 Open Access
 Total Downloads : 256
 Authors : Dr. K. Padma Priya
 Paper ID : IJERTV2IS3502
 Volume & Issue : Volume 02, Issue 03 (March 2013)
 Published (First Online): 23032013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Performance Analysis on SNR, BW, SSP, UBF, LBF to Get Acceptable Bit Error Rate To Improve Power Efficiency and Channel Capacity
Associate Professor, Department of Electronics and Communication Engineering, JNTUK College of Engineering, Vizianagaram
———————————————————————————————————————————————————

ABSTRACT
This paper describes the concepts of acceptable bit error rate, power efficiency(energy efficiency), band width efficiency, (SNR)Input, (SNR)output, significant side band pair(SSP), upper bound frequency(UBF), lower bound frequency(LBF).This paper also presents relation between SNR and band width in frequency modulation. Frequency modulation is frequently used modulation technique and is known as angle modulation. Angle modulation varies carrier(sinusoidal signal) signal in such a way that the angle of the carrier signal varies in according to the amplitude of the baseband modulating signal. In this method , the amplitude of the carrier wave is kept constant but in this paper I am changing the amplitude of the carrier and observed the what type of changes takes place in order to improve the understanding capability of the reader, two important classifications of angle modulation are i)frequency modulation ii) phase modulation.
There are different modulating techniques but some techniques are better in terms of bit error rate performance, some methods are better for band width efficiency. Here my intention is to make these methods good at both i.e acceptable bit error rate and band width efficiency.
Key words:, Efficiency(, Channel capacity Peak frequency deviation, Frequency modulation index, Modulation frequency,(SNR)in, (SNR)output, bit error rate,

INTRODUCTION
In a digital communications signal received at the receiver is the very important criteria if channel capacity is more signal will be very strength it will be possible only by maintaining proper signal to noise ratio, proper band width efficiency, low bit error rate,
proper significant side band pair, upper bound frequency, lower bound frequency, audio band width. By maintaining all the parameters above said then we will improve band width efficiency, power efficiency(energy efficiency) which leads to increase in channel capacity and throughput(2).
The signaltonoise ratio, the bandwidth, and the channel capacity of a communication channel are connected by the ShannonHartley theorem. Assumes thermal noise only C/BW measures the efficiency of a digital transmission, BW, S and N are not independent: (1)The noise N increases with the bandwidth of W (2) Inter modulation noise increases with the signal strength S. The bit error rate or bit error ratio (BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. BER is a performance measure, often expressed as a percentage (2). The BER may be improved by choosing a strong signal strength (unless this causes crosstalk and more bit errors), by choosing a slow and robust modulation.

SIGNAL TO NOISE RATIO (SNRatio)
Signaltonoise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise(3). It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise. While SNR is commonly quoted for electrical signals, it can be applied to any form of signal (such as isotope levels in an ice core or biochemical signaling between cells).
Signal to noise ratio:
(S/N)Db=10log (signal power/noise power.)
Typically measured at the receiver, because it is the point where the noise is to be removed from the signal.
The signaltonoise ratio, the bandwidth, and the channel capacity of a communication channel are connected by the ShannonHartley theorem.
Signaltonoise ratio is sometimes used informally to refer to the ratio of useful information to false or irrelevant data in a conversation or exchange. The theoretical maximum SNR assumes a perfect input signal. If the input signal is already noisy (as is usually the case), the signal's noise may be larger than the quantization noise. Real analogtodigital converters also have other sources of noise that further decrease the SNR compared to the theoretical maximum from the idealized quantization noise, including the intentional addition of dither(6).
Although noise levels in a digital system can be expressed using SNR, it is more common to use Eb/No, the energy per bit per noise power spectral density. The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal.

Band width efficiency explains about the ability of modulation scheme to accommodate data with in a limited band width .Band width efficiency reflects how efficiently the allocated band width is utilized and is defined as the ratio of throughput data rate per hertz in a given band width(6).
bandwidth Limitations arise from the physical properties of the transmission medium and from deliberate limitations at the transmitter to prevent interference from other resources.
Band width efficiency ()BW=data rate in bits per second/BW occupied by RF signal=DRATE/(BW)RF(3)

CHANNEL CAPACITTY(C)
A given communication system has a maximum rate of information known as the channel capacity.
If the information rate R is less than C, then one can approach arbitrarily small error probabilities by using intelligent coding techniques(8).
To get lower error probabilities, the encoder has to work on longer blocks of signal data. This entails longer delays and higher computational requirements
Nyquist's Law C = 2W log 2 M
Assumption: noiseless channel bits per second
BW = bandwidth
M = number of encoding levels in the signal
Binary signals can be reconstructed by taking 2W samples per second
A 5 kHz channel with binary signals can transmit at most 10,000 bps
The limitations is due to the effect of inter symbol interference, such as is produced by delay distortion.
Shannon's Law C = 2W log 2 (1 + SNRatio) S = signal strength
N = noise strength
Assumes thermal noise only C/BW measures the efficiency of a digital transmission .BW, S, and N are not independent: (1)The noise N increases with the bandwidth of W (2) Inter modulation noise increases with the signal strength S.
S.no
(AM)C
Peak frequency deviation
f=(AM)C x
1
5
50
2
10
100
3
15
150
4
20
200
5
25
250
6
30
300
7
35
350
8
40
400
30
S.no
(AM)C
Peak frequency deviation
f=(AM)C x
1
5
50
2
10
100
3
15
150
4
20
200
5
25
250
6
300
7
35
350
8
40
400

PEAK FREQUENCY DEVIATION AT CONSTANT GAIN 10KHZ/V. Let the gain is , peak frequency deviation f=(AM)CX (AM)C=Amplitude of carrier
9
45
450
10
50
500
TABLE
The bit error probability pe is the expectation value of the BER. The BER can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long time interval and a high number of bit errors(10).
Factors affecting the BER
In a communication system, the receiver side BER may be affected by transmission channel noise, interference, distortion, bit synchronization problems, attenuation, wireless multipath fading, etc.
The BER may be improved by choosing a strong signal strength (unless this causes crosstalk and more bit errors), by choosing a slow and robust modulation scheme or line coding scheme, and by applying channel coding schemes such as redundant forward error correction codes.
Figure1
We observed that the graph between (AM)C frequency deviation(f) is linear.

BIT ERROR RATE(BER)
&Peak
The transmission BER is the number of detected bits that are incorrect before error correction, divided by the total number of transferred bits (including redundant error codes). The information BER, approximately equal to the decoding error probability, is the number of decoded bits that remain incorrect after the error correction, divided by the total number of decoded bits (the useful information). Normally the transmission BER is larger than the information BER. The information BER is affected by the strength of the forward error correction code. The BER may be analyzed using stochastic computer simulations. If a
In digital transmission, the number of bit errors is the number of received bits of a data stream over a communication channel that have been altered due to noise, interference, distortion or bit synchronization errors.
The bit error rate or bit error ratio (BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. BER is a unit less performance measure, often expressed as a percentage(5).
simple transmission channel model and data source model is assumed, the BER may also be calculated analytically(7).

VARIATION BETWEEN PEAK FREQUEENCY DEVIATION(f) AND FREQUENCY MODULATION INDEX.
S. no
f(khz)
fmod
MINDEX= f/ fmod
1
50
10
5
2
100
10
10
3
150
10
15
4
200
10
20
5
250
10
25
6
300
10
30
7
350
10
35
8
400
10
40
9
450
10
45
10
500
10
50
S. no
f(khz)
fmod
MINDEX= f/ fmod
1
50
10
5
2
100
10
10
3
150
10
15
4
200
10
20
5
250
10
25
6
300
10
30
7
350
10
35
8
400
10
40
9
450
10
45
10
500
10
50

VARIATION OF CHANNNEL CAPACITY (C) WITH BAND WIDTH(RF) AND ( SNRATIO )output
C=(BW)RF LOG2(1+SNRATIO)
S.no
BW
(SNRATIO)OUTPUT
C
1
300hz
5dB
617.83
2
300hz
10 dB
1037.829
3
300hz
15 Db
1508.331
4
300hz
20 dB
1997.463
5
300hz
25 dB
2492.811
6
300hz
30 dB
2990.167
Table2
Table3
Chart2
Observations: By increasing peak frequency deviation there is 1/10TH increase in Modulation index.
Chart3

COMPARRISION BETWEEN f(KHZ), MINDEX(KHZ), SSP, UBF(KHZ), LBF(KHZ),Where( BW)AUDIO=15
Let f=peak frequency deviation, MINDEX=modulation index, SSP=significant side band pair, ,UBF=Upper bound frequency, LBF=Lower bound frequency
SSP=Mindex+1, ———————————————–
–(1)
UBF=2(MINDEX+1)(BW)AUDIO—————————————(2)
LBF=2Xf————————————————(3)
S. no 
f 
MINDEX 
SSP 
UBF 
LBF 
1 
50 
5 
6 
180 
100 
2 
100 
10 
11 
330 
200 
3 
150 
15 
16 
480 
300 
4 
200 
20 
21 
630 
400 
5 
250 
25 
26 
780 
500 
6 
300 
30 
31 
4930 
600 
7 
350 
35 
36 
1080 
700 
8 
400 
40 
41 
1230 
800 
9 
450 
45 
46 
1380 
900 
10 
500 
50 
51 
1530 
1000 
Table4
Figure4
Observation from this graph : For small audio band width there is large increase in Modulation index.
XIII. VARIATION OF CHANNNEL CAPACITY (C) WITH BAND WIDTH AT CONSTANT ( SNRATIO )output
C=(BW)RF LOG2(1+SNRATIO)
S.no 
BW(KHZ) 
(SNRATIO)OU TPUT 
C(kbps) 
1 
100KHZ 
10 dB 
345.9429 
2 
200KHZ 
10 dB 
691.886 
3 
300KHZ 
10 dB 
1037.829 
4 
100KHZ 
20 dB 
665.821 
5 
200KHZ 
20 dB 
1331.642 
6 
300KHZ 
20 dB 
1997.463 
7 
100KHZ 
30 dB 
996.722 
8 
200KHZ 
30 dB 
1.99mbps 
9 
300KHZ 
30 dB 
2.99mbps 
Table5
Figure5
S. no 
M index 
K 
(SNRatio) input 
1 
5 
8.334 
41.67 
2 
10 
8.334 
83.34 
3 
15 
8.334 
125.01 
4 
20 
8.334 
166.68 
5 
25 
8.334 
208.35 
6 
30 
8.334 
250.02 
7 
35 
8.334 
291.69 
8 
40 
8.334 
333.36 
9 
45 
8.334 
375.03 
10 
50 
8.334 
416.7 
S. no 
M index 
K 
(SNRatio) input 
1 
5 
8.334 
41.67 
2 
10 
8.334 
83.34 
3 
15 
8.334 
125.01 
4 
20 
8.334 
166.68 
5 
25 
8.334 
208.35 
6 
30 
8.334 
250.02 
7 
35 
8.334 
291.69 
8 
40 
8.334 
333.36 
9 
45 
8.334 
375.03 
10 
50 
8.334 
416.7 

VARIATION OF (SNRatio)index WITH FREQUENCY MODULATION INDEX (Mindex) AT CONSTANT(K)
Where f =(AMP)carrier ——(1) M index= f/f mod——————————(2)
From equations 1&2 Mindex=(AMP)carrier /fmod———(3) (AMP)carrier=( Mindexx fmod)/ —(4)
(or)
= ( Mindex x fmod)/ (AMP)carrier———(5)
Relation between (SNRatio)input and Mindex
carrier W RF
carrier W RF
(SNRatio)input, AM=(AMP)2 /2N (BW)
=[( Mindexx fmod)/ ]2/2NW(BW)RF——(6) (or)
[( M index x f mod)]2/2 2 NW(BW)RF——–(7) where N w= white noise,( BW)RF=RF Band width (SN Ratio)input, AM M2 index——(8)(SN Ratio)input=K M2 index———(9)
Where K= [( f mod)]2/2 2 NW(BW)RF——(10)
BY Substituting the values f mod=10 khz, =10
N w=200hz, (BW)RF=300HZ (at front end of the receiver.)(author)
Table6
Figure–6

POWER EFFFICIEENCY ()POWER
Performing power analysis and sample size estimation is an important aspect of experimental design, because without these calculations, sample size may be too high or too low. If sample size is too low, the experiment will lack the precision to provide reliable answers to the questions it is investigating. If sample size is too large, time and resources will be wasted, often for minimal gain(2&8).
In some power analysis software programs, a number of graphical and analytical tools are available to enable precise evaluation of the factors affecting power and sample size in many of the most commonly encountered statistical analyses. This information can be crucial to the design of a study that is costeffective and scientifically useful.
To ensure a statistical test will have adequate power, you usually must perform special analyses prior to running the experiment, to calculate how large an N is required.
Let's briefly examine the kind of statistical theory that lies at the foundation of the calculations used to estimate power and sample size. Return to the original example of the politician, contemplating how large an opinion poll should be taken to suit her purposes (11).
Statistical theory, of course, cannot tell us what will happen with any particular opinion poll. However, through the concept of a sampling distribution, it can tell us what will tend to happen in the long run, over many opinion polls of a particular size.

CONCLUSION
Now a days, an increasing demand of wireless& mobile communications it requires high quality of transmission with less price, it is possible only with high quality research .This paper may gives complete idea to minimize noise effects by maintain proper parameters by adopting the above numerical approximations, graphical representations and tabular forms.

ACK NOWLEDGEMENT
The author would like to thank to Pro.CH.D.V.Paradesi Rao, Arora Engineering College, Bhongiri, Hyderabad for giving their valuable suggestions& guide lines.

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