TELE4652 Mobile and Satellite Communications

Transcription

1 Mobile and Satellite Communications Lecture 5 Practical Antennae and Link Budget Analysis Recap - Elementary Dipole Antenna A infinitesimal piece of wire The simplest antenna l<<λ Can take the current as uniform over it s length All other antenna can be analysed as an infinite sum of these basic elements

2 Elementary Dipole Far-field Solution The far-field solution keep only the 1/r terms (the radiation field): H φ j λr j( ωt βr) ( r, t) il sinθe j µ j( ωt βr) ( ) E θ r, t il sinθe λr ε Radiation Pattern: F ( θ, φ) sinθ Elementary Dipole - Solution Directivity pattern: ( θ, φ) 4πI 3sin D( θ, φ) P rad θ Directivity of elementary dipole antenna -> maximum radiation is transmitted at θ π/, perpendicular to direction of current flow D dbi Receive Antenna effective area: A eff 3λ 8π Radiation Resistance: R rad l π λ

3 Elementary Dipole Java Applet Module 9.1 Demonstrates the solution for the radiation from an elementary dipole Geometry used for the solution Illustrates the accuracy of the far-field approximation Have-wave Antenna The simplest real antenna is just a piece of linear wire of length l Method of images a ground plate can be used to extend the effective length of the antenna It is common to choose l λ/, for reasons we shall soon see

4 Half-wave Antenna Note: linear antenna of length λ/ is equivalent to a linear antenna of length λ/4 sitting on a conductive ground plate Need to approximate the current distribution. A reasonable, simple assumption is: i sin( k( l z) ) for < z< l I( z) i sin( k( l+ z) ) for l < z< Sinusoidal distribution along the wire The dimensions are comparable to the wavelength, so can t assume the current is uniform Half-wave Antenna Find the field contribution at Q in the far-field from an elemental dipole dz along the wire: Using results above: jωµ I( z) dz jkr de θ ηdh φ sinθ e 4πr Far-field approximations: 1 1 r r θ θ r r + z zr cosθ r z cosθ

5 Half-wave antenna Sum up the contributions from all dipole elements l along the wire: Eθ deθ Straight-forward integral, using: l e ax ax e sin a + b ( bx+ c) dx [ a sin( bx+ c) b cos( bx+ c) ] The total field at Q from all elements of the antenna is: jηi jkr cos( kl cosθ) cos( kl) Eθ e π θ r sin Half-wave Antenna Special case when l λ/, the expression simplifies significantly: E θ 6 r π cos cosθ i sinθ Radiation patterns can be calculated. Amplitude field pattern. Directivity pattern (power) π cos cosθ F ( θ, φ) D θ ( θ, φ ) sin C in 4 ( π) π cos cosθ sinθ C in x 1 τ cos d τ ( x ) τ

6 Half-wave Dipole Radiation Pattern The directivity of this antenna is calculated as: D 1.64 This is equivalent to.15dbi. We define this to be dbd (decibels relative half-wave dipole) A practical experimental reference More directed beam Impedance Z A 73+ 4jΩ Linear Dipole Java Applet Module 9. Shows the radiation fields from a linear dipole, as a function of dipole length Also solves the radiation resistance and directivity Illustrates the current distribution

7 Quarter-wave monopole antenna λ/4 length of wire above a ground plate. Identical field to that of a half-wave antenna, due to method of images However, field only exists in top half hemisphere (no field inside ground plate) Directivity increased: D 3dBd (by a factor of ) Radiation resistance halved: R rad 36. 5Ω Yagi-Uda Antenna Dipole pair feeding circuit Passive arms act as directors/amplifiers -> focus the beam in a D plane Light-weight and low cost

8 Parabolic Reflector Antenna The general choice for satellite communications Focus radiation to a horn element Achieve high gains highly directed Gain given by: πd G ε λ Can approximate as a large number of virtual horn elements Helical Antenna Popular in mobile handsets Like a combination of loop antennae Fairly omni-directional Produces circularly-polarised radiation Very compact

9 Micro-strip Patch Antennae Use PCB technology to manufacture radiating structures on a ground-plane backed dielectric substrate Compact, low-manufacturing costs Limited antenna bandwidth Useful in antenna arrays (all elements produced on the same substrate) Base Station Antennae Aim to produce a radiation pattern that focuses the energy in a plane (Earth s surface) Elevated position (eg. Hata model) Often use a slight down-tilt

10 Antenna Arrays Base Stations are commonly implemented as antenna arrays A collection of closely-spaced antenna, acting in unison (order of λ) Beams from the Antennae are coherent -> interfere to produce a common beam In the far-field, radiation pattern looks like it comes from a single, complex antenna Beam-forming Positions, amplitudes, and phases of Antenna elements can be varied to produce radiation patterns with desired characteristics Can control the direction and width of main beam; side-lobe levels; and antenna directivity Can vary amplitude and phase of elements in real-time -> adaptive antenna, beamsweeping, etc.

11 Two-element Array The simplest case Two dipole antennae, separated by a distance d Same amplitudes, but phase difference α Two-element Array Far-field Determine net amplitude at Q by summing together amplitudes produced by the two elements In the far-field, can assume amplitude are the same and fields only differ in phase. Phase difference is due to difference in path length ra rb d cosθ

12 Two-element Array - pattern The total field in the far-field is: E jkra jα jkrb jkra jk( ra rb) + jα [ 1+ e ] jkra The radiation pattern: Q E e E e E e + E e e jkd cosθ+ jα [ 1+ e ] where: ψ kd cosθ + α jψ ( θ φ) E 1 e F +, Two-element Array - result Radiation pattern is the product of the radiation pattern of a single antenna element, and a term called the Array factor Array factor is dependant only on the array geometry and the relative firing phases and amplitudes Here: AF cos ψ ψ kd cosθ + α

13 Two-element Array - result For half-wave dipole elements: F π cos cosθ sinθ ψ ( θ, φ) cos ψ kd cosθ + α General case: F ψ ( θ φ) E ( θ, φ) cos, where E ( θ,φ) is the radiation pattern of the constituent element Array Patterns The relative phase between the elements can alter the direction of the main lobe Exact pattern depends on spacing and phase. Broadside and End-fire patterns possible.

14 Two Dipole Array Java Applet Module 9.5 Illustrates the radiation source for an array of two dipoles Allows the phase, amplitude, and element separation to be controlled Shows the relative current distribution Linear Array M equally spaced elements arranged in a line Assume same amplitude, but progressive firing phase shift of α relative phase between adjacent elements Total field in the far-field is: E Q E jψ jψ j( M 1) ψ [ + e + e + K+ e ] 1 ψ kd cosθ + α

15 Linear Antenna Array Use the simple mathematical result: Gives: E 1+ z+ z Q E e e jψ + K+ z jmψ 1 1 M 1 M z 1 z 1 Radiation pattern from a linear array: F ( θ φ), E Mψ sin ψ M sin ψ kd cosθ + α Linear Array - patterns Some example patterns For M 6 (six array elements), and spacing of d λ/ First pattern α (all elements in phase) -> note more directed beam Second pattern - direction to θ π α π 3, moving main lobe

16 Linear Array Pattern features Some useful results for a linear array: Main beam direction: α Beamwidth: θ λ Md cosθm kd Side - lobe Amplitude Main lobe Ampliude Side-lobe level: (to reduce side-lobe level, need to vary relative amplitudes of array elements) 3π Linear Antenna Array Java Applet Module 9.7 Demonstrates the array factor and individual element patterns, and resultant radiation pattern Examine radiation parameters as number of elements is increased Can also alter the elements spacing

17 Linear Array Java Applet Module 9.8 Can add an incremental phase between elements Increase the number of dipole elements significantly Spatial Filter General case for antenna array Transmission focus energy in particular, assigned directions Reception combine the signal from each array element to enhance signal in certain directions Control phase and amplitude of each antenna element Can represent this as a multiplicative complex number the element weight w w i i e jαi

18 Spatial Filter After weighting each signal, the combination gives: jψ jψ Mjψ ( θ, φ) E w + we + we + K w e F + Analogy to discrete-time filter Spatial 1 Filter wn w + wz 1 + w 1 [ ] + K M z Smart Antenna Systems Real-time adaptive array Aims to enhance desired signals and repress interfering signals, based on their direction Can be used for Space Division Multiple Access(SDMA) Improves radio link performance

19 Smart Antenna Systems Seen as a potential 4G technology System elements: 1. User Detection - determined by multiple access scheme. Direction of Arrival (DOA) estimation - algorithms like MUSIC, ESPIRIT 3. Adaptive Algorithm determine spatial filter coefficients - general adaptive filter techniques (MMSE, LMS, RLS) 4. Beam-forming form desired signal (receiving) or desired radiation pattern (transmitting) Mobile Station Antennae Generally designed to be omni-directional (though with multi-pathing this is less critical) Input impedance well-matched (low power loss). Wide bandwidth (and sometimes multi-band: GSM ) Efficient small unit, maximise RF power Manufacturability cheap, durable, robust Size must be portable

20 MS Antennae - Size At GSM frequency, f 9MHz, wavelength is λ 3cm (of this order) Half-wave dipole antenna 15cm -> too large for a portable handset Quarter-wave dipole? With case acting as ground plane. Problem: for stable operation ground plate should be several wavelengths... Practically, require electrically small antennae l < λ/6 MS Antennae - Issues Electrically small antenna have reduced bandwidths and radiation pattern performance Focus in MS antennae is on techniques to: Increasing bandwidth Increasing effective lengths Improving directivity Bandwidth can be increases with dual resonances

21 Resonance Antenna is a resonant circuit Performance depends on which modes are excited TM1, TE11, etc Classic RLC circuit: 1 f f R+ j ωl R 1+ jq ωc f f Z Resonant frequency and Q-factor: f 1 π LC f R Q f L 3dB Practical MS Antennae - Dipole Dipole in Sheave Bandwidth is proportional to ratio of (wire diameter)/(length) Surround lower edge of dipole by metal sheave fill space with dielectric material Increases effective length of antenna Phone casing acts as ground plate Can be coaxially fed

22 Practical MS Antennae - Helical Reduces physical size Typical: λ/1, when above ground plate Using physical phone casing as ground plate is heavily affected by the user Small antennae are easily shadowed Circularly-polarised. A good match to linearly-polarised base stations Practical MS Antennae Inverted F antennae Ground plane makes effective image radiator Reduced size required for ground plane effectiveness Length λ/4, and width λ/1 Difficult to manufacture

23 MS Antennae micro-strip patches Most popular these days due to ease of PCB manufacture Large dielectrics can be used to create very compact antennae Wide variety of structures and geometries, to maximise bandwidth and radiation pattern Can be built to be circular-polarised Mobile Antennae Two important characteristic performance measures: 1. Mean Effective Gain (MEG). Specific Absorption Rate (SAR)

24 Mean Effective Gain Due to random orientation and multi-path scattering, antenna gain is not useful in Linkbudget for a mobile MEG gain averaged over all angles MEG (total received power)/(sum of total available power in both H and V polarisations) G MEG Prec P + P H V P rec ππ [ PG V θ( θ, φ) Pθ ( θ, φ) + PHGφ ( θ, φ) Pφ ( θ, φ) ] sinθdθdφ Averaged over the two polarisations P V H, in terms of incident radiation fields P θ ( θ, φ) and antenna gains for the two polarisation states G θ ( θ, φ) P, Specific Absorption Rate The important measure of radiation absorption by the human body Power absorbed by human tissue per unit volume: 1 1 P J E σe σ is the human tissue conductivity SAR the power absorbed per unit mass of tissue: 1 SAR σ E ρ ρ is tissue density

25 Specific Absorption Rate Responsible for increasing the temperature of surrounding tissue: dt dt SAR ( heat capacity of tissue) ( rate of heat flow out) Specific Absorption Rate Measured using Phantoms ITU Guidelines: SAR Controlled Exposure limits For frequencies 1kHz to 6GHz Whole body:.4 W/kg Head: 8 W/kg Radiation field limits: (at 9MHz) Maximum Electric Field 3V/m Power density: 1mW/cm^

26 Link Budget Analysis Thus far, we ve talked about the factors that determine received power levels for general radio communication links (mobile, satellite, etc) P[ dbm] EIRP[ dbm] + G [ dbi] L [ db] L [ db] r r path feed We re generally interested in SNR -> What about Noise? Noise vs. Interference Interference unwanted signals entering the pass-band of interest from other intentional radiators of E/M waves (eg. co-channel and adjacent channel interference in cellular systems) Noise unwanted signals arising from natural phenomena or unintentional radiation from man-made systems

27 Noise Sources Natural Phenomena atmospheric noise extra-terrestrial radiation random motion of electrons Man-made Noise sources microwave ovens power generators automobile ignition systems electronic instruments Thermal Noise Device temperature implies random motion of electrons -> induced E/M noise Generally is the factor that determines the Noise Floor of a device Can determine the mean-square voltage spectrum due to random thermal electron current across a resistor, R S v ( f) hf R e h f kt 1 S N (f ) N channel bandwidth f

28 White Thermal Noise At room temperature (9K), the roll-off is at around 6GHz So, can approximate thermal noise as white around the spectral bands of our communication systems S v ( f) ktr Noise power delivered to a matched load: P av V ( t) R ktb White Thermal Noise Power spectral density (Watts/Hz) N ( f) 1kT S White same power in every frequency band AWGN channel approximation

29 Noise Equivalent Bandwidth Defined for a system System is described by some equivalent transfer function, H(f) We ask, if white noise is input to this system, what is the total power at the output? N N N [ N ] h( t) dt H ( f ) df N σ N E H ( f ) df Noise Equivalent Bandwidth Then, compare this output noise power to an ideal, brick-wall system, with gain H() and bandwidth B: σ N N Noise-equivalent bandwidth the bandwidth of an ideal, brick-wall system that would produce same noise at the output BH () H ( f ) df B neq H ()

30 Noise Equivalent Bandwidth In communications we often talk of gain ( f) H( f) G Noise equivalent bandwidth ( f) G B neq G Key point if white noise is input to the system, the output noise power will be: P df n G B neqn Of a device Noise Temperature N ( f) 1kTe Sn The temperature a resistor would have to have to deliver the same output noise power (in the given bandwidth) as the observed noise power Not the same as the physical temperature Accounts for other noise sources: device imperfections, inductive noises, etc

31 Antenna Noise Temperature The noise power at the input to an antenna An antenna detects noise from: electrical discharge in the atmosphere radiation from space, Earth, the Sun thermal noise in conducting elements For f < 3MHz, there is strong atmospheric 1 noise, and find T 1 K is common Above 3MHz, atmospheric noise is not as important For example, at 5GHz, can find noise temperatures as low as 5K Noise Figure Consider noise input to some device We standardise this to be a white noise source at room temperature, T 9K The noise at the output is the sum of the input noise and some additional noise created by the device

32 Noise Figure Noise Figure is ratio of input to output noise P F ktg neq Represents how much the device increases the amount of noise at its output Usually expressed in dbs ao B Must always have F > 1 (or db) a device cannot remove noise from a signal! Noise Figure The noise power at the output can be written as: P ktg B + ktg B ( F 1) ao neq neq Note: if temperature of input noise changes only the first term: P ktg B + ktg B ( F 1) ao neq neq The second term is a measure of noise generated by the device alone

33 Noise Figure Noise figure also represents the ratio between input and output SNR SNR F SNR input A device can t remove random noise from the spectrum of a signal Noise equivalent temperature when F 1, talk about temperature: T ( F ) T e Since output noise looks like it comes from a source with the above temperature output 1 Pao ktg Bneq + kteg B neq Noise Analysis A communication receiver is a cascade of several devices (antennae, amplifiers, filters, etc) How do we determine the output noise power? Obviously, the net gain is the product of the gains of each individual stage G G 1GG3

34 Noise Analysis Output noise from previous stage is the input noise to the next stage. Input noise is white noise at room temperature. Noise power out of first stage: P ( 1) ao1 ktg 1Bneq+ ktg 1Bneq F1 Noise power out of the second stage: P G ktg B + ktg B ( F 1 )} + ktg B ( F 1) ao { 1 neq 1 neq 1 neq Noise Analysis Finally, noise output power of third stage: P ao ktg G 1 + ktg G 3 3 B B neq neq + ktg G ( F 1) 3 1 ( F 1) + ktg G B ( F 1) Thinking of it as an equivalent single stage, with gain G, the equivalent noise G1GG3 figure of the system is: G 3 B neq F 1 F3 1 F F1 + + G G G P ao neq kt F ( 1) GBneq + ktgbneq

35 Equivalent Noise Temperature The equivalent noise temperature of the system is: e e Te 1+ + G1 Key to a good receiver: T Te G G Make the first stage low noise, high gain Called a LOW NOISE AMPLIFIER T The noise performance of subsequent stages has minimal impact 1 Example Satellite Receiver Example Satellite Receiver Front-end: Antenna, Low Noise Amplifier (LNA), Mixer (for down-conversion), Intermediate Frequency Amplifier (IF amp)

36 Example Satellite Receiver Antenna temperature: LNA noise temperature: LNA gain: Mixer noise temperature: Mixer equivalent gain: IF Amp noise temperature: IF Amp gain: T ant T LNA G LNA ( 3dB) G LNA G mixer System Bandwidth: 1MHz 5K T mixer 1( 3dB) 5K 5K.5 T IF ( 3dB) 1K Example Satellite Receiver Input Noise is from the Antenna Equivalent noise of the receiver Net gain is: G T mixer T eq TLNA+ + GLNA T eq TIF G G LNA mixer K.5 eq GLNAGmixerGIF G eq 1[ 5dB] [ db ] 3+ ( 3) + 3 5dB

37 P Example Satellite Receiver Input noise to the receiver (from the Antenna) Pn, in ktantb W -1dBm Output noise power ( T + T ) G B ( ) W -68dBm n, out k ant eq eq Note that input noise in band will also be amplified by the elements of the receiver exactly the same as the signal Mobile Phone Receiver Identical receiver analysis could be performed for a mobile phone:

38 Link Budget Analysis We now have the tools to determine both the signal level at the receiver, and the noise level at the receiver The SNR determines the BER (for digital system) Usually design link so that SNR is well above the minimum required -> safety margin This is called the link margin: [ db] ( E b N ) rec ( E b N ) req M Link Budget Analysis The link margin accounts for fading events For example, for cellular system -> lognormal shadowing model For a satellite system, this might be random rain-fade events In C-band systems, typical M 4dB. Ku band typical 6dB

39 Satellite Systems It is usual to calculate the received carrier power to noise spectral density ratio, C N Noise power spectral density comes from the effective receiver noise temperature and antenna temperature: Carrier power can be determined using propagation model Free space: P P r t GG r t ( 4π) ( ) N kt eq + T ant λ d Carrier power to noise spectral density If assume free space: C N ( EIRP) sat G r λ T e 4πd 1 k The ratio of receiver gain to receiver effective noise temperature is often called the recevier figure of merit For example, say a satellite at a distance 4km, transmitting an EIRP of 46.5 dbw at a frequency 1 GHz (Ku band) C N 93.8dB/Hz

40 Maximum Link Bit Rate Carrier power is the number of bits sent per second multiplied by the energy used per bit: E b C R b Hence, relates to performance of modulation scheme, ( E b N) req Note also that the modulation efficiency is at play behind the scenes SNR Can relate received C/N to bit rate: C P n E N b R B b neq ( Eb N) C N 1log1Rb req Example Satellite Receiver A common modulation scheme is 8-PSK Assuming coherent detection a bit error rate of.6 (6 out of every 1 bits received in error), the ( E b N) req required is 1.5 db Link margin of 6dB Ku band Maximum bit rate to be supported: 1log R b Solved as: R b 33.9Mbps

41 Question Is the cellular system link limited by the forward or the reverse link? Standard Transmission parameters: Base Station Mobile Station Power Output 43dBm 7dBm Connector Losses 1dB.1dB Feed Losses 4dB.5dB Antenna Gain 1dBd dbd Cellular links Receiver Parameters: Base Station Mobile Station Antenna Gain 1dBd dbd Feed Loss 4dB.5dB Noise Figure 8dB 8dB Receiver Gain 4dB 4dB Required SNR 1dB 1dB Antenna Temp 9K 6K Bandwidth 1kHz 1kHz

42 P Forward Link Receiver analysis: Noise figure: 8dB (6.31) Feed losses:.5db (1.1) Effective noise temperature: T ( F 1) 9 ( ) 154K Noise power at receiver output: Require signal strength to be 1dB higher 65dBm T e ( T + T ) GB ( ) W -77dBm n k e ant P r Cellular Links Gain of receiver is 4dB, so Say at 19MHz Add a link margin of 3dB Free space distance is: Pr[ dbm] EIRP[ dbm] Lpath Lsys Lm argin Gives -> d 73km Equivalent for reverse link 17km P r 15dBm L path

43 Cellular Links Free space model exaggerates values here Could use Hata model, etc Link margin from outage probability models (Rayleigh, Rician) Cellular system is Reverse Link Limited Mobile station limits range. Due to: limited antenna gain (close to omni) limited transmitted power (battery issues)