AN IMPROVE BER PERFORMANCE USING CONVOLUTION CODES AND ICI DUE TO FREQUENCY OFFSET IN OFDM SYSTEM

Mohammad Ammar1, Dr. Deepak Nagaria2

1. PG student, Dept. of Electronics and Communication Engineering, BIET Jhansi, U.P. India.

2.Associate professor, Dept. of Electronics and Communication Engineering, BIET Jhansi, U.P. India.

Abstract: In wireless communication, parallel transmission of symbols using multi carriers is applied to achieve high efficiency in terms of output and better transmission quality. OFDM (Orthogonal Frequency Division Multiplexing) is one of the techniques for parallel transmission. In multipath environment the performance of OFDM is improved by introducing some kind of channel coding. Coded Orthogonal frequency division multiplexing (COFDM) is an impressive technique in fading environments. In this paper, higher modulation schemes are considered with OFDM for a AWGN channel. Here, convolutional coding (CC) and TCM (Trellis coded modulation) are combined with OFDM. Trellis coded OFDM (TCM-OFDM) gives a better performance compared to convolutional coded OFDM (CC-OFDM) with a lower trellis complexity. And also the performance does not depend significantly on the frequency band. However due to lack of synchronization in transmitter and receiver, there may be a offset in transmitted and receiver frequencies which leads to degradation of orthogonality between transmit and receive pulse. Frequency offset causes lCI (inter carrier interference). In this paper our aim is to evaluate the performance of COFDM system in presence of frequency offset. COFDM is generated as per IEEE 802.lla specifications and TCM and viterbi decoder along with convolution codes are used for channel coding purpose. Channel used for consideration is AWGN. The performance is evaluated in terms of ICI value and BER(Bit Error Rate).

Keywords: OFDM, COFDM, BER, ICI, TCM, viterbi decoder, Convolution codes,

INTRODUCTION

OFDM is most preferred for high speed communication in multipath environment due to its immunity to ISI(inter symbol interference). OFDM avoids ISI problem by sending many low speed transmissions simultaneously. Coded OFDM is a modified version of conventional OFDM where OFDM is combined with channel coding techniques, resulting in to higher data transmission rates or lower BER in wireless fading medium 2,4. COFDM is currently most preferred choice for both DAB and DYB applications l. Time synchronization is needed between transmitted and received carriers both in time as well as frequency to maintain orthogonality. Time synchronization can be achieved using time stamp. However if there is an offset in carrier frequencies it leads to loss of orthogonality and distortion thus caused is ICI. Coded OFDM is currently the most sought choice for digital audio-video broadcasts. In this paper the ICI is measured for COFDM system using 1/2 convolution codes as a function of sub-carrier spacing, apart from this bit error rate is also evaluated for mapping schemes BPSK, QPSK and QAM-16 of COFDM system is used as per IEEE 802.11a standard. In this paper we have simulate and calculated the ICI caused by different frequency offset and then BER for COFDM and OFDM is calculated for various mapping schemes, and compared..

II. IEEE 802.11A SPECIFICATIONS

IEEE 802.11 5 is a set of standards carrying out wireless local area network (WLAN) computer communication in the 2.4, 3.6 and 5 GHz frequency bands. The IEEE 802.11 a standard specifies an OFDM physical layer (PHY) that splits an information signal across Maintaining the Integrity of the Specifications 52 separate sub-carriers. Four of the sub-carriers are pilot sub-carriers. The remaining 48 sub-carriers provide separate wireless pathways for sending the information in a parallel fashion. The resulting sub-carrier frequency spacing is 0.3125 MHz (64 possible sub-carrier frequency slots can be used for 20 MHz bandwidth,).The basic parameters for OFDM systems as per IEEE 802.lla standard are given in table 1.

Parameter Value

FFT size (nFFT) 64

Number of digital sub-carriers (nDSC) 52

FFT Sampling frequency 20 MHz

Sub-carrier spacing 312.5 KHz

Used subcarrier index {-26 to -1, +1 to +26}

Cyclic prefix duration, Tcp 0.8 µs

Data symbol duration, Td 3.2 µs

Total Symbol duration, Ts 4 µs

Modulation schemes BPSK,QPSK,16-QAM, 64-QAM

TABLE 1: OFDM Time based parameters in IEEE 802.lla

IMPLEMENTING CODED-OFDM SYSTEM AND ICI

Because the frequency spacing between adjacent sub carrier is 1/ T .which is very small symbol duration (T = 3.2µs), accurate frequency synchronization is an important constraint for OFDM systems. Such a high accuracy can not be catered by the local oscillator itself. The frequency offset ? has following effect 2 6

1) Othogonality between transmit and receive pulses will be degraded

2) Time variant phase rotation of received pulses.

Transmitted signal with N- sub carriers is represented by:

xn=1Nk=0N-1X(k)? = 0,1,2, … . . ? – 1(1)

where N is the total number of subcarriers. X (k) denotes the transmission modulated symbol on the subcarrier k with k= 0, 1, 2…N-1. The received signal after being passed through channel and effected by frequency offset can be written as:

yn=x(n)ej2?n?N+w(n) (2)

where ? is the normalized frequency offset and w (n) is the Additive White Gaussian Noise (AWGN) introduced in the channel.

At the reception, after FFT block the received signal on subcarriers k suffers frequency offset can be written as:

Yk=n=0N-1y(n)e-j2?nkN ? = 0,1 … . ? ? 1

=XkS0+l=0,l?kN-1XlSl-k+W(k) (3)

W(k) is the FFT of w(n), and S(l-k) are the complex coefficients for the ICI components in the received signal. The first term in the right hand side of Eq. 3 represents the desired carrier component. The second term in the same equation is the ICI component and the third term is AWGN.

The foremost reason of frequency offset at the receiver frequency instability of local oscillator, Doppler shift, different operating conditions at sender and receiver. The coded OFDM used in this paper implemented as given in Fig. 1, 1/2 convolution codes are used for introducing channel coding, The zero padding is done for confirming the IFFT/FFT size and cyclic prefix is 25% of the FFT/IFFT size thus making the total OFDM frame size 80 symbols. The cyclic prefix compensates the problem caused due to delay spread and to maintain continuity of the signal which ensures orthogonal reception of received signal subcarriers. The most widely used mapping schemes used in OFDM as per IEEE 802.lla standard are BPSK, QPSK, 16-QAM and 64-QAM. The theoretical expressions of SER 2 for various uncoded OFDM schemes are given in following equations.

-285750-28575Data Generator stream

Convolutional Encoder (TCM)

S/P

IFFT

Add CP

P/S

Channel

And AWGN

S/P

Remove CP

FFT

P/S

Convolutional (Viterbi) Decoder

Output Bit stream

Transmitter

Receiver

Data Mapping (BPSK)

Data Demapping

00Data Generator stream

Convolutional Encoder (TCM)

S/P

IFFT

Add CP

P/S

Channel

And AWGN

S/P

Remove CP

FFT

P/S

Convolutional (Viterbi) Decoder

Output Bit stream

Transmitter

Receiver

Data Mapping (BPSK)

Data Demapping

Fig l. Coded-OFDM system with convolution code

Ps,bpsk=12erfcEsN0 (4)

For QAM system,

Ps,M-QAM?21-1Merfc3Es2(M-1)N0 (5)

Since each symbol carries k bits, the symbol to noise ratio (Es / No) is k times the bit to noise ratio (Eb / No ), i.e. Es / No = k(Eb / No). The above discussion leads to bit en’or rate for the various QAM schemes. For QPSK system.

Pb,QPSK=12erfcEbN0 (6)

This shows that BER for QPSK and BPSK is same. For 16-QAM and 64-QAM the BER is

Pb,16-QAM=38erfc4Eb10N0 (7)

Pb,64-QAM=724erfc18Eb126N0 (8)

In OFDM transmission, out of the available bandwidth from -10 MHz to +10 MHz, only sub-carriers from -8.1250 MHz to +8.1250 MHz are used. This means that the signal energy is spread over a bandwidth of 16.250MHz, whereas noise is spread over bandwidth of 20 MHz (-l0 MHz to +l0 MHz), i.e.

(20 MHz) x Es = (16.25 MHz) x Eb (9)

Simplifying equation (9), we get Es / Eb = nDSC / nFFT . In an OFDM, the transmission of cyclic prefix does not carry ‘extra’ infonnation; the signal energy is spread over time Td + Tcp whereas the bit energy is spread over the time Td i.e. Es / Eb = Td /(Td + Tcp). Combining the above two aspects and converting in to decibels

EsN0dB=EbN0dB+10lognDSCnFFT+10logTdTd+Tcp+10logk (10)

A. Convolution codes

k bits are input, n bits are output 4-6 where k ; n are very small (usually k=1-3, n=2-6), Input depends not only on current set of k input bits, but also on past input5,6. The number of bits which affect current output code is called “constraint length” K.

Where K= code memory + k

The specification used for generating convolution codes here are as follows.

For 1/2 convolution code

1) Constraint length:7

2) Feedback connections: (171)8 ; (133)8

For 2/3 convolution codes

1) Constraint length (5,4)

2) Feedback connections: (23,35,0:0,5,13)8

B. TRELLIS-CODED MODULATION

The generic TCM system7 expands m message inputs x1,x2,…,xm to generate m+1 signal outputs y1,y2,…,ym+1 giving us M=2m+1 channel symbols that are then mapped to an M-ary signal constellation. The overall encoding rate is thus R=m(m+1) . The TCM structure includes using an mm+1 rate convolutional encoder, wherem is equal to number of coded message bits and m?m . This encoder expands m message bits into m+1 signal outputs.

TCM is a scheme that combines convolutional coding and modulation.

Minimizing errors requires that we maximize the euclidean distance between adjacent points.

C. VITERBI DECODER

1590675774700 BM

00 BM

3352800784225 SP

00 SP

4943475850900Decoded Data

00Decoded Data

2333625850900When a sequence of data is received from the channel, it is required obtain the output from the received data. The Viterbi Decoder is used for this purpose in convolutional coding technique. A Viterbi Decoder uses Viterbi algorithm to decode the received data which is encoded by the feed forward convolution coder. The block schematic of Viterbi Decoder is given below8.

-19050022225Received Signal

00Received Signal

408622540640SMU

0SMU

77152550165BMU

0BMU

240030031115ACSU

0ACSU

4600575279404762502794030003752794001295400374650

2571750-44440027717755080

240030067310PMM

0PMM

Fig 2. Block Diagram Viterbi Decoder

The main blocks of Viterbi Decoder are

(a) Branch Metric Unit BMU

(b) Add Compare and Select Unit ACSU

(c) Survivor Memory Unit SMU

(d) Lower Power Trace back PMM

With the help of Viterbi Algorithm first it adds two binary parallel bits and the BMU module finds the lowest Hamming Distance. ACS module now compares two hamming distance

obtained. The survivor paths are stored in each consisting of N branches in each stage. According to the survivor path values determines the original transmitted message9.

SIMULATION RESULTS

We have simulated the ICI as function of carrier spacing and BER performance, for COFDM system. Fig. 3 shows the BER performance for various mapping schemes in COFDM system using trellis encoder and viterbi decoder along with 1/2 convolution codes, where as in Fig. 4 compares ICI considering offset and complying with IEEE 802.11a specifications. From the simulation results it is clear that BER performance is better for higher mapping schemes while ICI for lower frequency offset is suitable for COFDM.

952527051000

Fig 3. BER performance of various mapping scheme in COFDM

-19812002543175(a)

00(a)

305371530670503048000-323850-4286253033395-476250-323850 (b)

48101252990215(d)

00(d)

(c)

48196505052060(b)

00(b)

9715504280535(a)

00(a)

Fig 4. ICI Calculation for various frequency offset values in COFDM , (a) ? = 0.5, (b) ? = 0.4, (c) ? = 0.25 (d) ? = 0.15

CONCLUSION AND FUTURE SCOPE

The ICI simulated values are much less for ? = 0.15 than that of ? = 0.5 on 0 to -30 dB SNR scale. Also, for higher mapping schemes like 16-QAM and 64-QAM worst than BPSK. However BER curves show that overall error rate for 64-QAM is lowest and increases for 16-QAM, QPSK, and BPSK. So above results strongly recommend the use of COFDM for digital broadcast applications.

VI. REFERENCES

1 Thenmozhi, K., Prithiviraj, V( 13-15 Dec.2007): Suitability of Coded Orthogonal Frequency

Division Multiplexing (COFDM) for Multimedia Data Transmission in Wireless Telemedicine Applications. In: IEEE Conference on Computational Intelligence and Multimedia Applications, Volume 4, pp.288 – 292,

2 Van Nee., Richard., Prasad, Ramjee(2000): OFDM for Wireless Multimedia Communications Boston: Artech House

3 Daoud, 0., AI-Qawasmi, A-R(23-26 Marh 2009 ): Efficient performance of COFDM-based DVBT. In: IEEE 6th International Conference on Systems, Signals and Devices, pp.I-4,

4 Joshi,Alok and Saini, Davinder S(March 2010): “Performance Analysis of Coded OFDM for

Various Modulation Schemes in 802.11a Based Digital Broadcast Applications”, in proceedings Intemational Conference (BAI P 20 I 0) , Kerala, IND IA.

5 IEEE 802.11 detailed documentation http://standards.ieee.org/getieee8026 Joshi, Alok and Saini, Davinder S, “COFDM performance in various Multipath fading environment “, in proceedings of IEEE International Conference (ICCAE 2010) ,vol.3, pp 127-131,Singapore, Feb 26-28 2010.

7Ungerboeck, G., (1987). “Trellis Coded Modulation with Redundixnt Signal Set”, IEEE Communications Magazine, Vol. 27, February, pp.5-21.

8William Stallings, Data And Computer Communications, Seventh edition., Chapter 6

9Y. Yasuda, K. Kashiki, and Y. Hirata, “High Rate Punctured Convolutional Codes for Soft Decision Viterbi Decoding,” IEEE Transactions on Communications, Vol. COM-32, March, 1984,pp. 315-319