Digital Companding Scheme using A I based custom constellation Mapping and

selection

K.Seshadri Sastry , Research Scholar ,

Department of CS &SE, Andhra University ,

Visakhapatnam , India , Email:Aditya_shas@yahoo.com.

Dr.M.S.Prasad Babu ,

Professor , Department of CS &SE ,

Andhra University , Visakhapatnam ,India

Email:drmsprasadbabu@yahoo.co.in

. Abstract-The data rate is important in telecommunication because it is directly proportional to the cost of transmitting the signal. Saving bits is the same as saving money. In this paper we propose new digital companding scheme based on using different constellation orderings (QAM modulator) , depending on the data to be transmitted . The proposed scheme was simulated in Matlab7.4 and it was shown that the proposed companding scheme effective with low compression error. Key words : digital companding ,QAM

1. Introduction Recently, there has been an interest [l, 2, 3,4] in the effect of the pulse code modulation (PCM) companding [5] mechanism (introduced to improve voice transmission), inherent in communication networks, on the detectability performance of digital Quadrature Amplitude Modulation (QAM) signals transmitted through these networks. As has been previously shown [l, 2, 3,4], the effect of the companding process is to introduce quantization noise which is multiplicative in nature. This noise is amplitude dependent, i.e., large amplitude signal points in the QAM constellation will be surrounded by more noise than signals closer to the origin. The effect of this noise is such that the outermost points in a simple rectangular constellation suffer more performance degradation than the smaller internal signals. Saltzberg and Wang in [4] made the observation that not only is the noise around each point dependent on its amplitude, but that this noise is elliptical and not circular, Le., the noise components in the two

dimensional QAM space are not equal. In [4], it was also shown that the two dimensional noise components are not only unequal, but also correlated for most choices of vector bases. These properties make the detection problem and the signal constellation design problem very interesting, and represent a new challenge in signal design. Quadrature Amplitude Modulation is best suited for high data rate transmission since it uses quadrature and in phase components to modulate the signal. Different combinations of quadrature and in phase components can be used to modulate the signal , which result in binary coded mapping , Gray coded mapping and custom mapping schemes .The performance of QAM will not change much with coding scheme adopted[5] . In this paper we propose a compression scheme which uses four types of constellation orderings to compress the signal depending on the data to be transmitted. This paper is organized as follows. In section 2 the proposed scheme is explained. In section 3 results are given and in section 4 paper is concluded.

2. Proposed Scheme The proposed scheme uses four types custom constellation ordering of QAM depending on the data to be transmitted to compress two bits. Similarly sixteen custom constellation orderings should be used to compress four bits. Custom constellation ordering used to compress data bits should use different inphase and quadrature components as shown in figure 1, 2 ,3 and 4.

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Fig 1 Constellation ordering A

Constellation ordering A in Fig 1 uses 3 , 1 , -3 and -1 as quadrature and -5 ,-3 ,3 and 5 as inphase components

Fig 2 Constellation ordering B

Constellation ordering B in Fig 2 uses 4 , 2 , -2 and -4 as quadrature and -5 ,-3 ,3 and 5 as inphase components

Fig 3 Constellation ordering C

Constellation ordering C in Fig 3 uses 3 , 1 , -1 and -3 as quadrature and -4 ,-2 ,2 and 4 as inphase components

Fig 4 Constellation ordering D

The constellation ordering shown above uses different in phase and Quadrature components. Constellation ordering D in Fig 4 uses 4 , 2 , -2 and -4 as quadrature and -4 ,-2 ,2 and 4 as inphase components . By observing inphase and quadrature components one can predict the constellation scheme.

2.1 Compressor Block diagram of the transmitter is shown in Fig 5. Compression is carried in transmitter. For demonstration purpose two bit compression is shown in paper (6 bits compressed to 4 bits) , which can be extended conveniently upto 4 bits. Incoming data from data source ( 6 bits) is divided into MSB and LSB parts . MSB consists of 4 bits of data and LSB consists of 2 bits of data . Depending upon the data of LSB one out of four constellation orderings shown in Fig 1,2 ,3 and 4 is selected. That is LSB bits Constellation ordering 00 Ordering A 01 Ordering B 10 Ordering C 11 Ordering D

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Depending upon the selection made by the constellation selector, selected constellation ordering was followed by QAM modulator to modulate incoming 4 bits of data. So the incoming 6 bits of data are compressed to 4 bits of data and these 4 bits of data are modulated and transmitted in channel

2.2 Expander The process of expansion is carried out in receiver section. Fig 6 shows the block diagram of the receiver. The incoming 4 bits are passed through Artificial Intelligence based decision block .

The block diagram of decision making circuit is shown in Fig7 The incoming signal is divide into Real part and imaginary part as shown in figure 8 . Depending on the constellation ordering followed in transmitter, incoming signal consists of unique imaginary and real values. For example if in transmitter Constellation ordering A is used then 3 , 1 , -3 and -1 values appear in imaginary part and -5 ,-3 ,3 and 5 values appear in real part , if Constellation ordering B is used then 4 , 2 , -2 and -4 values appear in imaginary part and -5 ,-3 ,3 and 5 values appear in real part , if Constellation ordering C is used then 3 , 1 , -1 and -3 values appear in imaginary part and -4

,-2 ,2 and 4 values appear in real part ., if Constellation ordering D is used then 4 , 2 , -2 and -4 values appear in imaginary part and -4 ,-2 ,2 and 4 values appear in real part . So by observing values in imaginary and real part constellation ordering followed in transmitter can be assumed. Since all four constellation ordering schemes are already known, the values which may appear in incoming signal by using four types of constellation schemes are placed in memory. The real and imaginary values in the incoming signal is compared with the values in memory. In transmitter only one constellation ordering is followed at a time , so only one set of values matches . Depending upon the set of matched values constellation ordering scheme is selected in receiver and the data is added as LSB to the final data as shown in Fig 6 . The addition of bits according to constellation ordering followed is shown below Constellation Bits Added ordering Ordering A 00 Ordering B 01 Ordering C 10 Ordering D 11

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The Demodulated 4 bit data is added with 2 bits( in LSB)of data to expand it to 6 bits.

1. Results The proposed scheme was simulated in Matlab7.4. For illustration purpose two bit compression is shown which can be conveniently extended to four bit compression .The compression error is uniform and negligible for all values of data( above 6 EbN0), since estimating the expanded signal is based on constellation mapping . The Bit Error Rate (BER) of companded signal is 0.1818 upto 6 Eb/No and 0 after 6 Eb/No. The comparison of companded and un companded signal is shown in Fig 9. In the proposed scheme six bits are compressed to four bits for example , if incoming data is “111111” , then it is divided to “1111” and “11” . Since LSB is “11” , “1111” is modulated and transmitted through channel using constellation ordering D . At receiver after comparing received real and imaginary components constellation ordering used at transmitter can be found . Since Constellation ordering D is used for demodulated signal “11” can be added at LSB part which will give expanded signal “111111” . In the proposed scheme 6 bits data is compressed to 4 bits and 16QAM is used to modulate . In uncompressed scheme 6 bits are modulated with 64 QAM and transmitted. The Bit Error Rate using proposed scheme is much less compared to uncompressed scheme.

Fig 9 Comparison of companded and

un companded signals

2. Conclusion Digital companding of the signal using constellation ordering of QAM signal improves the performance of transmission. Companding error obtained in this process is negligible since accurate estimation of expanded signal is possible.

References

1. K. Pahlavan and J. L. Holsinger, "A Model for the Effects of PCM Compandors on the Performance of High Speed Modems," GLOBECOM '85, New Orleans, December 1985, pp. 24.8.1-24.8.5.

2. K. Pahlavan and J. L. Holsinger, "A Method to Counteract rhe Effects of PCM Systems on fne Perfonnance of Ultra High Speed Voice Band Modems", ICC '86, Toronto, Canada, June 1986, pp. 50.2.1-50.2.5.

3. K. Pahlavan and J. L. Holsinger, "Expanded TCM for Channels with Multiplicative Noise," ICC '87, June 1987, pp. 12.3.1-12.3.5.

4. B. R. Saltzberg and 3.-D. Wang, "Second-Order Statistics of Logarithmic Quantization Noise in QAM Data Communication.'' IEEE Trans. on'commun., Vol. 39, October 1991.

5. K. W. Cattermole, "Principles of Pulse Code Modulation", Iliffe Books Ltd., London, 1969 - ChaptetIII

6. T. Jiang and Y. Wu, “An overview: peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast., vol. 54, no. 2, pp. 257-268, June 2008.

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