System Noise and Link Budget

SYSTEM NOISE AND LINK BUDGET

Updates: 9/24/13; 10/6/14 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! 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

http://homes.esat.kuleuven.be/~cuypers/satellite_noise.pdf Spectral Power Density of (white) Noise • Amount of thermal noise to be found in a bandwidth of 1Hz in any device or conductor is:

N0 = kT (W/Hz)

• N0 = noise power density (in watts) per 1 Hz of bandwidth • k = Boltzmann's constant = 1.3803 × 10-23 J/K (or W/ (K.Hz)) • T = temperature, in kelvin (absolute temperature) • Note Watt = J/sec = J.Hz Thermal Noise Noise Power

• Noise is assumed to be independent of frequency • Thermal noise present in a bandwidth of B Hertz (in watts):

N0 = kT (W/Hz) à N = kTB or, in decibel-watts N =10log k +10 log T +10log B 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 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 Noise random process has • Or in Watt/Hz: We call this noise power density : Gaussian Distribution with N = kT W/Hz zero mean and 0 ( ) some SD R Modeling the Thermal True RMS Vrms Multimeter

Noise (Open Circuit – No Load) Equivalent Thermal Noise Model • 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 = 1.3803 × 10-23 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

Vrms = AveragenoisePower = 4kTRB (V)

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. Noise Power Delivered to the Load

• The voltage delivered to the load is maximum when

Rs=RL=R 2 2 2 2 VL (t) [Vs (t) / 2] Vs (t) Vrms • Thus, VL(t) = Vs(t)/2 à P = = = = Load 2 R 4R 4R

• Spectral Noise Density at the load will be: kT/2=No/2 (W/Hz)

VL(t) Rs Sub RL Vs(t) system

Equivalent Thermal Noise Model Thermal Noise Power

%MATLAB CODE: T= 10:1:1000; Impact of temperature in generating thermal noise in dB k= 1.3803*10^-23;

2.15 B=10^6; -10 No=k*T;

N=k*T*B; 2.16 N_in_dB=10*log10(N); -10 semilogy(T,N_in_dB) 2.17 title(‘Impact of temperature in -10 generating thermal noise in dB’) xlabel(‘Temperature in Kelvin’) 2.18 -10 ylabel(‘Thermal Noise in dB’) in Noise dB Thermal

2.19 -10

2.2 -10 0 100 200 300 400 500 600 700 800 900 1000 Temperature in Kelvin Two-Ports Sub-System Noise Characterization

• A subsystem’s noise behavior can be characterized by several parameters: VL(t) • Available Gain (G) Rs Sub RL • Noise Bandwidth (B) Vs(t) system

• Noise Figure or Factor (F) Equivalent Thermal Noise Model

Input signal & output signal & noise noise G, B, F Two-Ports Sub-System Noise Characterization

• A subsystem’s noise behavior can be characterized by several parameters: • Available Gain (G) Input signal & output signal & noise noise G, B, • Noise Bandwidth (B) F

• Noise Figure or Factor (F) No /2 Sao & Pao • Available Gain: • The available output noise spectral density due to input white noise will be:

Sao = G ⋅ N0 / 2(W/Hz)

• The available output noise power due to input white noise will be:

Pao = G ⋅ 2B⋅ N0 / 2(W) System Noise Bandwidth (B)

Two-Ports System N S ( f ) = G( f )S ( f ) = G( f ) o o i 2 • Assuming the system is ∞ ∞ No driven by white noise! Pao = ∫ So ( f )df = ∫ G( f )df −∞ 2 −∞ • S is the available o P = G ⋅ 2B⋅ N / 2 W The available output power spectral ao 0 ( ) output noise 1 ∞ power due to density (W/Hz) → B = ∫ G( f )df input white noise 2G −∞ • Pao is the available output power (W) Input Power Output Power Spectrum Density Spectrum Density • G=Go is the mid-band Si(f) So(f) available gain (DC gain) G(f) 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): 1 G( f ) = 2 1+ ( f / f3dB ) • (2) Assuming the input of the system above is driven by white noise, find the output available power.

Input Power Output Power Spectrum Density Spectrum Density Si(f) So(f)

G(f)

f3dB Remember: Two-Ports Sub-System Noise Characterization

• A subsystem’s noise behavior can be characterized by several parameters: VL(t) • Available Gain (G) Rs Sub RL • Noise Bandwidth (B) Vs(t) system

• Noise Figure or Factor (F) Equivalent Thermal Noise Model

Let’s talk about Input signal & output signal & noise noise this! G, B, F 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-to- noise power ratio at the input to the signal-to-noise power ratio at the output.

F = SNRi / SNRo Te =1+ To http://cp.literature.agilent.com/litweb/pdf/5952-8255E.pdf System Noise Figure (F)

• We define the Noise Figure (Noise Factor) as: à F = SNRi / SNRo • We often express F in dB • Te Note that F>1 1 • Nr is the available output noise power due to the two-port = + sub-system To • Te is effective (internal) temperature of the subsystem • To is output equivalent temperature into the subsystem

Psi.G Pao(noise) = Input Signal Power Sub kTGB + kToGB(F −1) = =Psi System kGB(T +To(F −1))) = Available Noise Power Input Noise Power G, B, Due to input thermal noise: k(T +Te)⋅G ⋅ B Spectrum Density F, Te kTGB Sni=kT Available Noise Power Note: T=To Due to internal noise: kToGB(F-1) = Nr Find the expression for SNRi? SNRi = Psi/kToB 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

output signal & noise Gain = 100dB B=150 KHz Te = 140 K Cascaded System

Antenna (G, To, R) Unit 1 Unit 2 Unit 3 Or (F1, G1, B1) (F2, G2, B2) (F3, G3, B3) à(G, T) Pao R is the equivalent antenna resistance T is effective temperature resulting in noise

• Cascaded sub-systems can be simpliﬁes by combining available gains and noise properes (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 Example C Antenna Low Noise Amp Mixer To IF Amp (G, T) (F1, G1, B1) (F2, G2, B2) Cascaded System Pnd

Received Power RX Model Psd Antenna (F_total, G_total, Te, B) Pnd=Pao Noise

• 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!

Example D Wireless Transmier Pt

Power Amplifier RF Freq. Converter Matched (PA) Transmitter Digital Network Feedline Data

• 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 transmier more likely to be a handset or a base staon?

Do it on your own! Expression Eb/N0

• Ratio of signal energy per bit (J/b) to noise power density per Hertz (W/Hz) E S / R S b = = N0 N0 kTR • R = 1/Tb; R = bit rate; Tb = time required to send one bit; S = Signal Power

• Given a value for Eb/N0 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 Eb/N0

Eb = S . Tb = W x Sec / bit = Energy (J) / bit

Probability of Bit Error Rate (PBER)

Question: Assume we require 10^-4 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.

8.4 dB 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) Link Budget Detailed View

Pt Freq. Converter Power Amplifier RF Transmitter Digital Feedline Data

RF Unit Receiver Decoder Feedline Pn Digital (F, Go, B) Data 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 Dissipaon & Life Time & Cost & Complexity • Bit rate & Noise • Temperature & SNR • Let us see how through an example! à Pr Antenna (Go, To,R) RF Unit Psd Receiver Decoder Digital Example E (F2, G2, B2) Pnd Feedline Data (F1, G1)

• Assume the frequency of • Part I: Find the following operation is 1900 MHz. The – Total system noise figure following parameters are given – Total system gain – Noise power at the detector (Pn) • Antenna gain is 0dBd • Part II: Find the signal power • Feedline loss is 0.5 dB required into the detector in • Noise figure of the RF unit is 8 dB dBm • RF Unit gain is 40 dB • Part III: Find the RX power into • Antenna noise temp is 60 Kelvin the receiver (Pr) such that the • Detector BW is 100 kHz detector operates properly • Detector’s SNR is 12dB (Psen of the receiver) • Use a design margin of 3 dB (above the required sensitivity) • Part IV: The maximum dynamic • Transmit power is 43 dBm range Pr Antenna (Go, T) RF Unit Psd Example E – Receiver Decoder Pnd Digital Feedline (F2, G2, B2) Data Part I Soluon (F1, G1)

Received • No = KT Power RX Model Psd Antenna (F_total, G_total, Te, B) Pnd • F1= Feedline Loss Noise • G1 = 1/F1 = for Transmission Line Part II Soluon: • F_total = F1 + (F2-1)/G1 • Signal Power Required for the Detector – Noise Power = Psd – Pnd • Go=0 dB; G_total=Go.G1.G2 = SNR dB • Pnd = k.To.G_total.B.F_total Part III Soluon: • Te = (F_total – 1).To • Pr (min) + G_total = Psdà Psens = Psd – G_total Part IV Soluon: • L_path + Pt – P_marg = Psens (dB) Budget Link Analysis - Review Conflicting Parameters

• 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?

64000 x 7/8 = 56000 bit / sec 56000 x .01 = 560 data bits effected Other Types of Noise - Example

Intermodulation noise (Diff. signals sharing the Same medium)

Impulse noise

Crosstalk (coupling) What Next?

• Other types of impairments….. • Channel characteristics 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 Impairments Why are they important? 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.