Estimation of Bit Error Probability in Uncoded Fhss
ESTIMATION OF BIT ERROR PROBABILITY IN UNCODED FHSS Abid, Y. 1, Othman, S. 2, Farid, G., and Fadzli, M. 1,2
Collaborative MicroElectronic Design Excellence Center (CEDEC) School of Electric and Electronic, University Science Malaysia, 14300 Nebong Tebal, Pulau Penang, Malaysia.
[email protected]
ABSTRACT Spread spectrum technology has emerged into the commercial market place for improving business transactions. Frequency hopping is the easiest spread spectrum modulation to use. Any radio with a digitally controlled frequency synthesizer can, theoretically, be converted to a frequency hopping radio. The minimum frequency switching rate usable in a frequency hopping system is determined by the type of information being sent, its rate and the amount of redundancy used. This paper discusses the probability of error of uncoded frequency hopping with M-ary frequency shift keying (MFSK) and the system model designed in this paper shown that the bit error rate is decreasing by sending more chips for a bit. The simulation results have proved that frequency hopping is left unchanged and directly modulates a carrier of varying frequency and is not so sensitive to such interferers. Keywords: Frequency hopping spread spectrum, bit error rate, probability of error.
1.0 INTRODUCTION Recently, a new technology has emerged in the commercial market place. In today’s emerging wireless telemetry market, there are several technologies available, each with its own set of benefits and compromises. Current applications of spread spectrum technology include wireless LANs (local area network), bar code scanners,, and microphones. Spread spectrum technology is fairly simple compared to the wired technology in which businesses must develop a web of wires.
ISSN:1985-3157 Vol 1 No.1 Nov.-Dec. 2007
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1.1 Spread spectrum technology Spread Spectrum modulation techniques are defined as being those techniques in which the bandwidth of the transmitted signal is much greater than the bandwidth of the original message, and the bandwidth of the transmitted signal is determined by the message to be transmitted and by an additional signal known as the Spreading Code. In 1985, the US Federal Communication Commission (FCC) allocated three spectrum frequencies [1], [3], [6]. There are two methods for performing the spreading; frequency hopping and direct sequencing. This paper discusses here frequency hopping spread spectrum because of the following reasons. i.
ii.
iii.
Frequency hopping is one of the variants of spread spectrum technique which enables coexistence of multiple networks (or other devices) in the same area. FCC recognizes Frequency Hopping as one of the techniques withstanding “fairness” requirements for unlicensed operation in the ISM bands. Frequency Hopping is resistant to multipath fading through the inherent frequency diversity mechanism.
1.2 Frequency Hopping Spread Spectrum (FHSS) Frequency hopping is the easiest spread spectrum modulation to use. Any radio with a digitally controlled frequency synthesizer can, theoretically, be converted to a frequency hopping radio. This conversion requires the addition of a pseudo noise (PN) code generator to select the frequencies for transmission or reception. Most hopping systems use uniform frequency hopping over a band of frequencies. This is not absolutely necessary, if both the transmitter and receiver of the system know in advance what frequencies are to be skipped. Thus a frequency hopper in two meters could be made that skipped over commonly used repeater frequency pairs. A frequency hopped system can use analog or digital carrier modulation and can be designed using conventional narrow band radio techniques. De-hopping in the receiver is done by a synchronized pseudo noise code generator that drives the receiver’s local oscillator frequency synthesizer [2]. Frequency hopping spread spectrum splits the available frequency band into a series of small subchannels. A transmitter hops from subchannel to subchannel, transmitting short bursts of data on each channel for a predefined period, referred to as dwell time (the amount of time spent on each hop). The hopping sequence is obviously synchronized between transmitter and receiver to enable communications to occur. 62
ISSN:1985-3157 Vol 1 No.1 Nov.-Dec. 2007
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Estimation of Bit Error Probability in Uncoded Fhss
FCC regulations define the size of the frequency band, the number of channels that can be used, and the dwell time and power level of the transmitter. In the frequency hopping spread spectrum a narrowband signal move or hops from one frequency to another using a pseudorandom sequence to control hopping. This results in a signal’s lingering at a predefined frequency for a short period of time, which limits the possibility of interference from another signal source generating radiated power at a specific hop frequency.
2.0 SYSTEM MODEL In frequency hopping, carrier frequency is changing with some pseudorandom in order to generate spread spectrum signal as shown in fig.1. The most common modulation used with frequency hopping is M-ary frequency shift keying (FSK) [3]. One of the methods used for the performance estimation of FHSS is estimation of bit error probability [4]-[5]. The simulation computes an estimate for the bit error probability. At the transmitter end, random binary data is generated using the rand function in Matlab. The rand function generates random numbers chosen from a uniform distribution on the interval (0, 1). The generated bits are then M-ary FSK modulate. Spreading codes are then generated similar to the way data bits were generated. The length of spreading code is the processing gain (PG). The M-ary FSK is then multiplied with spreading code to obtain frequency hopping waveform. The bit rate Rb is normalized to one for convenience. M-ary FSK is used to transmit a block of k = log 2 M bits per signal waveform. In this case, the M signal waveforms maybe expressed: M = 2k
(1)
M simply represents a digit that corresponds to the number of conditions, levels or combinations possible for a given number of binary variables. It is often advantageous to encode at a level higher than binary (sometimes referred to as beyond binary or higher-than-binary encoding) where there are more than two conditions possible.
ISSN:1985-3157 Vol 1 No.1 Nov.-Dec. 2007
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s (t ) = 2
Es cos[2p f c t + 2p mDf t ] T
(2)
where Es = kEb is the energy per symbol, T = kTb is the symbol interval, and Df is the frequency separation between successive frequencies.
s (t ) = 2
Eb cos[2p t ( f c + mDf )] Tb
(3)
The Probability of error for uncoded bit with a noise jammer of constant power J is given by: æ E ö Pb = 1/ 2exp ç - b ÷ è 2NJ ø Eb PG = NJ J / S =
(5)
(Wss / Rb) (J / S )
(6)
N (J / S)
(7)
=
Figure 1. Structure of the transmitter and receiver of FFH system
64
(4)
ISSN:1985-3157 Vol 1 No.1 Nov.-Dec. 2007
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Estimation of Bit Error Probability in Uncoded Fhss
3.0 RESULTS AND DISCUSSION Data sequence of 20 bits is generated by using Matlab rand function as shown in Figure 1.This signal is then modulated with carrier wave to get the MFSK modulated signal which is shown in Figure 2 while Figure 3 represents the FFT of MFSK signal. Spread spectrum of the signal is obtained by generating 6 carrier frequencies range from 0.01 to 0.06 with 10 Hz bit frequency as shown in Figure 4. Figure5 is representing the transformation of MFSK into wider band in term of frequency hopping. Fig. 6 plots a graph of probability of error versus Eb / N J for different values of J / S and found that probability of bit error is decreasing for MFSK by increasing the values of Eb / N J . In direct spread spectrum the wide modulation is applied to a fixed frequency carrier signal for transmission. The spreading code directly spreads the information, and independent of the RF modulator. While in FH the information is left unchanged and directly modulates a carrier of varying frequency. From Figure 7 it is shown that, for a large out-of bound interferer, FHSS is not so sensitive to such interferers.
4.0 CONCLUSION The proper choice of FH as a spread spectrum technique depends on the actual environment in which the system will be deployed. In any large interfering signals, FHSS is likely to continue operating, even though the interference is not completely rejected. However, the multi-user situation while using Rayleigh Fading Flat channel should be used instead of communication channel, will be considered in future work.
REFERENCES [1] [2] [3]
[4]
Feher., K., 1995, Wireless Digital Communications, Modulation & Spread Spectrum Application, Prentice Hall. Dixon, R.D., 1984, Spread Spectrum Systems, (John Wiley & Sons, Inc. Lee, J.S., Miller, L.E., and Kim, T.K., 1983, Error performance of linear and nonlinear combining square-law receiver for L-hops per bit FH/ BFSK waveforms in worst-case partial-band jamming, in Proc. IEEE Military Commun. Conf., (1), pp. 23-28. Miller, L.E., Lee,J.S., and Kadrichu, A.P., 1986, Probability of error analysis of a BFSK frequency-hopping system with diversity under partial-band jamming interference-Part 111: Performance of a square- law self- normalizing soft decision receiver, IEEE Trans. Commun.,(34), pp. 669-675,
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[5] [6]
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Simon, M.K., Omura, J.K., Scholtz, R.A., and Levitt, B.K., 1985, Spread Spectrum Communications (1) , (Rockville, MD: Computer Science. SSS Online. Spread spectrum history page. Available from: http://sssmag.com/shistory.html.
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