Question 1 TELE4353. Average Delay Spread. RMS Delay Spread = = Channel response (2) Channel response (1)

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1 ELE4353 Mobile and Saellie Communicaion Syem uorial 3 (wee 7-8 S 4 Queion If a paricular modulaion provide uiable ER performance whenever σ / <., deermine he malle ymbol period (and hu he greae ymbol rae ha may be en hrough RF channel hown in he figure wihou uing an equalizer. Alo find. maximum exce delay ( d,. 9% correlaion coherence bandwidh, 3. 5% correlaion coherence bandwidh. uorial 3- Wee 7-8 uorial 3- Wee 7-8 Channel repone ( Channel repone ( ( ( dm dm - dm Indoor - dm Oudoor - dm - dm -3 dm -3 dm 5 75 Exce delay (n 5 Exce delay (µ uorial 3- Wee uorial 3- Wee ( ( ( ( Average Delay Spread Muli-pah rofile (Dicree ( a a ( ( ( ( ( ( RMS Delay Spread (( a a Muli-pah rofile (Dicree ( uorial 3- Wee uorial 3- Wee 7-8 6

2 Maximum exce delay (X d ( ( ( ( Muli-pah rofile (Dicree ime delay (wih reference o he fir arriving pah during which mulipah energy fall X d below he maximum. he ronge pah migh no be he fir arriving pah. ( Channel coherence bandwidh Channel paced frequency correlaion funcion anwer he queion: Wha i he correlaion beween he received ignal ha are paced in frequency ff -f? I can be meaured by ending wo inuoid eparaed in frequency by f, and cro-correlaing he wo eparaely received ignal and repeaing he proce for all f. Channel coherence bandwidh i a meaure of he range of frequencie over which he channel migh be conidered fla. aing all pecral componen wih equal gain and linear phae. uorial 3- Wee uorial 3- Wee Soluion o Q, Indoor channel ( (n ( * + *5 +.*75 +.* ( * + *5 +.*75 +.* 7.75 n ( ( dm - dm - dm -3 dm 5 75 Indoor Exce delay (n c.9 c.5 Soluion o Q, Indoor channel σ n σ. σ 7 n R 3.7 Mp 74 Hz 5σ 5*7n 7.4 MHz 5σ 5*7n From he fir figure, afer 75 n he power fall below d of he maximum x 75 n x - 75 n uorial 3- Wee uorial 3- Wee 7-8 Soluion o Q, Oudoor channel (.* + *5 +.* 5.4 µ (.+ +. ( 3.53 ( µ (.+ +..* + *5 +.* ( dm - dm - dm -3 dm 5 Oudoor Exce delay (µ c.5 Soluion o Q, Oudoor channel σ µ σ. σ 5.4 µ R p c Hz 5σ 5*.5µ 33.3 KHz 5σ 5*.5µ From he econd figure, afer µ he power fall below d of he maximum x µ x - µ uorial 3- Wee 7-8 uorial 3- Wee 7-8

3 Queion Aume ha θ o. he bi ream i o be en uing π/4 DQSK. he lefmo bi are fir applied o he ranmier. Deermine he phae of θ, and he value of I, Q during ranmiion. π/4 ranmiion echnique I and Q repreen recangular pule over one ymbol duraion having ampliude given by I Q coθ I θ θ inθ I + φ coφ Q inφ Q inφ coφ uorial 3- Wee uorial 3- Wee Conellaion diagram of a π/4 QSK a poible ae for θ when θ - nπ/4 b poible ae for θ when θ - nπ/ c all poible ae Carrier hae Shif Correponding o Variou Inpu i air Informaion bi m I, m Q hae hif φ π/4 a b c 3π/4-3π/4 -π/4 uorial 3- Wee uorial 3- Wee Generic π/4 QSK ranmier π/4 ranmiion echnique, con. Serial o arallel Converer Signal Mapping LF LF co ω c I( Q( Amplifier π / 4QSK where I( Q( ( I( coω Q( inω N N I p( / Q p( / c N c coθ p( / N inθ p( / -in ω c p( correpond o he pule hape and i he ymbol period uorial 3- Wee uorial 3- Wee 7-8 8

4 Soluion o Q, modulaion he fir wo bi are, which implie φ -3π/4 (from able θ θ +φ -3π/4 hi implie I co θ -.77 Q in θ -.77 and Soluion o Q, modulaion he econd wo bi are, which implie φ -π/4 (from able θ θ +φ -π hi implie I co θ - Q in θ and uorial 3- Wee uorial 3- Wee 7-8 Soluion o Q, modulaion he hird wo bi are, which implie φ 3 π/4 (from able θ 3 θ +φ 3-3π/4 hi implie I 3 co θ Q 3 in θ and loc Diagram of a aeband Differenial Deecor F co ω c -in ω c LF LF w co(θ -γ Compue x Sample a max. oupu for every Sample a max. oupu for every Compue y Deciion Device S I Muliplex S Q Deciion Device z in(θ -γ uorial 3- Wee 7-8 uorial 3- Wee 7-8 Soluion o Q, demodulaion he oupu of he differenial decoder i x w w co( θ co( θ co( θ θ + z z w z in( θ co( θ in( θ θ uorial 3- Wee 7-8 y z w + in( θ in( θ co( θ in( θ γ i a phae hif due o noie, propagaion, and inerference 3 Soluion o Q, demodulaion he phae difference beween hree differen received phae give θ - θ -3π/4--3π/4 θ - θ -π-(-3π/4 -π/4 θ 3 - θ -3π/4-(-π π/4 (x,y (-.77,-.77 (x,y (.77,-.77 (x 3,y 3 (.77,.77 uorial 3- Wee 7-8 4

5 Soluion o Q, demodulaion S I, if x > or S I, if x < S Q, if y > or S Q, if y < we ge he received equence Queion 3 Find he 3-d bandwidh for a Gauian low pa filer ued o produce.5 GMSK wih a channel daa rae of R b 7 bp. Wha i he 9% power bandwidh in he RF channel? uorial 3- Wee uorial 3- Wee Occupied RF andwidh Conaining a Given ercenage of ower. GMSK.5 GMSK.5 GMSK MSK 9% % % % Gauian MSK GMSK i he modulaion cheme ued in curren GSM yem I i a imple binary modulaion cheme which may be viewed a a derivaive of MSK he modulaing waveform i paed hrough a premodulaion Gauian pule haping filer π π ln h G ( exp where α α α uorial 3- Wee uorial 3- Wee From given R b, we ge R b 7 Soluion o Q µ Solving for, where Hz Soluion o Q3, con. hu 3 d bandwidh i Hz. o deermine he 9% power bandwidh, from he able we ge.57 R b, i.e. RF W.57R b Hz uorial 3- Wee uorial 3- Wee 7-8 3

6 Queion 4 Deermine he maximum hroughpu ha can be achieved uing ALOHA and loed ALOHA proocol. raffic occupancy, R Aume ha he yem ue fixed pace ize and fixed channel daa rae ace are generaed by uer randomly and pace ranmiion occur wih a oion diribuion having a mean arrival rae of λ pace / ec. If i he pace duraion, in econd, he raffic occupancy R λ. R - normalized channel raffic in uni of Erlang. < R <. uorial 3- Wee uorial 3- Wee oion pace generaion he probabiliy ha n pace are generaed by he uer populaion during a given ime inerval i oion diribued ( n r pace during ime n λ ( λ e n! For example he probabiliy ha pace are generaed during inerval i: r( e λ e R hroughpu, he average no of meage uccefully ranmied per uni ime. I can be hough of a he fracion of ime (fracion of an Erlang he channel i uilized. R * rob[no colliion] λ * rob[no colliion] uorial 3- Wee uorial 3- Wee Vulnerable period he ime inerval during which he pace are ucepible o colliion ace ace Will collide wih ace A ace A ace C ace C will no collide wih pace A ure ALOHA Vulnerable period i double he pace period. he probabiliy ha pace are generaed during vulnerable period i: ( n ( R e r e n! R * rob[no colliion] R*e -R R n R uorial 3- Wee uorial 3- Wee

7 Maximum hroughpu in pure ALOHA R*e R / -R ( e -R*e e -R -R -R -R R / / * e.839 Sloed ALOHA Vulnerable period i one pace period. he probabiliy ha pace are generaed during vulnerable period i: ( R n R e r ( e n! R * rob[no colliion] R*e -R n R uorial 3- Wee uorial 3- Wee Maximum hroughpu in loed ALOHA R*e R -R ( -R -R -R e -R*e e -R R e.3679 uorial 3- Wee