UNIT-IIIFREQUENCY HOPPING SS SYSTEM

MPN^FH DE-MOD123DECODERM ENERGY DETECTORSCODERFH MODMFSK MODJAMMERBINARYK-TUPLEBINARYK-TUPLEBINARYK-TUPLEBINARYDATANON-COHERENT FH SYSTEM MODEL:

FIG: FUNCTIONAL BLK. DIAGRAM OF FH/MFSK SYSTEM PERUBED BY JAMMIMNGTransmit one of M=2k tones, carrier is hopped to one of 2k frequencies determined by k-chip segments of PN code, dehopping requires derived PN reference (pN)^, non coherent detection.On a single hop, the system occupies a BW similar to conventional MFSK, which smaller than spread spectrum BW WSS. But with multiple hops the FH/MFSK System occupies the entire SS bandwidth.Frequency hop BW is of the order of several Ghz, which is larger than direct sequence BW.With successive frequency hops, coherent demodulation is not possible so, we discuss the system with non coherent demodulation. The system is said to be fast frequency hopped (FFH), when the hop rate FH is an integer multiple of the MFSK symbol rate Rs.The system is said to slow frequency hopped (SFH), when the MFSK symbol rate RS is an integer multiple of the hop rate Rh.Chip refers to the individual FH/MFSK tone of shortest duration.In an FFH system where there are multiple hops per M-ary symbol, each hop is a chip.In an SSH system, a chip denotes an M-ary symbol,Chip rate Rc=max (Rh,Rs).With non coherent detection, the MFSK tons on a given hop must be separated in frequency by an integer multiple of Rc to provide orthogonality.Fig. shows the implementation in which the entire SS band it portioned into Nt = Wss/Rc, Equally spaced FH tones, where PG=NtRc/RbThen these are grouped into Nb=Nt/M adjacent, non overlapping M-ary bands, each with Band Width MRc.Under this arrangement, any Nb=2k carrier frequency is FH modulated by binary k*PN, to produce a specific, hop invariant M-ary symbol.

MRc

M-ARY BAND

2114324231

Rc

Wss=Nt Rc

MRcFrequency structure for FH/MFSK systems with Nt tones equally separated by Rc in M-ary bands contiguous and non overlapping.

Rc

21

Rc

Wss=Nt R

Bands are shifted by Rc, which scrambles the FH tone/M-ary symbol mapping.(M=4 here). As a method of scrambling, H is allowed to hop the carrier at all M slots of Nt available frequencies only once. A more jam-resistant approach is to use M=distinct frequency synthesizers.In addition to anti jam capability, the SS signal is generally difficult to detect and even harder to decipher by an unauthorized receiver, it is referred as low probability of intercept (LPI)The LPI advantage of an SS signal is that its power is spreaded over large BW.The processing gain PG can be defined as the ratio of the SNRs at the output and input of the despreader and can be expressed as PG = Wss/Rb.In frequency hop systems, PG can be defined as the number of available frequency choices.In FH/MFSK system, Nt= Wss/Rc and so PG=NtRC/Rb. For BFSK or MFSK with M=2. Rc = Rb, so PG=Nt.

MRcM-ARY BAND

wRc

In MFSK with overlapping bands, with w0 with non overlapping bands, Wss=Nb M Rc.UNCODED FH/BFSK SYSTEM:Taking a basic modulation technique and changing the carrier frequency in some pseudo random manner is the frequency hopping method of spread spectrum. Most common method of modulation used with frequency hopping is M-ary frequency shift keying (M-FSK)Ordinary BFSK signals have the form, s(t)=2s sin [wot+dnwt];nTbt e- -1, e+ e-UNCODED FH/BFSK PERFORANCE UNDER CONSTANT POWER BROADBAND JAMMER: For each Tb time interval, the bit error probability is the amount of jammer power in the instantaneous bandwidth of the signal that contributes to the energy term e+ & e-. The overall bit error probability is the average of these particular bit error probabilities where average is taken overall frequency hopped shifts. Assume the jammer transmits broadband noise over the total spread spectrum band with constant power J. At any time interval Tb, regardless of the carrier frequency shift, there will be an equivalent white noise, with spectral density Nj=J/Wss. Since an equivalent white Gaussian noise process is encountered at all parts, the bit error probability for all uncoded FH/BFSK system is same as that of conventional BFSK system. Pb=1/2 e-(Eb/2Nj)

UNCODED FH/BFSK PERFORMANCE UNDER PARTIAL BAND NOISE JAMMER:Assume that the jammer transmits noise over a fraction P of the total spread spectrum signal band.-P=WJ/Wss1, where WJ is the jammed frequency band and Wss is the total spread bandwidth.The noise power spectral density can be given by J/WJ=J/Wss,Wss/WJ=WJ/P.Assume a jammer state parameter Z for each time interval Tb, whereZ= 1, signal in jammed band 0, signal not in jammed band,With Pr {z=1} =P and Pr {z=0}=1-P,Then the bit error probability is Pb=Pr {e+>e-1|d=-1} =Pr {e+>e-1|d=-1, z=1} pr {z=1}+Pr {e+>e-1|d=-1, z=1} pr {z=0}=P/2e-P (Eb/2Nj)Where there are no errors when the signal hops out of jammed band.

Fig: FH/BFSK: PARTIAL BAND NOISE JAMMER Fig: FH/BFSK AGAINST JAMMERThe value of P that maximizes Pb is easily obtained by differentiation.P*= 2/ (Eb/Nj), Eb/Nj>2 1, Eb/Nj2This yields the maximum value of Pb,Pb= e-J/(Eb/Nj), Eb/Nj>2 1/2e-(Eb/Nj), Eb/Nj2The partial band noise jammer on uncoded FH/BFSK system is analogous to pulse noise jammer effect on uncoded DS/BFSK system.UNCODED FH/BFSK PERFORMANCE UNDER MULTITONE JAMMER:For the total spread spectrum signal bandwidth Wss, there are N=Wss Tb possible orthogonal tone position.Consider a jammer that transmits many tones each of energy SJTb with total power J.There are almost Nt=J/SJ jammer tones randomly scattered across the band.The probability that any given signal tone position is jammed with a jammer tone is, P=Nt/N= J/ SJ WssTb, where P is a fraction of the signal tone positions that are jammed.Assuming jammer tone occurs only in alternate tone position, we may ignore the smaller probability of a jammer tone in both positions.Assuming an error occurs only if a jammer tones with power SJS occurs in alternate tone position, the probability of a bit error is Pb=P=J/SJWss Tb, provided SJ>SThe worst choice of SJ=S resulting in the maximum bit error probability, Pb*=J/SWss Tb = 1/Eb/NJThe bit error probability is slightly larger than the worst partial band noise jammer performance.

CODED FH/BFSK PERFORMANCE FOR PARTIAL AND MULTI TONE JAMMER:Assume that mFH/BFSK tones are transmitted for each bit.Assume the simple repeat m code, where for each data bit, m identical BFSK tones are sent, with each tone are hopped separately.With m chips make up a single data bit, the chip duration is Tc=Tb/m.Requiring each of the chip tones to be orthogonal results in, Nc=WssTc=WssTb/mChoose SJ=S so that the probability that a particular chip tone postion is jammed is given by, =Nt/Nc = (J/S)/Wss Tb/m= m/ (Eb/Nj)at receiver, the error on decision making is made only if a jammer tone occurs in all m of the chip tone frequencies corresponding to the BFSK frequency that was not transmitted.This occurs with probability Pb=mPb= (m/ (Eb/Nj)) m, since each chip is independently hopped.This analysis ignored the effects of jamming tones occurring in the same frequencies as the transmitted chips.

The bit error probability is plotted for various values of m.M=1 case is the uncoded case.Note that there exists a value of m that achieves a bit error probability close to the baseline case of broad band noise jamming.Repeat code is a simple code of rate R=1/m bits per coded bit. It is also referred as diversity of order m.Diversity technique is useful in combating deep fades in a fading channel. For similar reasons, diversity is effective for multitone jamming and for worst case partial band jamming. As with DS/BPSK, use of coding did not change the data rate of total spread spectrum BW Wss. only the instantaneous BW associated with each coded bit or chip.PERFORMANCE OF FH/MDPSK IN THE PRESENCE OF PARTIAL BAND MULTITONE JAMMING:The average symbol error probability performance of MDPSK on an additive white Gaussian noise (AWGN) channel is given by, /2PS (M) = sin/ [1+ (log2M) Eb/No (1+cossin )] *exp[-(log2M)Eb/No(1-cossin )]dd, /M 0Where Eb/No is the bit energy to noise ratio.

The double integral can be expressible as a single integral as,

/2Ps (M) = (sin (/m) / ) exp [-(log 2 M) Eb/No (1-cos (/M) cos)] 0* d 1-cos /m cos To obtain the performance of FH/MDPSK in partial band noise jamming, we have o replace Eb/Nj by Peb/NJ.So the bit error probability performance of FH/MDPSK in partial band noise jamming is/2Pb(m\M)=Pm/2(M-1) (sin (/m)/ ) exp[-(log2M)PEb/NJ(1-cos (/m)cos )] 0 * d

1-cos (/M) cos /2(Eb/NJ)-1(M/2(M-1))*[Z (sin (m)/) exp [-(log2M) Z (1-cos (/M) cos )] * d 0Where Z=PEb/NJThe worst case jammer strategy corresponds to a partial band fraction,Pwc=(Eb/NJ)-1Zmaxand the max. bit error probabilityPbmax = (Eb/NJ)-1[Mpmax-2(M-1)], Eb/NJZmax /2 M/2(M-1) (sin(/m)/m) exp[-(log2M)Eb/NJ(1-cos(/m) cos)]0*d1-cos (/m) cos

For 2ary MDPSK,Ps(2)=Pb(2)=1/2exp(-Eb/NJ)For FH/DPSK in partial band noise jamming Pb(2)=P/2.exp(-PEb/NJ)Differentiating this with respect to P and equating to zero yields the worst case performance.Pwc=(Eb/NJ)-1 andPbmax= 1/ [2e (Eb/NJ)], Eb/NJ1 1/2exp (-Eb/NJ),Eb/NJ