TELE4652 Mobile and Satellite Communications

Transcription

1 TELE465 Mobile and Saellie Communicaions Assignmen (Due: 4pm, Monday 7 h Ocober) To be submied o he lecurer before he beginning of he final lecure o be held a his ime.. This quesion considers Minimum Shif Keying (MSK). Each symbol one of he following wo signals is ransmied: E s () = cos( ), for πf T T, oherwise E s () = cos( ), for πf T T, oherwise a) Compue he energy of hese signals, s ( ) and s ( ), for f T, ft >>. b) Explain why MSK is considered a consan envelope modulaion echnique. Wha is he aracion of his consan envelope propery in cellular sysems? c) Find he condiions on he frequencies f and f, expressed in erms of he bi duraion T, o ensure boh ha hese signals are orhogonal and ha s ( ) = s ( T ) = s( ) = s( T ). Explain he imporance of he second propery in his modulaion echnique. d) For he parameer choice in c), deermine and skech he signal consellaion. e) Assume hese signals are ransmied over an AWGN channel. Draw a block diagram of a possible implemenaion of an opimal deecor for his MSK signal. f) Obain an expression for he BER in erms of he E b N, for your deecor srucure in e).. A sysem has wo diversiy branches, each of which can be modelled as an independen Rayleigh fading channel. The probabiliy of he signal ampliude being a on one of he links is given by, a a σ P( a) = e σ where he average power on he branch, E [ a ] = σ, is he same for he wo branches. Denoe he average SNR on each branch as γ. Assume ha BPSK is used wih non-coheren deecion, and ha he operaion of co-phasing he mulipah componens can be carried ou perfecly. Le he hreshold SNR a he oupu be denoed as γ. a) Derive an expression for he ouage probabiliy a he receiver when Selecion Combining (SC) is used. b) Derive an expression for he mean SNR a he oupu wih (SC).

2 c) Derive he expression for he bi error rae a he oupu when selecion combining is used. d) Now, repea pars a)-c) when he receiver used equal gain combining (EGC). ζ ζ y Hin: If z = x + y, hen P( z < ζ ) = P ( x) P ( y) dx dy. You may no be able o obain closed analyic expressions for every par here. Go as far as you can and leave wha you canno evaluae in inegral form. e) Repea pars a)-c) when Maximum Raio Combining (MRC) is used. f) Numerically calculae he ouage probabiliy, mean oupu SNR, and oupu BER when SC, EGC, and MRC are each used, for γ = 8 db and γ = 3 db. Commen on your answers. X Y 3. Consider a convoluional encoder (3,,) wih ocal represenaion [7 5 3]. a) Draw a shif regiser implemenaion of his convoluional encoder. b) Draw sae and rellis diagrams for his encoder. c) Encode he following daa using he encoder: d) The curren Vierbi pah able is: Sae Inpu Bi sequence Hamming disance Updae his able, using he Vierbi algorihm, for he nex received bis,,. Hence find he oupu bi sequence. e) How many errors does i appear he encoder has been able o correc? Is i possible o have a block code ha could correc his fracion of bi errors? If so, wha is he size of he block code required? 4. An 8-bi Frame Qualiy Indicaor in cdma is generaed by a polynomial g ( x) = x + x + x + x + x + The polynomial is used o generae pariy bis for error deecion (bu no correcion). a) Generae he pariy bis o he inpu word. b) How many errors can be deeced? Does his depend on he size of he inpu word? c) Assume ha he probabiliy ha a given bi is in error is p and ha he probabiliy of each bi being in error is independen of every oher bi. Find an expression for he probabiliy ha an error goes undeeced if he codeword size is n. d) Evaluae his probabiliy for he above 8-bi pariy check resuling in he 8-bi resulan sysemaic code paern, when p = 4. e) Repea he above calculaion of error probabiliy for inpu words of size, 5, and bis, for p = 4 and p = 5. Commen on your resuls.

3 5. Ulrawideband (UWB) sysems spread a daa signal over a very wide bandwidh such ha he power per Herz of he signal is small (and ypically below he noise floor). Hence such sysems can coexis wih oher sysems wihou causing hem much inerference. Consider a baseband UWB sysem wih BPSK modulaion. The daa bis are modulaed wih a recangular pulse g ( ) has a very narrow ime duraion T, compared o he bi period T b. The UWB signal can be wrien as s ( ) = d g( ) n n nt b where d n = ± and T b >> T. The diagram below shows an UWB signal for alernaing and bi values. Le T = ns and T b = µs. a) Wha is he approximae bandwidh of s()? b) One of he selling poins of UWB is ha is signals do no experience fla fading in ypical channels. Consider a single-bi ransmission, s() = d g(). Suppose his signal s() is ransmied hrough a channel described by a wo ray model, h( ) = α δ ( ) + αδ ( τ ). Skech he oupu for τ << T and τ >> T. Which case is more likely o depic he oupu of a real wireless channel? Why does his imply ha UWB signals don ypically experience fla fading? c) Consider a channel wih a mulipah delay spread of σ τ = µs. Wha is he exac maximum daa rae ha can be sen over his channel wih no ISI? Is he bandwidh of s() less han he channel coherence bandwidh a his daa rae? d) Le F( z) = α + αz + α z denoe he composie ransfer funcion of he ransmier, channel, and mached filer in his UWB sysem. Find a wo ap digial equaliser H eq ( z) = w + w z ha approximaes an IIR zero-forcing equaliser for F(z). e) For he equaliser you designed in par (d), suppose he sysem has a daa rae of kbps and ha your equaliser requires a raining sequence of bis o rain. Wha is he maximum channel Doppler spread such ha he equaliser coefficiens converge before he channel decorrelaes? f) Explain carefully he pracical problem wih a ZF equaliser. Describe in deail a pracical form of equaliser as would be implemened in a real cellular sysem.

4 6. A direc sequence spread specrum (CDMA) sysem uses a RAKE receiver. The sysem communicaes over a mulipah channel wih impulse response, h () = α δ ( ) + αδ ( τ ) + α δ ( τ ) The ampliudes of he mulipah componens are described by Rayleigh disribuions, however he mean power level varies due o shadowing evens. The probabiliy disribuions for he mean power levels on each pah are,.5, α = 5.5, α =.75, α = 5 P ( α ) P ( α ) P ( α ).5, α =.5, α =.5, α = All he above unis are linear. The ransmi power and he noise power are such ha a spread specrum receiver locked ono he ih mulipah componen will have an SNR of α i in he absence of oher mulipah componens. a) Le T b denoe he bi period and consider he spread specrum receiver locked ono he LOS signal componen (wih zero delay and gain α ). Explain he imporance of he auocorrelaion funcion of he spreading code in deermining he noise of he oher users on his recovered signal componen. b) Consider ha one of he m-sequences generaed in Tuorial 3, Quesion, is used as he spreading code (eiher one will do). Generae a polar NRZ line code plo of his sequence wih MATLAB, using en samples per chip period T c. Find and plo he auocorrelaion funcion of his sequence. Commen on he resul obained. Is his sequence suiable for use in a sysem employing a RAKE receiver? Wha requiremens are here on he delays of he oher mulipah componens τ and τ for he differen mulipah componens o be resolvable in he RAKE receiver? For he remainder of he quesion assume ha he spreading codes each have an auocorrelaion funcion equal o a dela funcion. DPSK modulaion is used wih noncoheren deecion. c) Deermine he ouage probabiliy for a single branch receiver locked ono he LOS componen, a P = 3 eb (average insananeous BER). d) Find he ouage probabiliy a P = 3 eb for he hree branch RAKE receiver, where each branch is locked ono one of he mulipah componens and selecion combining is used o combine he pahs. e) Suppose receiver complexiy is limied such ha only a wo branch RAKE wih Selecion Combining can be buil. Find which wo mulipah componens he RAKE should lock o in order o minimise he ouage probabiliy a P = 3, and hen find his minimum ouage probabiliy. eb 7. Consider a 4/ GHz saellie sysem, in which a saellie receives he signal a 4 GHz from Earh Saion A, hen down-convers his signal o GHz and ransmis i o Earh Saion B. The modulaion used is QPSK wih a bi duraion-bandwidh produc of.6. The ransmission bi rae is 9 Mbps. The Earh Saion A uses a 7.7 m diameer parabolic anenna wih an efficiency of.55, and is locaed a Longiude 5 E and Laiude 35 S. The saellie is in geosaionary orbi (so above he equaor) a 3 W. Recall ha he radius of he Earh is 637 km. The Earh Saion uses a High Power

5 Amplifier (HPA), raed a. kw. To avoid disorion o amplifier is operaed 3dB below his maximum power level, called he oupu back-off. The waveguide loss is.5 db, he combining loss a he ransmier is.5 db, and he uplink racking and amospheric losses are.3 db. a) Calculae he power flux densiy a he saellie. The saellie s gain o noise emperaure is.6 db/k and he inpu back-off o he Travelling Wave Tube Amplifier (TWTA) is 3 db. b) Deermine he carrier o noise for he Uplink, ( C N ) u. (Noe ha N = kte B is he oal noise power, where B is he noise equivalen bandwidh). This quaniy is expressed in db. The saellie sauraion EIRP is 44 dbw and he TWTA oupu back-off is.4 db. Earh Saion B is locaed a Longiude 3 E and Laiude 8 S. This Earh Saion uses an idenical anenna and HPA as Earh Saion B. The receiver noise emperaure is 6 K. Downlink racking and amospheric losses are.9db. c) Consider ransmission from he saellie o Earh Saion B alone. Deermine he Downlink carrier o noise power raio, ( C N ) d. d) Show ha, for he full Uplink and Downlink communicaion sysem, he oal carrier o noise power raio can be expressed as C C C = + N N u N d e) Is his saellie sysem Downlink or Uplink limied? (Tha is, is one of he erms in he above equaion dominan in deermining he link performance?) f) Calculae he overall carrier o noise power raio for his saellie ransponder link. g) Deermine he oupu E b N. h) Assuming coheren deecion, wha is he oupu BER? 8. a) Following he MATLAB from he lecure, generae a CDMA spread signal wih spreading facor 64 and a sampling frequency en imes he chip rae. Selec one of he lengh 64 Walsh codes as he spreading sequence, and use BPSK a he baseband as in he lecure example. Obain a plo of he BER as a funcion of he oupu SNR for ransmission and deecion over an AWGN, for E b N = o db. Noe ha by his we mean he SNR a he oupu, afer de-spreading. You will need o ge a reasonable amoun of daa o measure he BER accuraely (hink of looping he program and cumulaively couning he bi errors as you go). b) Add anoher user ono your sysem, giving hem a differen spreading code bu he same signal power as he firs user. Regenerae BER versus SNR plo for he deecion of he firs user s signal. Repea wih oher users and hen oher users, each wih differen Walsh codes. Commen on your resuls. c) Repea par b) bu his ime offse each of he inerfering user s signals by a random amoun of ime ha is less han he chip period (his can be done by generaing a random number beween and 9, and using circshif()). Commen on your resuls.

6 d) Formulae a heoreical model o explain he resuls you obained in par c). How well does he model accoun for he observaions?