nalyze BER Performance of Wireless FSK System Microwaves & RF; Nov009, Vol. 48 Issue 11, p80 Hamood Shehab Hamid 1 Ekhlas Kadhum,,Widad Ismail 3, Mandeep Singh 4 1 School of Electrical and Electronics Engineering, Universiti Sains Malaysia, Seri mpangan, 14300 Nibong ebal, Seberang Perai Selatan, Pulau Pinang, Malaysia Email:hash_30165 @yahoo.com,3 School of Electrical and Electronics Engineering, Universiti Sains Malaysia, Seri mpangan, 14300 Nibong ebal, Seberang Perai Selatan, Pulau Pinang, Malaysia el: +6 04-5995999 ext. 6050, Email: eewidad@eng.usm.my bstract: his paper presents the implementation and investigates the nature of the gap by simulating, 4 and 8-level FSK systems in additive white Gaussian noise channel using MLB, measuring the performance of theoretical systems using FSK is about 1 db at a bit error rate (BER) of 10-3 and widens as BER decreases. Key words: simulation, M-FSK, digital communication, BER. 1. Introduction Modern communication systems use digital modulation techniques. dvancement in very large-scale integration (VLSI) and digital signal processing (DSP) technology have made digital modulation more cost effective than analog transmission systems. Digital modulation offers many advantages over analog modulation. Some advantages include greater noise immunity and robustness to channel impairments, easier multiplexing of various forms of information (for example, voice, data, and video), and greater security. Further more, digital transmissions accommodate digital error-control codes which detect and/or correct transmission errors, and support complex signal conditioning and processing techniques such as source coding, encryption, and equalization to improve the performance of the overall communication link. In digital wireless communication systems, the modulating signal (e.g., the message) may be represented as a time sequence of symbols or pulses, where each symbol has m finite states. Each symbol represent n bits of information, where n = log m bits/symbol. Many digital modulation techniques are used in modern wireless communication systems, and many more are sure to be introduced. Some of these techniques have subtle differences between one another, and each technique belongs to a family of related modulation methods. For example, Frequency Shift Keying (FSK) 1
may be either coherently or no coherently detected; and may have two, four, eight or more possible levels per symbol, depending on the manner in which information is transmitted within a single symbol [1]. he paper is organized as follows. In Section factors that influence the choice of digital modulation wireless communication is explained. Section 3 introduces the FSK background. Simulations and results of FSK wireless receiver are presented in Section 4 and with conclusions discussed in Section 5. - Factors hat Influence the Choice of Digital Modulation Several factors influence the choice of a digital modulation scheme. desirable modulation scheme provides low bit error rates at low received signal-to-noise ratios, performs well in multipath and fading conditions, occupies a minimum bandwidth, and is easy and cost effective to implement. Existing modulation schemes do not simultaneously satisfy all of these requirements. Some modulation schemes are better in terms of bit error rate performance, while others are better in terms of bandwidth efficiency. Depending on the demands of a particular application, tradeoffs are made when selecting a digital modulation. he performance of a modulation scheme is often measured in terms of its power efficiency and bandwidth efficiency. Power efficiency describes the ability of a modulation technique to preserve the fidelity of the digital message at low power levels. In a digital communication system, in order to increase noise immunity, it is necessary to increase the signal power. However, the amount by which the signal power should be increased to obtain a certain level of fidelity (i.e., an acceptable bit error probability) depends on the particular type of modulation employed. he power efficiency (sometimes called energy efficiency) of a digital modulation scheme is a measure of how favorable this tradeoff between fidelity and signal power is made, and is often expressed as the ratio of the signal energy per bit to noise power spectral density (Eb/No) required at the input of the receiver for a certain probability of error (say 10-3 ). Bandwidth efficiency describes the ability of a modulation scheme to accommodate data within a limited bandwidth. In general, increasing the data rate implies decreasing the pulse width of a digital symbol, which increases the bandwidth of the signal. hus, there is an unavoidable relationship between data rate and bandwidth occupancy. However, some modulation schemes perform better than others in making this tradeoff. Bandwidth efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the ratio of the throughput data rate per Hertz in a given bandwidth. If R is the data rate in bits per second, and B is the bandwidth occupied by the modulated radio frequency signal, then bandwidth efficiency η is expressed as B R (.1) B B in terms of bit per second that means the number of bits that are conveyed or processed per unit of time he system capacity of a digital communication system is directly related to the bandwidth efficiency of the modulation scheme, since a modulation with a greater value of ή B will transmit more data in a given spectrum allocation. here is a fundamental upper bound on achievable bandwidth efficiency. Shannon s channel coding theorem states that for an arbitrary small probability or error, the maximum possible bandwidth efficiency is limited by the noise in the channel, and is given by channel capacity formula. he Shannon s bound for additive white
Gaussian noise (WGN) non-fading channel is given by; C S B max log(1 ) (.) B N where C is the channel capacity in bits per second, B is the radio frequency (RF) bandwidth, and S/N is the signal-to-noise ratio. In design of a digital communication system, very often there is a tradeoff between bandwidth efficiency and power efficiency. For example, adding error control coding to a message increases the bandwidth occupancy (and this, in turn, reduces the bandwidth efficiency), but at the same time reduces the required power for a particular bit error rate, and hence trades bandwidth efficiency for power efficiency. On the other hand, higher level modulation schemes (Mary keying), except M-ary FSK, decrease bandwidth occupancy but increase the required received power, and hence trades power efficiency for bandwidth efficiency. While power and bandwidth considerations are very important, other factors also affect the choice of a digital modulation scheme. For example, for all personal communication systems which serve a large user community, the cost and complexity of the subscriber receiver must be minimized, and a modulation which is simple to detect is most attractive. he performance of a modulation scheme under various types of channel impairments such as Rayleigh and Ricean fading and multipath time dispersion, given a particular demodulator implementation, is another key factor in selecting a modulation. In wireless systems where interference is a major issue, the performance of a modulation scheme in an interference environment is extremely important. Sensitivity to detection of time jitter, caused by time-varying channels, is also an important consideration in choosing a particular modulation scheme. In general, the modulation, interference, and implementation of the time-varying effects on a channel as well as the performance of the specific demodulator are analyzed as a complete system using simulation to determine relative performance and ultimate selection [1-8]. 3-FSK Background: s its name suggests, a frequency shift keyed transmitter has its frequency shifted by the message [1-15]. lthough there could be more than two frequencies involved in an FSK signal, in this experiment the message will be a binary bit stream, and so only two frequencies will be involved. he word keyed suggests that the message is of the on-off (mark-space) variety, such as one (historically) generated by a more key or more likely in the present context, a binary sequence. he output from such a generator is illustrated in Figure 1 below. [] Fig (1)FSK waveform, derived from binary message Fig.(1) Output waveform generation Conceptually, and in fact, the transmitter could consist of two oscillators (on frequencies f 1 and f ), with only one being connected to the output at any one time. his is shown in block diagram form in Figure below [3]. 3
Fig () FSK transmitter block diagram Unless there are special relationships between the two oscillator frequencies and the bit clock there will be abrupt phase discontinuities of the output waveform during transitions of the message. In a FSK system, the binary symbols are represented by 1/. We can take (t) =cos πf 0 t and (t) =sin π f 1 t as the orthogonally basis functions [3]. he applicable signal constellation diagram of the orthogonal BFSK signal is shown in Figure 3[3] S 0 =cos(лf 0 t) 0 <t< (3.1) S 1 =cos(лf 1 t) Elsewhere (3.) where is a constant, f 0 and f 1 are the transmitted frequencies and is the bit duration. he signal has a power P = /, so that = P. hus equation (3.1, 3.) can be written as { p cos F 0 t 0 <t< { p cos F 1 t Elsewhere Figure (3) Orthogonal BFSK signal Constellation diagram. It can be seen that phase continuity is maintained at transitions. Further, the BFSK signal is the sum of two BSK signals generated by two modulating signals m0(t) and m1(t). herefore, the Fourier transform of the BFSK signal s (t) is s( f ) j j ft m o ( t) e fot e dt { p cos F 0 t 0 <t< { p cos F 1 t Elsewhere (3.3) { p cos F 0 t 0 <t< s( f ) s( f ) j j ft m o ( t) e fot e dt j j ft m o ( t) e f 1t e dt (3.4) { p cos F 1 t Elsewhere Where E = P is the energy contained in a bit duration. For orthogonally, f 0 = m/ and f 1 = n/ for integer n > integer m and f 1 - f 0 must be an integer multiple of s( f ) j j ft m o ( t) e f 1t e dt s( f ) M O( F F O) M O( F F O) 4
s( f ) M O( F F 1) M O( F F 1) Figure 4 shows the amplitude spectrum of the BFSK signal when m 0 (t) and m 1 (t) are periodic pulse trains. Figure 4 (a) Modulating signals, (b) Spectrum of (a), and (c) spectrum of BFSK signal (positive frequencies only)[3]. n alternative representation of the BFSK signal consists of letting f0 = fc - Δf and f1 = fc + Δf. hen f1 - f0 = Δf (.4) nd s (t) = cosδ ( fc + Δf)t (4.5) where fc is the carrier frequency, Δ f = B is the frequency deviation, modulation index, and B = 1/ is the bandwidth of the modulating signal. When Δ f >> 1/, we have a wideband BFSK signal. he bandwidth is approximately equal to Δ f. When Δ f << 1/, we have a narrowband BFSK signal. he bandwidth is approximately equal to B 4 Simulations and Results: his section presents the simulation of, 4, and 8-level FSK systems in GWN channel and the results obtained. 4.1 Simulation of dditive White Gaussian Noise (WGN) Channel From probability theory it is known that a Raleigh distributed random variable R, with probability distribution function F(R) = { 0, R<0 {1- e -R/σ,R 0 is related to a pair of Gaussian random variables X and X through the transformation X 1 =Rcosθ (4.1) X =Rsinθ (4.) Where θ is a uniformly distributed variable in the interval (0, θ) and the parameter σ is the variance of X 1,X. Now, generating a Rayleigh distributed random variable with the computer, we have F(R) =1- e - R /σ =M (4.3) Where M is a uniformly distributed random variable in the interval (0, θ). Solving equation (4.3) results in 1 R ln (4.4) 1 M If we generate a second uniformly distributed random variable N, and definenπθ=, then from equations (4.1), (4.) and (4.4) we obtain two independent Gaussian distributed random variables X and X as 1 x1 ln COS ( ΠN) 1 M 1 x ln SIN ( ΠN) 1 M 4. Simulation of Binary FSK System in WGN Channel In this section, simulations in additive white Gaussian channel and results for both coherent and no coherent (square-law detection) binary FSK systems are presented 5
4..1 Coherent System model for the simulation of coherent binary FSK system in WGN channel is shown in Figure 4.1. Figure 4.1 Simulation model for coherent binary FSK system []. Since the signals are orthogonal, when a 0 (signal s 1 (t)) is transmitted, the correlation are outputs are r o = E b +n 1 and r 1 =n 1 When a 1 (signal S (t)) is transmitted, the correlate outputs are r 1 =n 0 Figure 4. shows the results of the simulation for the transmission of 40,000 bits at several different values of Eb\ N0o and how it compares with theory. 4.. No coherent (square-law detection) System model for the simulation of no coherent (square-law detection) binary FSK system in WGN channel is shown in Figure 4.3. Since he signals are orthogonal, when s (t) is 1 transmitted, the first demodulator output is E cos n r I b 1I r Q E sin nq b and the second demodulator output is r I =n I r Q =n Q Where n 1I, n 1Q n I n 1Q are mutually statistically independent zero-mean Gaussian random variables with variance σ and represents the channel-phase shift. he square-law detector computes r 1 =r 1I +r 1Q r =r I +r Q, and selects the information bit corresponding to the larger of these two decision variables. Figure 4.3 Simulation model for non coherent binary FSK system []. Figure 4. Performance of simulated coherent binary FSK system Figure 4.4 shows the results of the simulation for the transmission of 40,000 bits at several different values of Eb/NO and how it compares with theory. he result is acceptable and theoretical is similar to simulation. 6
Figure 4.4 Performance of simulated no coherent binary FSK system 4.3 Simulation of 4 and 8-level FSK Systems in WGN Channel model for the simulation of coherent 4- level FSK system in WGN channel is shown in Figure 4.5[]. he block diagram of the simulation of no coherent 4-level FSK system in WGN channel is similar to that in Figure 4.3, the only difference being the number of correlate (demodulator) outputs. he block diagram of the simulation of coherent 8-level FSK is similar to that depicted in Figure 4.5, whiles the model for simulation of no coherent 8-level FSK systems is similar to that shown in Figure 4.3 Figure 4.5 Simulation model for coherent 4- level FSK system. Figures 4.6-4.9 illustrates the results of the simulations for the transmission of 40,000 symbols at several different values of Eb/NO and how it compares with theory. When the M- increase the bit error rate is decrease also we Need E b N o is smaller in M-8 than M-4. Figure 4.6 Performance of simulated coherent 4-level FSK system. 7
he comparison of simulated bit and symbol error probabilities for coherent and no coherent, 4, and 8-level FSK systems are shown in Figures 4.10-4.13. Figure 4.7 Performance of simulated no coherent 4-level FSK system. Figure 4.10 Comparison of simulated symbol error probabilities for coherent M-ary FSK. Figure 4.8 Performance of simulated coherent 8-level FSK system Figure 4.11 Comparison of simulated bit error probabilities for coherent M-ary FSK. Figure 4.9 Performance of simulated no coherent 8-level FSK system. 8
Fig 4.1 Comparison of simulated symbol error probabilities for no coherent M-ary FSK Figure 4.13 Comparison of simulated bit error probabilities 5 Conclusions In this paper, binary and M-ary FSK modulation techniques are extensively studied. he performance of, 4 and 8-level FSK systems in additive white Gaussian noise channel are evaluated and compared on the basis of the simulations in MLB. he primary objective of paper, is to show the advantage of FSK modulation technique, factors influencing the choice of a particular digital modulation scheme, a model for WGN channel, generation and detection of binary and M-ary FSK modulated signals, and error performance of binary and M-ary FSK modulation systems in WGN channel MLB and results show that the gap between the performance of theoretical and simulation l M-ary FSK systems widens as the bit error rate (BER) decreases, with theoretical FSK systems always performing better. References [1] Feher; pplication of Digital Wireless echnologies to Global Wireless Communications; Prentice Hall 1997. for no coherent M-ary FSK. herefore, it can be observed from the graphs that at a particular error probability, the required energy efficiency ((Eb/N0) is lowest for 8-level FSK and largest for binary FSK. Or equivalently, at a constant (Eb/N0), 8-level FSK has the lowest error probability, and binary FSK the largest. Hence, the curves in Figures 4.10 4.13 confirms that M-ary FSK is a power efficient modulation scheme whose power efficiency increases as the number of frequencies employed increases [] W.omasi; Electronic Communications Systems, Prentice Hall,004 [3] mplitude Shift Keying & Frequency Shiftkeying,ww.ele.uri.edu/courses/ele4 36/labs/ PDF [4] Lawrence E Larson; RF and Microwave Circuit Design for WirelessCommunications;rtech House; 1996. [5] introduction to digital Modulation chemes www.plextek.co.uk/papers /schmsv6.pdf 9
[6] K. rshak, E. Jafer, D. McDonagh and C.S. Ibala "Modelling and simulation of wireless sensor system for health monitoring using HDL and Simulinkw mixed environment", # he Institution of Engineering and echnology 007 [7] heodore S. Rappaport, Wireless Communications: Principles and Practice, Prentice Hall, Second Edition. [8] J. G. Proakis, M. Saheli, Communication Systems Engineering, Prentice Hall, Second Edition. [9] Fuqin Xiong, Digital Modulation echniques, rtech House Publishers, 00. [10] J. G. Proakis, M. Saheli, Digital Communication, Prentice Hall, hird Edition. [11] lister Burr, Modulation and Coding for Wireless Communications, Prentice Hall, 000 [1] M.Schwartz, Information ransmissio,modulation, and Noise, 4/e, McGraw Hill, 1990. [13] P. Z. Peebles, Jr., Digital Communication Systems, Prentice Hall, 1987. [14] H. aub and D. L. Schilling, Principles of Communication Systems, /e, McGraw Hill, 1986 [15] F. Xiong, Digital Modulation echniques, rtech House, 000. 10