is assumed to be available at the transmitter.to achieve the acceptable target BER (P target ), the number of bits transmitted in each subchannel can be derived from equation (3.7) as 1.6 H [ m, k ] [ m, k ] log 1 0. ln P t arg et (3.10) Therefore, the average spectral efficiency R is R E [ m. k] (3.11) H[ m. k] In ideal adaptive OFDM, the CSI is assumed to be perfect, but this is not the case in practical. The effect of CFO is not considered in existing adaptive OFDM. The average received SNR is attenuated by CFO, hence it leads to have low spectral efficiency. This problem is alleviated by compensating the CFO before performing the adaptive modulation.

10 PROPOSED ADAPTIVE MODULATION WITH CFO CORRECTION TECHNIQUE The spectral efficiency of the proposed adaptive modulation with CFO has been derived theoretically and it is expressed as follows. 1.6 ( ) H [ m, k ] [ m, k ] lo g 1 0. ln P t a rg e t (3.1) ( ) is the average SNR in the presence of CFO for AWGN channel and can be expressed as C (0) ( ) m (1 C (0) ) 1 m (3.13) where C m sin (0) (3.14) N sin( / N ) The average SNR ( ) in the absence of CFO is attenuated by the factor C (0 m ). The CFO will directly affect the received average SNR. This attenuation is more noticeable when SNR is large. Due to this the adaptive modulation without CFO correction will not maximize the spectral efficiency. The proposed method corrects the CFO before the estimation of CSI that is threshold is measured after the CFO correction. Thus by introducing the CFO correction in adaptive modulation, the attenuation of SNR is compensated and hence the spectral efficiency is improved. This spectral efficiency improvement is validated using extensive simulation results.

11 Proposed Adaptive Modulation Algorithm Step 1 : Estimate the threshold SNR (i.e. region boundaries) for the given target BER using the following equations 1 1 [ erfc (. BER)] n n K0( 1); n 0,,3..., N, 3 N 1 where K 0 ln(5. BER) Step : Estimate the CFO using equation (3.5) and compute C (0 m ) using equation (3.13) Step 3 : Step 4 : Determine the average SNR of the received signal using C (0) ( ) (1 m C m (0) ) ( ) Compare this received average SNR with threshold SNR and select the constellation size M. If 1 then no transmission If 1 then M = (BPSK or QAM) If 3 then M = 4 (QPSK or 4QAM) If 3 4 then M = 16 (16QAM) and so on. Step 5 : Perform the adaptive modulation with respect to the size M.

12 SIMULATION RESULTS AND DISCUSSION Monte Carlo simulation is performed to evaluate the average SNR in the presence of CFO. In this work, MLE is used to estimate the CFO. The proposed adaptive modulation algorithm for the OFDM system has been implemented and the results are validated using Matlab 7.1. The channel is considered to be Rayleigh fading channel and the noise is assumed to be AWGN. The simulation parameters are summarized in Table 3.1(Yue Rong et al 006 and Jungwon Lee et al 006). Table 3.1 Simulation parameters Parameter Value Bandwidth for each user 0MHz Number of subcarriers 64 Number of pilots 4 Subcarrier frequency spacing MHz IFFT/FFT period 3. µs Guard interval duration 0.8 µs Modulation method Adaptive modulation ( BPSK, QPSK, 16QAM, 64QAM) To measure the boundary SNR regions for adaptive modulation, the OFDM system has been implemented with different fixed modulation schemes such as BPSK, QPSK, 16 QAM and 64 QAM, which is shown in Figure 3..

13 QAM 16QAM QPSK BPSK BER SNR(dB) Figure 3. SNR versus BER for the OFDM system using different modulation schemes Figure 3. shows the comparison of SNR vs BER for different modulation techniques. It shows that the BER rate mainly depends on the constellation size M. BPSK provides good BER performance, but its spectral efficiency is only 1bps/Hz, which is very low compared to other modulation schemes. At the same time 64QAM will able to provide better spectral efficiency that is 6bps/Hz, but it fails to maintain good BER performance and thus low QoS. These modulation techniques are fixed modulation techniques. It provides fixed data rate irrespective of channel conditions. To maximize the spectral efficiency with achieving target BER, adaptive modulation technique is used in practice. The adaptive modulation scheme relies on the estimated CSI. Conventionally CSI could easily be affected by CFO. So in this proposed method the CFO correction is first done using ML before estimating the CSI. The range of average SNR for the various modulation schemes have been derived from step 1 of the proposed algorithm or the threshold SNR (i.e. region boundaries) have been measured using Figure 3.. These boundary values are tabulated in Table 3..

14 57 Table 3. Required SNR and corresponding modulation technique for different target BER Types of Modulation Technique BPSK QPSK 16QAM 64QAM Target BER db 18 db 7 db 3 db db 16 db 5 db 30 db db 15 db db 7 db For a particular target BER, with respect to the received SNR the proposed algorithm selects an optimal cancellation size to maximize the spectral efficiency of the OFDM system. Initially a low rate modulation technique is chosen and then the instantaneous SNR of the channel with CFO is measured and it is shown in figure 3.3. Figure 3.3 shows that SNR degradation is more when CFO is higher. Also the result shows that SNR degradation is more for the higher values of actual SNRs than for the lower values of actual SNRs. These SNR degradations for different CFO are tabulated in Table 3.3. Figure 3.4(a) shows that the spectral efficiency of adaptive modulation with different value of CFO. The adaptive modulation with CFO = 0. and CFO=0.3 at the SNR of 5dB gives average spectral efficiency of 1.6 bps/hz and 0.9 bps/hz respectively which is much less than the non adaptive modulation technique.

15 58 Avg SNR in presence of CFO (db) CFO=0.1 CFO=0.05 with absence of CFO Avg SNR in absence of CFO(dB) Figure 3.3 Average SNR in the presence of CFO From the results shown in Figure 3.4 (a), it can be observed that the high CFO leads to low spectral efficiency. Whereas the proposed algorithm compensates the attenuation level in SNR due to CFO. This is the main reason for the proposed algorithm to achieve high spectral efficiency. Figure 3.4(b) shows that the spectral efficiency of non adaptive modulation is poor. Adaptive modulation with CFO = 0.05 has a better spectral efficiency than the adaptive modulation with CFO = 0.1 and non adaptive modulation scheme. The proposed adaptive modulation with CFO correction technique gives better performance than the adaptive modulation with CFO and non adaptive modulation techniques. The proposed algorithm gives the spectral efficiency improvement of 5 bps/hz which is comparatively greater than non adaptive modulation technique and adaptive modulation with CFO.

16 59 Avg Spectral Efficiency(bps/Hz) Adaptive Mod with CFO=0.3 Adaptive Mod with CFO=0. Adaptive Mod with CFO=0.1 Adaptive Mod with CFO=0.05 Proposed SNR(dB) Figure 3.4 (a) Average spectral efficiency for adaptive OFDM with different CFO in CSI and Ptarget=10-3 Avg Spectral Efficiency(bps/Hz) Non Adaptive Mod Adaptive Mod with CFO=0.1 Adaptive Mod with CFO=0.05 Proposed SNR(dB) Figure 3.4 (b) Average spectral efficiency of OFDM system with adaptive modulation with CFO and non adaptive modulation

17 60 The average spectral efficiency is higher for the case without CFO for a given P target. Also the performance in spectral efficiency varies with P target i.e. decreasing the P target will result in small reduction in spectral efficiency as shown in Figure 3.5. The proposed adaptive modulation algorithm gives a very small reduction in the spectral efficiency for the low target bit error rate. This small spectral efficiency reduction of bps/hz for a change in target BER of 0.01 to is within the acceptable range which is shown in Figure 3.6. Average Spectral Efficiency(bps/Hz) CFO=0.1 with Ptarget=0.001 Proposed with Ptarget=0.001 Proposed with Ptarget= CFO=0.1 with Ptarget= SNR(dB) Figure 3.5 Average spectral efficiency of adaptive OFDM with different CFO for different Ptarget Figure 3.7 shows the comparison of SNR verses BER for adaptive modulation using feedback and other modulation schemes. BER performance of adaptive modulation technique is same as the performance of BPSK modulation scheme. Adaptive modulation provides better BER performance than the QPSK, 16QAM and 64QAM modulation techniques. Thus the proposed adaptive modulation with CFO correction maximizes the spectral efficiency and provides good BER performance than the fixed modulation schemes.

18 61 Avg Spectral Efficiency (bps/hz) Ptargat=0.01 Ptarget=0.001 Ptarget= Ptarget= SNR(dB) Figure 3.6 Average spectral efficiency of proposed adaptive modulation for OFDM systems with different Ptarget QAM 16QAM QPSK Adaptive modulation BER SNR(dB) Figure 3.7 SNR versus BER for adaptive modulation with CFO correction

19 6 3.7 CONCLUSION In this thesis, the influences of the CFO on adaptive modulation in OFDM transmission over AWGN and fading channels have been investigated. In systems that use a fixed modulation scheme (non adaptive modulation schemes) the subcarrier modulation must be designed to provide an acceptable BER. This results in most systems using BPSK or QPSK. However these modulation schemes give a poor spectral efficiency of 1 - bps/hz. Simulation results show that the adaptive modulation with CFO=0.05 achieves average spectral efficiency of 4 bps/hz and with CFO=0.1, it gives the maximum spectral efficiency of 3 bps/hz for the target BER of The proposed adaptive modulation scheme maximizes the average spectral efficiency up to 8 bps/hz for the target BER (Ptarget) of The proposed adaptive modulation technique is manifested by computer simulations and the simulation results exhibit better performance than the conventional adaptive and non adaptive modulation techniques. In this chapter, adaptive modulation scheme with CFO correction has been proposed to maximize the spectral efficiency of OFDM systems. Even though it maximizes the spectral efficiency, system capacity is not improved significantly. So, the resources such as subchannel, bit and power are needed to be optimized to increase the system capacity of the multiuser OFDM systems. A novel ARA algorithm for multiuser OFDM system has been proposed to maximize system capacity and to achieve good QoS, which is presented in chapter 4.

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