EE 499: Wireless & Mobile Communiaions (08) Leure : Modulaion Tehniques or Mobile Radio Dr. Wajih. bu-l-saud mpliude Modulaion Tehniques mpliude Modulaion (Full M or Double Sideband wih Carrier) The general orm or a Full M signal (whih we someimes all DSB wih Carrier or simply M modulaions) is [ ] s () = + µ m()os( π ), M is he ampliude o he unmodulaed arrier signal, m () is he message signal wih ampliude less han, µ is he modulaion index wih 0 µ, and is he arrier requeny in Hz. In requeny domain, he M signal has sperum given by SM = ( ) + ( + ) + M( ) + M( + ) [ δ δ µ µ ] This basially says ha he ull M modulaed signal onains an unmodulaed arrier a he arrier requeny along wih wo shied versions o he sperum o he message signal ha are shied by he arrier requeny o he le and o he righ. The ollowing igures show represenaions o he message signal and he ull M modulaed signal boh in ime and requeny domain. For a message signal m () wih bandwidh BW equal o BW m (), he bandwidh o he ull M signal (or DSBSC) signal is BW Full M = BWm Unorunaly, in addiion o he a ha ull M is bandwidh ineiien (i uses Hz o he hannel o ransmi eah Hz o he message signal) i is also power ineiien (mos o he ransmied power arries no inormaion a all (wased in he unmodulaed arrier). To see his, noe ha he power o he Full M signal is = + () + () PFull M µ m µ m m () is he average o m () and m () is he power o m (). Le us assume ha he message signal m () has no DC value (zero average). This is a valid assumpion or mos analog inormaion signals. In his ase, he power o he ull M signal beomes
EE 499: Wireless & Mobile Communiaions (08) Dr. Wajih. bu-l-saud Leure : Modulaion Tehniques or Mobile Radio PFull M = µ m + = + µ m () Power o Unmodulaed Carrier (Wased Power) Power o DSBSC Modulaed Signal (Useul Power) m() M() Message +m() ( M() DC Message s M () + m() Frequeny = S M () Un-modulaed arrier DSBSC signal USB LSB LSB USB m() So, he power eiieny o he ull M signal is equal o
EE 499: Wireless & Mobile Communiaions (08) η Full M Leure : Modulaion Tehniques or Mobile Radio UseulbPower UseulbPower = = Toal Power UseulbPower + Wased Power µ m () = + µ m () µ m () = + µ m Dr. Wajih. bu-l-saud Consider a message signal ha is a sinusoid wih ampliude o (noe ha his is a praial assumpion sine mos message signals an be represened using a inie number o sinusoids), he power o he message signal beomes equal o 0.5 and he power eiieny beomes η µ = + µ Full M I is lear ha or 0 µ, he power eiieny has a range rom 0 o 0.333. Thereore, he maximum power eiieny o ull M is only 33.3%. In mos praial ull M sysems, a praial value o µ = 0.7 is used. In his ase, he power eiieny is approximaely equal o 0. (or 0%), whih means ha 80% o he ransmied power is wased in he unmodulaed arrier. Single Sideband (SSB) Modulaion The general orm or a single sideband signal is s () = m()os( ) m()sin( ), SSB is he ampliude o he wo omponens ha mae he SSB signal, m () is he message signal, and m ˆ () is he Hilber ransorm o he message signal. I he sign beween he wo erms is negaive, we ge an upper sideband (USB) signal, and i i is posiive we ge a lower sideband (LSB) signal. Tha is susb () = m()os( ) m()sin( ) s () = m()os( ) + m()sin( ) LSB The Hilber ransorm o he message signal is nohing bu a iler ha perorms a 90 phase shi o eah omponen o he signal (his is dieren rom a delay ha delays all omponens o he signal by a onsan amoun beause a 90 phase shi o eah omponen orresponds o a dieren delay o eah requeny omponen o he signal). Thereore, in ime domain, he Hilber ransorm o m () and he impulse response o he Hilber ransorm iler are 3
EE 499: Wireless & Mobile Communiaions (08) Leure : Modulaion Tehniques or Mobile Radio m ˆ () = m ()* hht () = π π Dr. Wajih. bu-l-saud and in requeny domain he Hilber ransorm o m () and he ranser union o he Hilber ransorm iler are Noes: ˆ jm < 0 j < 0 M ( ) = HHT () = jm > 0 j > 0. Full M modulaion an be demodulaed using oheren or non oheren demodulaion ehniques and DSBSC modulaion an be demodulaed using oheren demodulaion. For he oheren demodulaion o boh o hese ehniques, he arrier signal a he reeiver mus be regeneraed wih he same requeny an phase o he arrier o he reeived signal. Carrier aquisiion ehniques exis or generaing his arrier signal loally a he reeiver.. Carrier aquisiion in he same manner used wih ull M or DSBSC does no wor wih SSB modulaion. Thereore, a very small unmodulaed arrier is always ransmied wih SSB signals o allow he reeiver o demodulaed hem. This ype o SSB is alled pilo one SSB. The level o he un modulaed arrier is very low (around 0 db below he larges requeny omponen in he signal) and is purpose is only o allow he reeiver o generae a arrier wih he same requeny and phase as ha o he reeived signal. The pilo one an eiher be insered in he band o he modulaed signal or ouside o is band. ngle Modulaion There are wo amous lavors o angle modulaion: ) Phase Modulaion (PM), ) Frequeny Modulaion (FM). Frequeny Modulaion The general orm o a requeny modulaed signal is sfm () = os π π m( α) dα +, is he ampliude o he modulaed signal, and is he requeny deviaion sensiiviy (Hz/V) ha deermines how many Hz does he insananeous requeny o he signal hange as he message signal inreases by Vol. 4
EE 499: Wireless & Mobile Communiaions (08) Dr. Wajih. bu-l-saud Leure : Modulaion Tehniques or Mobile Radio The requeny modulaion index β relaes he message ampliude o he FM signal bandwidh: β m = = π W W and m is he pea value o he message signal, W is he bandwidh o he message signal (in Hz), is pea requeny deviaion o he FM signal (in Hz). The bandwidh o he FM signal has a maximum value given by he Carson s rule given below: ( β ) BW = + W = + W in Hz FM Phase Modulaion The general orm o a phase modulaed signal is spm () = os π + pm(), is he ampliude o he modulaed signal, and p is he phase deviaion sensiiviy (radians/v) ha deermines how many radians does he phase o he signal hange as he message signal inreases by Vol. The phase modulaion index β p relaes he message ampliude o he PM signal bandwidh: β = = p p p m Radians). m is he pea value o he message signal, and p is pea phase deviaion o he PM signal (in 5