Bandpass Modulation and Demodulation 2-Digital Communications-Lecture Slides, Slides of Digital Communication Systems

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Chapter 4: Bandpass Modulation and Demodulation ® docsity.com  | 4.5.4 Required Tone Spacing for Noncoherent Orthogonal FSK Signaling = FSK is usually implemented as orthogonal signaling, but not all FSK signaling is orthogonal = How can we tell a Ifthe two tones f1 and f2 are orthogonal to each other a Or they are uncorrelated over symbol time T = Property: any pair of tones in the set must have a frequency separation that is a multiple of 1/T Hz =» A tone with frequency f1 that is switched on for a symbol duration T seconds and then switched off can be analytically described as: S,(t) = (cos(277,t) rect(t/T)) 1 for-T/2<t<T/2 rect(t/T) = rect I={) for |t|>T/2 ® docsity.com  Example 4.3: Non-coherent FSK signaling = Two waveforms for:cos(27 f+) and cos 2z f,t where f1>f2, the symbol rate 1/T and = a constant arbitrary angle (a) Prove that the minimum tone spacing for non coherently detected orthogonal FSK signaling is 1/T Tr [cos(2z fr+)cos2xf,rdr=0 (eq 4.45) 0 T T cos | cos 2z fit cos 2x f,tdt—sin pl sin2z ft cos2x ft di =0 0 0 cos #{[cos 2m(f, +f)t +cos2a(f, — f)tldt -sing | [sin2x(f, +f,)t +sin27(f — f,)t]dt=0 ® docsity.com  sg| meal + fi)t + sin2z(f,-f5 *) aft Sr) If, F2) Io T 1 sin gl 2a +h sett Lo) 2a fit hy) 2a(fi- fr) 0 cong| 2 +A , sin2zth =F) 2a(fith) orf fy) sing) — —= 2m( firth) 2a(fi- fy) Assume that f1+f2 >> 1 sin2a(f,+ fT __ cos 2a(f, +A )T <0 2m(fi+ fy) 2a(fit fr) SOP SAT =}, S082RUL = TI 6 (eq 4.49) (eq 4.50) @ docsity.com  Combining eq-4.49 & eq-4.50 cos gsin 27(f, — f,)T +sing[cos 2a(f, - f,)T -1] 0 (eq 4.51) Note that for arbitrary ¢, the terms eq4.51can sum to 0 only when sin 27(f, — f,)T =0 and simultaneously cos 27(f, — f,)T =1 sinx=0 forx=nz and cosx=1 for x =2ka wherenand k are integers for arbitrary ¢: 2n(f,—f)P=2ke or f-f == (eq 4.52) l. f-h= F (minimum tone spacing at k =1) & docsity.com  = Analytical expression can be written as S(t)=A g(t)cos[a,t+é(O], O<rsT7,, i=1,2,....,M where a g(t) is signal pulse shape a A=amplitude of the signal a @=carrier phase = The range of the carrier phase can be determined using _ 2n(i-1) 9 (1) = —— i=1,....M grees ® docsity.com  =n Wecan now write the analytical expression as s= Fs cos t+ +20) O<1<T,, and i=1,2,...M r, M LY a eeer phase changes Constant envelope abruptly at the beginning of each signal interval 180-phase 0-phase -90-phase shift shift shift PP UNIV VV, = In PSK the carrier phase changes abruptly at the ve beginning o of each signal interval while the amplitude remains constant ® docsity.com  = We can also write a PSK signal as: s(t) = “Eco 0 20D) T M 2E 2r(i-1) . 2n(i-l) . = |_| cos ——— cos@,f-—sin———sin__ @f T M M = Furthermore, s,(t) may be represented as a linear combination of two orthogonal functions w,(t) and w(t) as follows s,(t) = VE 008, - VE sin =) w(t) Where y(t) = = cos| and y,(t) = = sin{o ® docsity.com  M-ary PSK = In MPSK, the phase of the carrier takes on one of M possible values 27 (i-1 0) =2 Daa, = Thus, MPSK waveform is expressed as k , M=2 MPSK s,(t) = 2k co out anti >| 2 BPSK T 4 OPSK onli -1 8 8— PSK s(t) = g(0)603 0 + a 4 16 16 — PSK = Each s/t) may be expanded in terms of two basis function ¥,(f) and W,(t) defined as 2 2. Wi(t)= 7 0s ot, Yo) = 7 ot, CS docsity.com  Quadrature PSK (QPSK) = Two BPSK in phase quadrature = QPSK (or 4PSK) is a modulation technique that transmits 2-bit of information using 4 states of phases = For example Each symbol corresponds to two bits = General expression: [2E, 2eG-1)] S ops (t) = TO cos ar. + 7-9, l= 1,2,3,4 O<r< T, ® docsity.com  The signals are: 2E _ |2Es Ty Sy = ar cos(w,t) sS= op coset +a) =~ S S,= 2k, cos(@,f +7) =—- cos(@,1) Ss s 2E 37 2E, Ss, =,/— cos(a@,t + —) = |= sin(@.\1) YT, 2 17 Sy) =+ Js cos@,t, o—shift of 0° and 180° 8,,()=+ = sin@,t, shift of 90° and 270° Ss E,. = sin(@,t) s & docsity.com  = Interms of basis functions W(t) = = cos2af.t and y,(t)= = sin 27f.t we can write Sops,(t) as Sorse (= NE cos] 20D (0 - JE, sin] 20D by cn} = With this expression, the constellation diagram can easily be drawn = For example: ® docsity.com  Coherent Detection 1. Coherent Detection of PSK Coherent detection requires the phase information =» Acoherent detector operates by mixing the incoming data signal with a locally generated carrier reference and selecting the difference component from the mixer output tsT I NA “ame LPF cos(ar) ‘ aq) 7 > S(t) AC e08( uct) a Multiplying r(t) by the receiver LO (say A cos(w,t)) yields a signal with a baseband component plus a component at 2f, a TheLPF eliminates the high frequency component a The output of the LPF is sampled once per bit period a The sampled value z(T) is applied to a decision rule = Z(T) is called the decision statistic & docsity.com  = Matched filter receiver r(t) h(t) =s(F,,-1) TD | | si Zoos filter pair i cos(a, A cos(«, f} a AMF pair such as the root raised cosine filter can thus be used to shape the source and received baseband symbols a Infact this is a very common approach in signal detection in most bandpass data modems docsity.com