Error Analysis in Different ICI Cancellation Techniques in OFDM
(Paper ID: 60300720144)
Rajni kant Manoj Kumar
University School of Information and Communication Technology, GGSIPU, Delhi, India.
Associate Professor in University School of Information and Communication Technology, GGSIPU, Delhi, India E-mail: [email protected] E-mail: [email protected]
Abstract: Orthogonal frequency division multiplexing (OFDM) is multi carrier modulation scheme, main disadvantage of OFDM system is its sensitivity against inter carrier interference (ICI). ICI is introduced in the OFDM system due to offset between the transmitted and received carrier frequencies. ICI cause the loss of orthogonaility and degrade the performance of the system. This paper presents the ICI analysis in standard OFDM system and techniques to reduce the effect of inter carrier interference (ICI). The techniques used to reduce the effect of ICI are self cancellation technique maximum likelihood estimation technique and extended kalman filter technique. Theoretical bit error rate expression of the standard OFDM system has been discussed and a comparison has been made of different ICI reducing techniques.
Keywords: Orthogonal frequency division multiplexing (OFDM), offset carrier frequency; inter carrier interference (ICI), self cancellation (SC), kalman filter, maximum likelihood estimation.
I. INTRODUCTION
Orthogonal frequency division multiplexing system (OFDM) [1] the system in which input bit stream multiplexed into N symbols with the interval Ts and each symbol stream use to modulate parallel synchronous sub carrier. The sub carriers are spaced by 1/NTs in frequency domain. They are orthogonal over interval up [0, Ts]. A DT OFDM transceiver is shown in Fig.. 1 First (s/p) serial to parallel converter converts the group of input bits from the source encoder into the group of log2M bits, where m alphabet, total N such symbols, Xm are created, and then N symbols are mapped.
There IFFT [2] correspondence to the orthogonal subcarrier of OFDM symbols. OFDM symbols can be expressed as
(1)
Where Xm’s are baseband symbols on each sub-carrier D/A converter then and creates analog time domain signals.
Fig.1. Baseband OFDM transceiver system.
At receiver end signal is converted back to discrete N point sequence y(n), corresponding to each subcarrier. This discrete signal is demodulated using N point FFT.
Demodulated symbol stream can be given by.
(2)
Where W(m) is Baseband signal on each sub carrier.
Digital to analog converter converts and create analog time domain signal.
(3) Where w(n) is corresponds to additive white Gaussian noise [3] in the channel. Received signal is given by
II. ANALYSIS OF ICY
Due to difference in the frequency of local oscillators at transmitter and receiver, small difference
in the frequency is present called as frequency offset that is the cause of ICI.[3]
Fig. 2. Frquency offset model.
Where ε is normalized frequency offset, and is given by ΔfNT is the frequency difference. Ts is the sub-carrier symbol period. The effect of this frequency offset on the received symbol stream can be understood by considering received symbol Y [K] on kth subcarrier.
(4)
K=0, 1, ---N-1.
Where N is total number of sub carrier, X[k] is the transmitted symbol for kth subcarrier, nk is the FFT all W(n), S(l-k) is the complex coefficients for the ICI components in the received signal. The complex coefficient can be given by.
(5)
0 5 10 15
0 0.5 1
Subcarrier index k
|S(l-k)|
0 5 10 15
0 0.2 0.4 0.6 0.8
Subcarrier index k
Real(S(l-k))
0 5 10 15
-0.5 0 0.5
Subcarrier index k
Imag(S(l-k))
Fig. 3. ICI coefficents
Carrier to interference ratio is the ratio of signal power to the power in the interference components. It indicates the signal quality and can be given by.
(6)
III. SELF CANCELLATION TECHNIQUE
ICI self cancellation [4], [5], [6], scheme required that the transmitted signal to be constrained such that X(1) = - X(0), X(3) = -X(2), X(N-1) = -X(N-2) and so on. This transmitted symbol allows the received signal on the subcarrier k and k+1 to be written as.
(7)
(8) and ICI coefficient S’(l-k) is defined as
S’(l-k) =S(l-k)-S(l+1-k)
0 10 20 30 40 50 60
-70 -60 -50 -40 -30 -20 -10 0
Subcarrier index k
dB
Comparrison of |S(l-k)|, |S`(l-k)|, and |S``(l-k)| for = 0.2 and N = 64
|S(l-k)|
|S`(l-k)|
|S``(l-k)|
Fig. 4.Comparison of |S(l-k)|,|S’(l-k)|, and |S”(l-k)|
IV. ICICANCELLING DEMODULATION
ICI modulation schemes introduce redundancy in the received signal since each pair of subcarriers transmit only
one data symbol. This redundancy can be exploited to improve the system power performance while it surely decreases the bandwidth efficiency. To take advantage of this redundancy, the received signal at the (k+1)th subcarrier ,where k is even ,is subtracted from kth subcarrier. This is expressed mathematically as
(9) Subsequently, the ICI coefficients for this received signal becomes
(10)
When compared to the two previous ICI coefficients |S(l- k)| for the standard OFDM system and |S’(l-k)| for the ICI canceling modulation, |S’’(l-k)| has the smallest ICI coefficients, for the majority of l-k values, followed by |S’(l- k)| and |S(l-k)|. This is shown in Fig. 5 for N = 64 and ε = 0.4. The combined modulation and demodulation method is called the ICI self-cancellation scheme.
The reduction of the ICI signal levels in the ICI self- cancellation scheme leads to a higher CIR. The theoretical CIR can be derived as
(11)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-10 0 10 20 30 40 50 60
Normalized Frequency Offset
CIR (dB)
CIR versus for a standard OFDM system
Standard OFDM system ICITheory
Fig. 5. CIR versus ε for a standard OFDM system
Fig. 5 shows the comparison of the theoretical CIR curve of the ICI self-cancellation scheme and the CIR of a standard OFDM system. As expected, the CIR is greatly improved using the ICI self-cancellation scheme. The improvement can be greater than 15 dB for 0 < ε < 0.5.
The redundancy in this scheme reduces the bandwidth efficiency by half. This could be compensated by transmitting signals of larger alphabet size. Using the theoretical results for the improvement of the CIR should increase the power efficiency in the system and gives better results for the BER.
Hence, there is a tradeoff between bandwidth and power tradeoff in the ICI self-cancellation scheme.
V. MAXIMUM LAKLIHOOD ESTIMATION TECHNIQUE
When OFDM symbol of sequence length N is replicated, the receiver in the absence of noise, 2N point sequence
(12) Where k = 0, 1, ----N-1, N≥2k+1
Where [X(k)] are the 2k+1 complex modulation value used to modulate 2k+1 sub carriers, N(k) is the channel transfer function for kth carrier and ε is the normalized frequency offset of the channel.
The first set is demodulated using another N point FFT to the sequence R1[k] and second set is demodulated using another N point FFT to the sequenceR2(k). The frequency offset is the phase difference between R1(k) and R(k)2 , that is
R2(k)=R1(k)ej2πε Adding the AWGN
Y1(k)=R1(k)=W1(k) Y2(k)=R1(k)ej2πε+w2(k) K=0,1, N-1
The maximum likelihood estimate [9], [10], of normalized frequency offset is given by.
(13)
Once the frequency offset is known the ICI distortion in the data symbol is reduced by multiplying the received symbol with the complex conjugate of frequency shift and applying the FFT,
(14)
Fig. 6. Error respose improvement.
VI. EXTENDED KALMAN FILTER.
The Kalman filter[11] is recursive estimation algorithm that has found various applications in the communication.
The recursive filters are particularly applicable to the non stationary processes such as signal is transmitted in the time variant radio channel. The Kalman filter computes estimates of its own performance as the part of recursive and use then information to update the estimate at each step. The estimation procedure is adjusted to the time variant statistical characteristic of the random process.A state space model of discrete Kalman filter is defined as
Z(n)=a(n)d(n)+v(n) (14)
Where the observation Z(n) has a linear relationship with the desired value of d(n). By using the discrete Kalman filter, d(n) can be recursively estimated based on the observation of Z(n) and update estimation in each recursion. Received symbol are
Y(n)=x(n)e2πε(n)/N+w(n) (15)
Where y(n) is nonlinear relationship with desired value of E(n)
Y(n)=f[ε(n)+w(n)]
(16)
Where f[ε(n)=x(n)e2πε(n)/N First order taylor’s expression.
(17)
Where is the estimation of Computation procedure
1) Initialize the estimate e(0) and corresponding state error P(0).
2) Compute the H(n), the derivative of y(n) with respect to e(n) the estimate obtained in the previous iteration.
3) Compute the time varying Kalman gain k(n) using error variance p(n-1), H(n) and t2
4) Compute the estimate y(n) using x(n) and e(n-1), i.e.
based on observation up to time n-1, compute the error between y(n)(true observation) and y(n).
5) Update the estimate e(n) by adding the K(n).
weighted error between the observation y(n) and y(n) to the previous estimation e(n-1).
6) Compute the state error p(n) with Kalman gain k(n), N(n) and previous error p(n-1).
7) If n is less then Np increment n by 1 and go to step z;
otherwise stop.
VII. BIT ERROR RATE OF ICIDIFFERENT CANCELLATION
TECHNIQUE
To calculate bit error rate [12] the key point to obtain the corresponding ICI coefficient. At the transmitter side of such system, the condition ak=-ak+1(k=0,2,…….N-2) holds for each pair of (k,k+1) sub carrier. The exact received information signal is the sum of each pair of signal (yk,yk+1).
That is the signals for making decision is yk given by
Y’k=Y-Y,K=0,2,---N-2 (18)
So corresponding ICI coefficient can be derived as
S’K=-SK-1+2Sk-Sk+1
(19)
K=0,2---N-2 The expected signal is
d’=[-SN-1+2S0-S1]a0
(20)
and ICI signal can be given by
I’ +2Sk-Sk+1]ak]
(21)
Fig. 7. Error respose of different ici cancellation scheme.
VIII. CONCLUSION
The choice of which method to employ depends on the specific application. Self cancellation does not require very complex hardware or software for implementation. It is not bandwidth efficient as there is a redundancy of 2 for each carrier. The ML method also introduces the same level of redundancy but provides better BER performance, since it accurately estimates the frequency offset. Its implementation is more complex than the SC method. On the other hand, the EKF method does not reduce bandwidth efficiency as the frequency offset can be estimated from the preamble of the data sequence in each OFDM frame.
In this paper, the simulations were performed in an AWGN channel. This model can be easily adapted to a flat- fading channel with perfect channel estimation. Further work can be done by performing simulations to investigate the performance of these ICI cancellation schemes in multipath fading channels without perfect channel information at the receiver. In this case, the multipath fading may hamper the performance of these ICI cancellation schemes.
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