38963, VU Mobile Kommunikaion Miderm Exam: Insiu für Nachrichenechnik und Hochfrequenzechnik When answering he following 5 quesions, always remember ha here is someone who has o grade hem So please use legible handwriing - You can answer he quesions in German and/or English - here is a oal of 3 poins in his exam esresul = floor(sum(poins)/3); Problem : Assume ha inphase and quadraure componen of a received baseband signal look he following if Symbol has been ransmied: I() Q() - s - s Furhermore assume ha he ransmier ransmis 4 symbols (Symbol,, 3, and 4) equally probable and if - Symbol has been ransmied, you receive -I() and Q() - Symbol 3 has been ransmied, you receive I() and -Q() - Symbol 4 has been ransmied, you receive -I() and -Q() he receiver employed - samples he inphase componen a he ime insan s where s is equally disribued beween and / - samples he quadraure componen a he same ime insan s p Skech he PDF of he magniude of he complex baseband samples obained by he receiver (label he axes) p Skech he PDF of he phase of he complex baseband samples obained by he receiver (label he axes)
38963, VU Mobile Kommunikaion Problem : Assume ha inphase and quadraure componen of a received baseband signal look he following if Symbol has been ransmied: I() Q() I Q - - he receiver employed - samples he inphase componen a he ime insan I where I is equally disribued beween and / - samples he quadraure componen a a differen ime insan Q where Q is equally disribued beween and / and saisically independen from I Assuming ha Symbol has been ransmied p 3 Sae he join PDF of he inphase and he quadraure componen of he baseband samples obained by he receiver 3 p 4 Calculae analyically he PDF of he magniude of he complex baseband samples obained by he receiver (Hin: disinguish beween he cases r and r ) p 5 Skech he PDF of he magniude of he complex baseband samples obained by he receiver (label he axes) Assume now ha he ransmier ransmis 4 symbols (Symbol,, 3, and 4) equally probable and if - Symbol has been ransmied, you receive -I() and Q() - Symbol 3 has been ransmied, you receive I() and -Q() - Symbol 4 has been ransmied, you receive -I() and -Q() p 6 Sae he PDF of he magniude of he complex baseband samples obained by he receiver (in erms of he PDF obained in quesion number 4)
38963, VU Mobile Kommunikaion Problem 3: Noe: Erlang ables are aached a he end of his es Consider an analog Advanced Mobile Phone Sysem (AMPS) operaor (AMPS is a pure FDMA sysem): - he operaor has a license for a 5 MHz specrum - Each frequency channel is 3 khz (including guard bands) wide - he signal o inerference raio (SIR) for saisfacory call qualiy is 8 db - he fading margin is 5 db, consider he fading margin only once - he power decrease is assumed o follow he d 4 law You now have o design a radio access nework saisfying he following assumpions and consrains: - Less han 3% of he calls are blocked - Your nework has 5 subscribers - he coverage area is 64 km - One hird of he subscribers are acive - And he average call duraion is 9 seconds p 7 Wha is he reuse disance? p 8 Wha is he cluser size for hexagonal layou? p 9 How many carrier frequencies does he operaor provide? p How many frequency channels are required per cell? p How many subscribers can be maximally assigned o one cell? p How many cells should your radio access nework have if you guaranee ha no more han 3% of he calls will be blocked on average? p 3 Wha is he base saion s cell densiy per square kilomeer? p 4 Suppose ha wo operaors share he same above menioned 5 MHz frequency band? Does he average offered raffic of he nework: a) enlarge b) say equal c) decrease Subsaniae your claim! 3
38963, VU Mobile Kommunikaion Problem 4: Assume ha he 4 QAM depiced in he following signal space diagram I 4 3 Q is ransmied over a channel disruped by addiive whie Gaussian noise Noise ransmi Symbol MAP Deecor Receive Symbol Symbols,, and 3 are ransmied equally probable Symbol 4 is never ransmied, and his fac is known o he receiver p 5 Draw he decision region ha he MAP deecor has o employ in order o minimize he average symbol error rae p 6 Derive a funcion P = f(q, v) where - P = P {s s s } is he probabiliy ha Symbol is ransmied bu some oher symbol is deeced a he receiver, - q = Q ( γs ), - v = Q ( γ s ), - γ s is he signal o noise raio (SNR) before he MAP deecor, ( - and Q (x) = π x e ξ dξ = erfc x ) 3 p 7 Derive a funcion P = f(q, v) where P = P {s s s } is he probabiliy ha Symbol is ransmied bu some oher symbol is deeced a he receiver p 8 Derive a funcion P s = f(q, v) where P s = P {E s } is he average symbol error probabiliy for he given ransmission p 9 Draw a new symbol consellaion, such ha, while keeping he average symbol energy equal, he average symbol error probabiliy is minimized (You do no have o calculae he new symbol error probabiliy) 4
38963, VU Mobile Kommunikaion Problem 5: On he saic Gaussian noise channel, he probabiliy of bi error for binary differenial phase shif keying (binary DPSK) is P b = e γ b () where γ b is he raio of energy per bi o noise power specral densiy (E b /N ) Figure : Hin from a mah book 3 p Calculae he probabiliy of bi error for DPSK in a fla Rayleigh fading channel in erms of γ b, he mean value of γ b p Given a bi error probabiliy of in a saic AWGN scenario, by how many db do you have o increase he ransmi power o achieve he same average bi error rae in a Rayleigh fading scenario (Hin: use he figure on he nex page) p Is he probabiliy of bi error, for he same γ b, in a channel employing Ricean fading higher han in a channel employing Rayleigh fading? Explain your answer p 3 In wha scenarios is a saic channel usually observed? Give examples of ypical mobile communicaion sysems (Make clear, why he channel in hese scenarios is no fading) p 4 In wha scenarios is Rayleigh fading usually observed? Give examples of ypical mobile communicaion sysems (Make clear, why he channel in hese scenarios is no saic) p 5 In wha scenarios is Ricean fading usually observed? Give examples of ypical mobile communicaion sysems (Make clear, why he channel in hese scenarios is no saic) 5