SYSTEM NOISE AND LINK BUDGET. Updates: 9/24/13; 10/6/14
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1 SYSTEM NOISE AND LINK BUDGET Updates: 9/24/13; 10/6/14
2 Introduction Any system (wired or wireless) receives and generates unwanted signals Natural phenomena or man-made (Noise) Unwanted signals from other systems (Interferences) Man-made Noise: due to other subsystems (e.g.; power supply) Natural Noise: due to random movements and agitation of electrons in resistive components (e.g., due to temperature) We focus on system thermal noise!
3 Thermal Noise Characteristics Thermal noise due to agitation of electrons Except at absolute zero temperature, the electrons in every conductor (resistor) are always in thermal motion Function of temperature Present in all electronic devices and transmission media Cannot be eliminated Particularly significant for satellite communication The Sun contributes to the thermal noise at the receiver
4 Spectral Power Density of (white) Noise Amount of thermal noise to be found in a bandwidth of 1Hz in any device or conductor is: N = kt ( W/Hz) 0 N 0 = noise power density (in watts) per 1 Hz of bandwidth k = Boltzmann's constant = J/K (or W/ (K.Hz)) T = temperature, in kelvin (absolute temperature) Note Watt = J/sec = J.Hz
5 Thermal Noise Noise Power Noise is assumed to be independent of frequency Thermal noise present in a bandwidth of B Hertz (in watts): N 0 = kt ( W/Hz) or, in decibel-watts N à N = ktb = 10 log k + 10 log T + 10log B
6 Thermal or White Noise From the plot of the spectral density of thermal noise over frequency, can see that the noise is flat frequency spectrum till around 100GHz or so and starts to fall off at around 1TeraHz
7 Thermal Noise Model At any temperature, thermal motion of electrons result in thermal noise This is due to difference between the resistor s terminals The thermal noise source in the resistor delivers a power to the load (watt) N ktb Or in Watt/Hz: We call this noise power density : N 0 = kt ( W/Hz) = Noise random process has Gaussian Distribution with zero mean and some SD
8 Modeling the Thermal Noise (Open Circuit No Load) The noise generated due to temperature T by a resistive component has normalized power spectrum (also called mean-square voltage spectrum): 2RkT(V^2/Hz) k = Boltzmann's constant = J/K T = temperature, in kelvin (absolute temperature) Therefore the average power that a voltage or current source can deliver (available) is: 2RkT.2B=4RkTB (V^2) The RMS voltage equivalent of the thermal noise will be V rms = AveragenoisePower = 4kTRB ( V ) Vrms Equivalent Thermal Noise Model R True RMS Multimeter Example A: Calculate the open-circuit Vrms reading when we connect a true RMS voltmeter to a 100Kohm resistor at room temperature (20 deg. C) with BW=1MHz to measure the generated thermal noise. Draw the equivalent circuit.
9 Noise Power Delivered to the Load The voltage delivered to the load is maximum when Rs=RL=R Thus, VL(t) = Vs(t)/2 à P Load = V L(t) 2 = [V s(t) / 2] 2 = V s(t) 2 2 R 4R = V rms 2 4R Spectral Noise Density at the load will be: kt/2=no/2 (W/Hz) Vs(t) Rs Sub system VL(t) RL Equivalent Thermal Noise Model
10 Thermal Noise Power %MATLAB CODE: T= 10:1:1000; k= *10^-23; B=10^6; No=k*T; N=k*T*B; N_in_dB=10*log10(N); semilogy(t,n_in_db) title( Impact of temperature in generating thermal noise in db ) xlabel( Temperature in Kelvin ) ylabel( Thermal Noise in db ) Thermal Noise in db Impact of temperature in generating thermal noise in db Temperature in Kelvin
11 Two-Ports Sub-System Noise Characterization A subsystem s noise behavior can be characterized by several parameters: Available Gain (G) Noise Bandwidth (B) Noise Figure or Factor (F) Vs(t) Rs Equivalent Thermal Noise Model Sub system VL(t) RL Input signal & noise G, B, F output signal & noise
12 Two-Ports Sub-System Noise Characterization A subsystem s noise behavior can be characterized by several parameters: Available Gain (G) Noise Bandwidth (B) Noise Figure or Factor (F) Available Gain: Input signal & noise N o /2 The available output noise spectral density due to input white noise will be: S ao = G N 0 / 2( W/Hz) The available output noise power due to input white noise will be: G, B, F P ao = G 2B N 0 / 2( W) output signal & noise S ao & P ao
13 System Noise Bandwidth (B) Two-Ports System Assuming the system is driven by white noise! S o is the available output power spectral density (W/Hz) P ao is the available output power (W) G=Go is the mid-band available gain (DC gain) S o ( f ) = G( f )S i ( f ) = G( f ) N o 2 N P ao = S o ( f )df = o G( f )df 2 P ao = G 2B N 0 / 2 W B = 1 2G Input Power Spectrum Density Si(f) G( f )df G(f) ( ) The available output noise power due to input white noise Output Power Spectrum Density So(f)
14 Example A (1) Find the BW for a first-order low-pass Butterworth filter whose gain is given as follow (assume DC gain Go=1): G( f ) = (2) Assuming the input of the system above is driven by white noise, find the output available power ( f / f 3dB ) 2 Input Power Spectrum Density Si(f) Output Power Spectrum Density So(f) G(f) f 3dB
15 Remember: Two-Ports Sub-System Noise Characterization A subsystem s noise behavior can be characterized by several parameters: Available Gain (G) Noise Bandwidth (B) Noise Figure or Factor (F) Vs(t) Rs Equivalent Thermal Noise Model Sub system VL(t) RL Let s talk about this! Input signal & noise G, B, F output signal & noise
16 System Noise Figure (F) The most basic definition of noise figure came into popular use in the 1940 s when Harold Friis defined the noise figure F of a network to be the ratio of the signal-tonoise power ratio at the input to the signal-to-noise power ratio at the output. F = SNR i / SNR o =1+ Te To
17 System Noise Figure (F) We define the Noise Figure (Noise Factor) as: à We often express F in db Note that F>1 Nr is the available output noise power due to the two-port sub-system Te is effective (internal) temperature of the subsystem To is output equivalent temperature into the subsystem F = SNR i / SNR o =1+ Te To Input Signal Power =Psi Input Noise Power Spectrum Density Sni=kT Sub System G, B, F, Te Psi.G Available Noise Power Due to input thermal noise: ktgb Available Noise Power Due to internal noise: ktogb(f-1) = Nr Pao(noise) = ktgb + ktogb(f 1) = kgb(t +To(F 1))) = k(t +Te) G B Note: T=To Find the expression for SNRi? SNRi = Psi/kToB
18 Example B Assume the antenna contributes to the input thermal noise of the system by T=10K Find the available input noise spectral density (Sai) Find the available output noise spectral density (Sao) Find the available output noise power (Pao) Find the noise figure for the system (F) Draw the thermal noise circuit model for the antenna Antenna Gain = 100dB B=150 KHz Te = 140 K output signal & noise
19 Cascaded System Antenna (G, To, R) Or à (G, T) Unit 1 (F1, G1, B1) R is the equivalent antenna resistance T is effective temperature resulting in noise Unit 2 (F2, G2, B2) Unit 3 (F3, G3, B3) Pao Cascaded sub- systems can be simplifies by combining available gains and noise proper7es (B=B1=B2=B3.) G_total = Go = G1.G2.G3.. F_total = F1 + (F2-1)/G1 + (F3-1)/(G1.G2) +. Te_total = (F_total 1).Toà F_total = 1+[Te_total /To] Note that: Total Gain
20 Example C Cascaded System Antenna (G, T) Low Noise Amp (F1, G1, B1) Mixer (F2, G2, B2) To IF Amp Pnd Received Power Antenna Noise RX Model (F_total, G_total, Te, B) Psd Pnd=Pao T_ant=20K For LNA: G1=10 db, F1 = 3 db For Mixer: G2 = 9 db, F2 = 6.5 db Find G_total, F_total, Te, Noise Power, Pnd Simplified Model: G_total = G1.G2 F_total = F1 + (F2-1)/G1 Te = (F_total 1).To See notes!
21 Example D Wireless Transmi`er Pt Digital Data Freq. Converter Power Amplifier (PA) RF Transmitter Matched Network Feedline Assume PA=40dBm, for the antenna Gt = 10dBd, Feedline loss = 3dB, Loss through the matched network is 0.5dB. Find EIRP and ERP for a dipole antenna. Is this RF transmi`er more likely to be a handset or a base sta7on? Do it on your own!
22 Expression E b /N 0 Ratio of signal energy per bit (J/b) to noise power density per Hertz (W/Hz) E b N S / R N S TR R = 1/Tb; R = bit rate; Tb = time required to send one bit; S = Signal Power 0 = 0 = k Given a value for E b /N 0 to achieve a desired error rate, parameters of this formula can be selected As bit rate R increases, transmitted signal power must increase to maintain required E b /N 0 Eb = S. Tb = W x Sec / bit = Energy (J) / bit
23 Probability of Bit Error Rate (PBER) Question: Assume we require Eb/No = 8.4 db for bit error of 10^-4. Assume temperature is 290 Kelvin and data rate is set to 2.4 Kbps. Calculate the required level of the received signal. 10^ db
24 Link Budget Analysis Reverse link (upload) Forward link (download) Link characteristics (in terms of power, capacity, and frequency of operation) Noise Analysis is generally significant to characterize the received signal by the receiver System is generally balanced in term of dynamic range (in TX and RX directions) Design Objective: Offer good quality of service (QoS) Provide high signal level (SNR and SNIR) Guarantee intelligibility and fidelity (PBER) High accuracy (BER) Conflicting Parameters (next slide)
25 Link Budget Detailed View Pt Digital Data Freq. Converter Power Amplifier RF Transmitter Feedline Pr Feedline RF Unit Receiver (F, Go, B) Pn Decoder Digital Data
26 Budget Link Analysis - Conflicting Parameters BW & QoS & Thermal Noise SNR & QoS/Fidelity & Pt & Cost BER & QoS & SNR & Pt & Cost Freq. & Fidelity & Dynamic Range System Loss & Dynamic Range & QoS & Material & Cost Quiescent Power Dissipa7on & Life Time & Cost & Complexity Bit rate & Noise Temperature & SNR Let us see how through an example! à
27 Pr Example E Antenna (Go, To,R) Feedline (F1, G1) RF Unit Receiver (F2, G2, B2) Psd Pnd Decoder Digital Data Assume the frequency of operation is 1900 MHz. The following parameters are given Antenna gain is 0dBd Feedline loss is 0.5 db Noise figure of the RF unit is 8 db RF Unit gain is 40 db Antenna noise temp is 60 Kelvin Detector BW is 100 khz Detector s SNR is 12dB Use a design margin of 3 db (above the required sensitivity) Transmit power is 43 dbm Part I: Find the following Total system noise figure Total system gain Noise power at the detector (Pn) Part II: Find the signal power required into the detector in dbm Part III: Find the RX power into the receiver (Pr) such that the detector operates properly (Psen of the receiver) Part IV: The maximum dynamic range
28 Example E Part I Solu7on No = KT F1= Feedline Loss G1 = 1/F1 = for Transmission Line F_total = F1 + (F2-1)/G1 Go=0 db; G_total=Go.G1.G2 Pnd = k.to.g_total.b.f_total Te = (F_total 1).To Part IV Solu+on: Antenna (Go, T) Pr Feedline (F1, G1) Received Power Antenna Noise L_path + Pt P_marg = Psens (db) RF Unit Receiver (F2, G2, B2) Psd Pnd Decoder RX Model (F_total, G_total, Te, B) Digital Data Psd Pnd Part II Solu+on: Signal Power Required for the Detector Noise Power = Psd Pnd = SNR db Part III Solu+on: Pr (min) + G_total = Psdà Psens = Psd G_total
29 Budget Link Analysis - Review Conflicting Parameters BW & QoS & Thermal Noise SNR & QoS/Fidelity & Pt & Cost BER & QoS & SNR & Pt & Cost Freq. & Fidelity & Dynamic Range System Loss & Dynamic Range & QoS & Material & Cost Quiescent Power Dissipa7on & Life Time & Cost & Complexity Bit rate & Noise Temperature & SNR
30 Other Types of Noise Intermodulation noise occurs if signals with different frequencies share the same medium Interference caused by a signal produced at a frequency that is the sum or difference of original frequencies Crosstalk unwanted coupling between signal paths Impulse noise irregular pulses or noise spikes Short duration and of relatively high amplitude Caused by external electromagnetic disturbances, or faults and flaws in the communications system Question: Assume the impulse noise is 10 msec. How many bits of DATA are corrupted if we are using a Modem operating at 64 Kbps with 1 Stop bit? x 7/8 = bit / sec x.01 = 560 data bits effected
31 Other Types of Noise - Example Intermodulation noise (Diff. signals sharing the Same medium) Impulse noise Crosstalk (coupling)
32 What Next? Other types of impairments.. Channel characteristics
33 Other Impairments Atmospheric absorption water vapor and oxygen contribute to attenuation Multipath obstacles reflect signals so that multiple copies with varying delays are received Refraction bending of radio waves as they propagate through the atmosphere
34 Impairments Why are they important?
35 References Black, Bruce A., et al. Introduction to wireless systems. Prentice Hall PTR, 2008, Chapter 2 Stallings, William. Wireless Communications & Networks, 2/E. Pearson Education India, 2009; Section 5.3 M F Mesiya, Contemporary Communication Systems, First edition Chapter 6.
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