Wireless Communications ECE 4606
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Date Created: 11/02/15
l Shadowing Also called sow sdhg i Log normal Shadowmg Accounts for random variations in received power obsened over distances 1 t t I M A I comparable to the widths of buildings 5 ruc or39 39 39 gram Extra transmit power a dIrg margin must be provided to compensate for these fades Local Average Power Measurements I Scanning in 3D Take ower maaanarnme in Watts as the antenna is moved in quot392 an a an npna order Ufa few wavelengths 39 After the cart 395 smblllZEd39 l Average these naaswanana to gives local average pawa the XYZ actuators move an mammal 2 3 local power measurement H H H One local average power is VelotilY of antenna computed for each cart n locatio Points wnevE Dower measuvem ents are made Scan volume Same stance Measurements g Repeat for Multiple Distances Local averages are made for many Similar collections of average powers different locations keeping the same are made for other TxRx distances transmitterreceiver istance These local averages will vary randomly with ocation manna mu luatiunswimin i a Rum ar a buildi g Likelihood of Coverage At a certain distance d what is the probability that the local average received power is below a certain threshold 7 PPd lt 7 PthG LLdL Kolstanoe dependence shown expllcltlv RM Likelihood of Coverage cont d Since only the path loss Ld is random the probability can be expressed as a probability involving path loss PRdlt7PLdgtJ maxlmum tolerable patn loss Typical Macrocell g Characteristics nut veal data The set of average at about 4km 10logm46 Total paun Loss as 10logmDlstarlce from Base Stauorl mp Path Loss Assumptions The mean loss in dB follows the power law d Ld e Ldo10nlogmz The measured loss in dB varies about this mean according to a zeromean Gaussian RV X0 with standard deviation 5 Ld Zdo10n1ogmdi X g Typical Data Characteristics mm veal data Best Flt Pam Loss Exponent 4 o is usually Sr 12 dB for moblle comm Total paun Loss as 10logmDlstarlce from Base Stauorl mp g Probability Calculation Since Ld is Gaussian we need to know how to calculate probability involving Gaussian RVs PLdgt3 SI Q Function IfX is a Gaussian RV with mean ovand standard deviation 0 then PX gt b Q T where Q is a function defined as 1 W x2 QZ W PXPE g The Problem with Q The integrand of Q has no antiderivative Q is found tabulated in books Q can be calculated using numerical integration What is Lognormal Shadowing IfY is a Gaussian RV and Z is defined such that YlogZ then Z is a log normal RV Shadowing is lognormal shadowing when the path loss in dB is Gaussian this means that the path loss expressed as a ratio is lognormal g Inverse Q Problems Sometimes the probability is speci ed and we must nd one of the parameters in the argument of Q PXgtbQb1 T Suppose the value of PX gtb is given along with values ofb and a Solve for a Must look up the argument of Q that gives the speci ed value g Example Inverse Q Problem Suppose the mean of the local average received powers at a certain distance is 30dBm that the smndard deviation of shadow fading is 9 dB and that the observed received power is above the threshold 95 of the time what is the threshold power 5 7 730 PRgtbQ 095 Q is uslally tabulated for argumenE of 05 and less so we must use the act at 921sQszgt The argument of Q that yields 005 is about 165 7165andb4485 dBm g Boundary Coverage Suppose that a cell has radiusR and y is the minimum acceptable received power level Then PPRgty is the 39VkeI39 ood of coverage at the boundary of the cell PRR gt y is also the WadDH oftme that a mobile s signal is acceptable at a distance R from the transmitter assuming the car moves around that circle Percentage of Useful Service I Area By integrating these probabilities over all the circles within a disk one can compute the fraction of the area within the cell that will have acceptable power levels 1 m 00 7W PBr gt7rdrd y Integral Evaluated Assuming lognormal shadowing and the power path loss model the fraction of useful service area 39 my 717 erfa ip 1 39bsz1 7 af ID W here and 510nlogm2 m5 I The Error Function erf c is another form of the Gaussian integral like QM erf c has odd symmetry with extreme values 1 110 erfx 7 j d n N 71 Note that some authors may define erf differently l erf and Q The erf function and Q are related erfz 17 2QJiz When the Average Boundary Eh Power is Acceptable Summary Local averages in dB of received power or path loss tend to be Gaussian when e ensemble is all TxRx locations with the sa dis nce in the same type of envir The mean local average path loss follows the standard power model proportional to 10logdquot Can use Q or erfto calculate the likelihood of boundary coverage or the percent of useful service area Introduction to Digital Modulation Instructor MA Ingram ECE4823 Digital Communication Transmitter A simplified block diagram antenna waveforms s mbols 39 Frequency uprconverson and ampli cation Digital Communications Receiver A simplified block diagram waveforms bols Lowrnoise ampli cauon of 011001 ownrconversion Symbols In each symbol period TS a digital modulator maps Ncoded bits word to a transmitted waveform from a set of M 2 possible waveforms Each waveform corresponds to an information symbol x For Binary symbols N1 Detection The job of the receiver is to determine which symbols were sent and to reconstruct the bit stream that created them Definitions Bit Rate bits per sec or bps Bandwidth Efficiency bpsHz 775 R B where B is the bandwidth occupied by the signal TS Shannon Theorem I In a nonfading channel the maximum bandwidth efficiency or Shannon Capacity is 77 log1SNR SNR signaltonoise ratio Pulses l A symbol period TS suggests a localization in time I Localization in frequency is also necessary to enable frequency division multiplexing l Regulatory agencies provide spectral masks to limit the distribution of power in the frequency domain Example Linear Modulation I Mt is the output ofthe modulamr I g is the complex envelope I p is the basic pulse I x is the nth symbol I A is the ampli cation in the transmitter sl Re gayW g0 AZ 96170 nTS Rectangular Pulses I Suppose 11 is a rectangular pulse I This pulse is not used in practice but is OK for illustration pt Binary Phase Shift Keying BPSK I For BPSK each symbol carries one bit of information x 6 711 g0 BPSKModulated Carrier l The information is in the phase of the carrier st Power Spectral Density PSD of Linear Modulation Assume that the symbol sequence xn is iid and zero mean Then the PSD of 31 is ssltgtsltefsglteem where AZEM 2 sgmeTlel and Pf is the Fourier Transform of pf Bandwidth Properties The RF bandwidth of the modulated carrier is two times the baseband bandwidth of m Ion 2T s f IPfl2 which is clearly seen to depend on the bandwidth of the pulse Fourier Transform of the Rectangular Pulse PU fplttexpe 127th T Tlexpc Mm WZexpwmquot JZepoZWSH T 7124 n T 7124 WEMMexpewssznsmctm S PSD for BPSK and the Rectangular Pulse IPfl2 norclam 34f lacan 1 ARM 3 f AZE lb 2 plt2 fa f39 5 2T Azsinc2 S Sm bn iexirxsinc2eexinl g Received Signal The received signal has been attenuated by path loss and multipath fading and has added noise rt atAZ xnpt 7 FITS cos2rft 6 nt 2 tA a0 T Channel BPSK Demodulator The output of the correlator is a sequence of nelsy verSIons of the transmitted symbol sequence o modulated received symbols 957103r102937 858174 r To deinterleaver and decoder cos27fr 1 Z Aat T Automauc Gall i Control Integrate and Dump Output Consider one symbol period and the rectangular pulse channel galnsand TX power lumped into 5 R Twoncos zg tjdt 11x Ecos27gftntJZcosZiftgtdt n T n T T E T i ji an ifnltrgtcos27yrldr xMEw T n T n v is a zeromean Gaussian RV with variance N a n Conditional PDFs Recall Rxn 55m Zr fMJ39 1 mp funw 1 Expquot gtz Conditional Probability of Bit Error If x is 1 then an error happens ifRgt0 meaUlX 1 Pmmrm r1 PR gt0le r1 Ifm mxw mm D Conditional Probability of Error Expression Tfm len 1drQ Hg 7 Q Same for other kind of error by symmetry Unconditional Probability of Bit Error Assume the two possible values of x are equally likely I 1 P2rmr 3mm i x 71 513mm i x 1 9 Nu How to Improve System Performance Increase symbol energy Eb Decrease average noise power N z Perror Q