Radiocommunication Channel and Digital Modulation: Basics

Transcription

1 ICTP-ITU/BDT-URSI School on Radio-Based Computer Networking for Research and Training in Developing Countries The Abdus Salam International Centre for Theoretical Physics ICTP, Trieste (Italy), 7th February - 4th March 2005 Radiocommunication Channel and Digital Modulation: Basics Prof. Dr. R. Struzak r.struzak@ieee.org Note: These are preliminary notes, intended only for distribution to participants. Beware of misprints!

2 Outline Radiocommunication channel Modulation Spreading spectrum Nonlinearities & intermodulation Summary Property of R. Struzak 2

3 Microwave radio link Property of R. Struzak 3

4 Property of R. Struzak 4

5 Wireless Local Loop BSS Property of R. Struzak 5

6 PTP, PMP, Mesh A point-to-point (PTP) link is one station (node) communicating with another one A point-to-multipoint (PMP) network is one node (base station) communicating with more than one other nodes Mesh network (fully connected): A network topology in which there is a direct communication path between any two nodes Mesh and PMP topologies share communication resources (media) In a fully connected network with n nodes, there are n(n-1)/2 direct paths, i.e., branches. Property of R. Struzak 6

7 FDD radio links Two stations can talk and listen to each other at the same time (time-sharing). This requires separate (static) frequency channels a technique known as Frequency Division Duplex (FDD) TX Frequency Channel 2 RX Station 1 RX TX Station 2 Frequency Channel 1 Property of R. Struzak 7

8 TDD radio links Two stations can talk and listen to each other using the same frequency channel (frequency-sharing), one after another. This requires time synchronization/ handshaking a technique known as Time Division Duplex (TDD) Single Frequency Channel TX TX Station 1 Station 2 RX RX Property of R. Struzak 8

9 Radio Link model Environment Noise Original message/ data Transmitter T-antenna Propagation medium R-antenna Receiver Reconstructed message/ data Coding/ Processing Time series EM waves: timedistancedirectionpolarization Time series Processing/ De-coding Property of R. Struzak 9

10 Transmitting station Electrical current EM wave Original signal Transmitter (signal processing) RF cable (signal attenuation) Transmitting antenna Radio wave Focus of the school Electrical signal is represented by a function of time. Radio wave transmitted is represented by a function of time, distance, direction, and polarization. Property of R. Struzak 10

11 Receiving station EM wave Electrical current Radio wave Receiving antenna RF cable (signal attenuation) Receiver (signal processing) Recovered signal Focus of the school Radio wave received is represented by a function of time, distance, direction, and polarization that depends on signalpath environment Electrical signal is represented by a function of time. Property of R. Struzak 11

12 Modern radio: details ANTENNA SWITCH RF AMPLIFICATION RF FILTER RF FILTER RF UP/ DOWN CONVERSION SYNTHETIZER IF GAIN & SELECTIVITY IF FILTER CRYSTAL REFERENCE MODULATION & DEMODULATION FILTER SYNTHETIZER FILTER DAC BASEBAND PROCESSING & PC INTERFACE ADC TRANSMITTER COMMON PART RECEIVER Property of R. Struzak 12

13 RADIO WAVE PROPAGATION PATH From other sources Beamforming Freq. spread Modulation Multiplex Format Encryption Encoding Analog/Digital Beamforming Freq. despread Demodulation Demultiplex Format Decryption Decoding Digital/ Analog To other destinations Modern radio = combination of radio and computer hardware & software Software-defined radio Systems with most functions defined by software Automatically and/or at distance Information source Information sink Property of R. Struzak 13

14 Outline Radiocommunication channel Modulation Spreading spectrum Nonlinearities & intermodulation Summary Property of R. Struzak 14

15 Modulation m(t) s(t) Modulator/ Signal Processing f(t) Carrier Generator TRANSMITTER RADIO ENVIRONMENT s'(t) Demodulator/ Signal Processing RECEIVER m'(t) = process of translation the message from baseband signal to bandpass (modulated carrier) signal at frequencies that are very high compared to the baseband frequencies. Demodulation is the reverse process Note: An information-bearing signal is non-deterministic, i.e. it changes in an unpredictable manner. Property of R. Struzak 15

16 Original message m(t) Transmitter s(t) = U(m, f) Transport medium x(t) = V(s, ξ) Receiver y(t) = W(x) Reproduced (received) message y = W{V[ξ,U(m,f)]} Communication Channel m(t) = message (information, data) s(t) = signal carrying the message f = f(a,b,c,, t) (carrier function) a,b,c, = modulation parameters U, V, W = operators ξ = noise, fading, perturbations x(t) = perturbed signal at the receiver input y(t) = reproduced message Task: make y m (within an acceptable error) Property of R. Struzak 16

17 1 2 3 Modulation Process ( ) f = f a, a, a,... a, t (= carrier) a, a, a,... a (= modulation parameters) t (= time) n n Modulation implies varying one or more characteristics (modulation parameters a 1, a 2, a n ) of a carrier f in accordance with the information-bearing (modulating) baseband signal Each of the parameters a, b, c... carrying information can be modulated independently, increasing communication capacity at a cost of complexity. Property of R. Struzak 17

18 The carrier is generated in the transmitter It may be a continuous (e.g. sinusoidal) current of radio frequency, a sequence of short pulses, or noise Systems using pulse sequences are also called carrierless or impulse systems It may also be a number of carriers, such as in Orthogonal Frequency Division Multiplexing (OFDM) systems. For instance, one of standards Wireless Local Area Networks (WLANs) foresees 52 carriers spaced khz apart Property of R. Struzak 18

19 Why Carrier? To radiate EM waves effectively Radiation efficiency requires antenna dimensions to be comparable with the radiated wavelength Antenna for 30 khz would be 10 km long Antenna for 3 GHz carrier is 10 cm long To assure signal orthogonality (avoiding mutual interference by using orthogonal frequencies) Note: There are also other methods of avoiding interference (e.g. time- or code-orthogonality) Standards and RR impose limitations on carrier frequencies (interference, intercommunications) Property of R. Struzak 19

20 Property of R. Struzak 20

21 Property of R. Struzak 21

22 Continuous carrier In the case of sinusoidal carrier, three modulation parameters can be varied: the amplitude, the frequency, and the phase of the sinusoid (+ polarization). This generates three distinct modulation types: the amplitude modulation (AM), the frequency modulation (FM) and the phase modulation (PM) Each of these may be continuous, when the instantaneous amplitude, frequency and phase of the sinusoid are continuous functions of time, or may be pulsed, when the variations occur instantaneously Property of R. Struzak 22

23 Carrier: A sin[ωt +ϕ] + polarztn.; A, ω, ϕ, polarztn. = const Amplitude modulation (AM) A = A(t) ω = const ϕ = const Frequency modulation (FM) A = const ω = ω(t) ϕ = const Phase modulation (PM) A = const ω = const ϕ = ϕ(t) Polarization modulation Not used in radio communications (used in some optical communications) Property of R. Struzak 23

24 Amplitude Shift Keying (ASK) Baseband Data ASK modulated signal Acos(ωt) Acos(ωt) Pulse shaping can be employed to remove spectral spreading ASK demonstrates poor performance, as it is heavily affected by noise, fading, and interference Property of R. Struzak 24

25 Frequency Shift Keying (FSK) Baseband Data BFSK modulated signal f 1 f 0 f 0 f 1 where f 0 =Acos(ω c - ω)t and f 1 =Acos(ω c + ω)t Example: The ITU-T V.21 modem standard uses FSK FSK can be expanded to a M-ary scheme, employing multiple frequencies as different states Property of R. Struzak 25

26 Phase Shift Keying (PSK) Baseband Data BPSK modulated signal s 1 s 0 s 0 s 1 where s 0 =Acos(ω c t) and s 1 =Acos(ω c t + π) Major drawback rapid amplitude change between symbols due to phase discontinuity, which requires infinite bandwidth. Binary Phase Shift Keying (BPSK) demonstrates better performance than ASK and BFSK BPSK can be expanded to a M-ary scheme, employing multiple phases and amplitudes as different states Property of R. Struzak 26

27 PSK graphic representation -A Im(s) A Decision: s = s 0 Decision: s = s Re(s) The two signals s 0 =Acos(ωt) s 1 =Acos(ωt + π) can be represented by two vectors (or points) in the signal plane [Re(s), Im(s)] Noise & interference can change positions of the points and modify decision: 0 or 1 Property of R. Struzak 27

28 Differential Modulation In the transmitter, each symbol is modulated relative to the previous symbol and modulating signal, for instance in BPSK 0 = no change, 1 = In the receiver, the current symbol is demodulated using the previous symbol as a reference. The previous symbol serves as an estimate of the channel. A no-change condition causes the modulated signal to remain at the same 0 or 1 state of the previous symbol. Property of R. Struzak 28

29 DPSK = Differential phase-shift keying: In the transmitter, each symbol is modulated relative to the phase of the immediately preceding signal element transmitted Differential modulation is theoretically 3dB poorer than coherent. This is because the differential system has 2 sources of error: a corrupted symbol, and a corrupted reference (the previous symbol) Property of R. Struzak 29

30 Pulse trains as Carrier A carrier = a train of identical pulses regularly spaced in time Example 2003 : Ultra Wideband (UWB) systems Systems that use time-domain modulation and signal processing methods (e.g., pulse-position modulation) Used for sensing, short-range radar, and telecommunication applications Employ short pulses (duration of ~1 to 10 ns), occupying the bandwidth of more than 1.5 GHz (or more than 25% of the center frequency) Property of R. Struzak 30

31 In pulse-frequency modulation (PFM), the pulse repetition rate is varied in accordance with the modulating signal; in Pulse-Amplitude Modulation (PAM), the amplitude of individual pulses in the pulse train is varied In pulse-time modulation (PTM) generic class, the time of occurrence of some characteristic of the pulsed carrier is varied, eg. Duration (PDM) or position (PPM) Property of R. Struzak 31

32 In pulse-position modulation (PPM), the temporal positions of individual pulses are varied in relation to the reference positions, in accordance the modulating signal Property of R. Struzak 32

33 Noise (random processes), and pseudo-random processes can also be used as carriers Example: spread-spectrum systems In some systems, the carrier and modulation format change during the transmission Independently of the modulation type, spectra of signals used in radiocommunications are, contained between 9 khz and 275 GHz, as defined in ITU Radio Regulations Property of R. Struzak 33

34 Demodulation & Detection Demodulation Is process of removing the carrier signal to obtain the original signal waveform Detection extracts the symbols from the waveform Coherent detection Non-coherent detection Property of R. Struzak 34

35 Coherent (synchronous) Detection Signal change introduced by the channel (phase and attenuation) is estimated. It is then possible to reproduce the transmitted signal and demodulate. Requires a replica carrier wave of the same frequency and phase to be delivered at the receiver. The received signal and replica carrier are crosscorrelated using information contained in their amplitudes and phases. Property of R. Struzak 35

36 Carrier recovery methods include Pilot Tone (such as Transparent Tone in Band) Less power in the information bearing signal, High peak-tomean power ratio Carrier recovery from the information signal E.g. Costas loop Applicable to Phase Shift Keying (PSK) Frequency Shift Keying (FSK) Amplitude Shift Keying (ASK) Property of R. Struzak 36

37 Non-Coherent Detection Requires no reference wave; does not exploit phase reference information (envelope detection) Applicable to Differential Phase Shift Keying (DPSK) Frequency Shift Keying (FSK) Amplitude Shift Keying (ASK) Non coherent detection is less complex than coherent detection (easier to implement), but has worse performance. Property of R. Struzak 37

38 Geometric Representation Digital modulation involves choosing a particular signal s i (t) form a finite set S of possible signals. For binary modulation schemes a binary information bit is mapped directly to a signal and S contains only 2 signals, representing 0 and 1. For M-ary keying S contains more than 2 signals and each represents more than a single bit of information. With a signal set of size M, it is possible to transmit up to log 2 M bits per signal. Property of R. Struzak 38

39 Any element of set S can be represented as a point in a vector space whose coordinates are basis signals φ j (t) such that φ i () φ () t t dt = 0, i j; (= are orthogonal) () 2 E = φ i t dt = 1; ( = normalization) Then j N () = φ () s t s t i ij j j= 1 Property of R. Struzak 39

40 Example: BPSK Constellation Diagram 2E b 2E b S = s () t = cos( 2 π f t), s ( t) = cos( 2 π f t) ; ; 0 t T E = energy per bit; T = bit period BPSK 1 c 2 c b Tb Tb For this signal set, there is a single basic signal φ S 1 b 2 t = cos 2 fct ; 0 t T T () ( π ) BPSK b { } = Ebφ1() t, Ebφ1() t b b Q I - E b E b Constellation diagram Property of R. Struzak 40

41 Constellation diagram = graphical representation of the complex envelope of each possible symbol state The x-axis represents the in-phase component and the y-axis the quadrature component of the complex envelope The distance between signals on a constellation diagram relates to how different the modulation waveforms are and how easily a receiver can differentiate between them. Property of R. Struzak 41

42 QPSK Quadrature Phase Shift Keying (QPSK) can be interpreted as two independent BPSK systems (one on the I-channel and one on Q), and thus the same performance but twice the bandwidth efficiency Large envelope variations occur due to abrupt phase transitions, thus requiring linear amplification Property of R. Struzak 42

43 QPSK Constellation Diagram Q Q I I Carrier phases {0, π/2, π, 3π/2} Carrier phases {π/4, 3π/4, 5π/4, 7π/4} Quadrature Phase Shift Keying has twice the bandwidth efficiency of BPSK since 2 bits are transmitted in a single modulation symbol Property of R. Struzak 43

44 Q Types of QPSK Q Q I I I Conventional QPSK Offset QPSK π/4 QPSK Conventional QPSK has transitions through zero (i.e phase transition). Highly linear amplifiers required. In Offset QPSK, the phase transitions are limited to 90 0, the transitions on the I and Q channels are staggered. In π/4 QPSK the set of constellation points are toggled each symbol, so transitions through zero cannot occur. This scheme produces the lowest envelope variations. All QPSK schemes require linear power amplifiers Property of R. Struzak 44

45 Multi-level (M-ary) Phase and Amplitude Modulation 16 QAM 16 PSK 16 APSK Amplitude and phase shift keying can be combined to transmit several bits per symbol. (Often referred to as linear as they require linear amplification. More bandwidth-efficient, but more susceptible to noise.) For M=4, 16QAM has the largest distance between points, but requires very linear amplification. 16PSK has less stringent linearity requirements, but has less spacing between constellation points, and is therefore more affected by noise. Simulation: Property of R. Struzak 45

46 Decision region Property of R. Struzak 46

47 Decision region Distortions Perfect channel White noise Phase jitter Property of R. Struzak 47

48 Eye Diagram Magnitude Time (symbols) If the eye is not open at the sample point, errors will occur due to signal corruption Eye pattern is an oscilloscope display in which digital data signal from a receiver is repetitively superimposed on itself many times (sampled and applied to the vertical input, while the data rate is used to trigger the horizontal sweep). It is so called because the pattern looks like a series of eyes between a pair of rails. Property of R. Struzak 48

49 GMSK Gaussian Minimum Shift Keying (GMSK) is a form of continuous-phase FSK in which the phase change is changed between symbols to provide a constant envelope. Consequently it is a popular alternative to QPSK The RF bandwidth is controlled by the Gaussian low-pass filter bandwidth. The degree of filtering is expressed by multiplying the filter 3dB bandwidth (B) by the bit period of the transmission (T), i.e. by BT GMSK allows efficient class C non-linear amplifiers to be used Property of R. Struzak 49

50 Outline Radiocommunication channel Modulation Spreading spectrum Nonlinearities & intermodulation Summary Property of R. Struzak 50

51 Modulation Spectra Relative Magnitude (db) Nyquist Minimum Bandwidth Adjacent Channel Frequency The Nyquist bandwidth is the minimum bandwidth that can carry a given volume of information The spectrum occupied by a signal is usually larger and spill over adjacent channels causing interference The spectrum occupied by a signal can be reduced by application of filters Technical standards and RR impose limits on spectral masks Property of R. Struzak 51

52 Capacity of communication system C = B*log 2 {1 + [S/(N o *B)]} Noise density, W/Hz Received signal power, W Bandwidth, Hz Capacity, bit/s The capacity to transfer error-free information is enhanced with increased bandwidth B, even though the signal-to-noise ratio is decreased because of the increased bandwidth. Property of R. Struzak 52

53 SS communications basics Original information Original signal Spread signal Spreading Propagation effects Transmission Unwanted signals + Noise De-spreading Spread signal+ Reconstr. signal Reconstructed information Property of R. Struzak 53

54 SS: basic characteristics Signal spread over a wide bandwidth >> minimum bandwidth necessary to transmit information Spreading by means of a code independent of the data Data recovered by de-spreading the signal with a synchronous replica of the reference code TR: transmitted reference (separate data-channel and reference-channel, correlation detector) SR: stored reference (independent generation at T & R pseudo-random identical waveforms, synchronization by signal received, correlation detector) Other (MT: T-signal generated by pulsing a matched filter having long, pseudo-randomly controlled impulse response. Signal detection at R by identical filter & correlation computation) Property of R. Struzak 54

55 SS communication techniques FH: frequency hoping (frequency synthesizer controlled by pseudorandom sequence of numbers) DS: direct sequence (pseudo-random sequence of pulses used for spreading) TH: time hoping (spreading achieved by randomly spacing transmitted pulses) Random noise as carrier Hybrid combination of the above Other techniques (radar and other applications) Property of R. Struzak 55

56 Multiple-access techniques FDMA: frequency-division multiple access TDMA: time-division multiple access CDMA: code-division multiple access Other (e.g. OFDM) Property of R. Struzak 56

57 FDMA FDMA Power density Frequency Time Frequency Bc Bm Frequency channel Time Transmission is organized in frequency channels. Each link is assigned a separate channel. Example: Telephony Bm = 3-9 khz Property of R. Struzak 57

58 TDMA TDMA Power density Frequency Time-frame Time Frequency Time slot Time Transmission is organized in repetitive time-frames. Each frame consists of groups of pulses - time slots. Each user/ link is assigned a separate time-slot. Example: DECT (Digital enhanced cordless phone) Frame lasts 10 ms, consists of 24 time slots (each 417µs) Property of R. Struzak 58

59 FH SS (CDMA) Frequency Bm Bc CDMA Time Power density Frequency Time-frequency slot Time Transmission is organized in time-frequency slots. Each link is assigned a sequence of the slots, according to a specific code. Property of R. Struzak 59

60 DS SS: transmitter Modulator X Antenna [A(t), ϕ(t)] Information [g 1 (t)] Carrier cos(ω 0 t) Modulated signal S 1 (t) = A(t) cos(ω 0 t + ϕ(t)) band Bm Hz Spread signal g 1 (t)s 1 (t) band Bc Hz Bc >> Bm g i (t): pseudo-random noise (PN) spreading functions that spreads the energy of S 1 (t) over a bandwidth considerably wider than that of S 1 (t): ideally g i (t) g j (t) = 1 if i = j and g i (t) g j (t) = 0 if i j Property of R. Struzak 60

61 DS SS-receiver antenna Linear combination g 1 (t)s 1 (t) g 2 (t)s 2 (t). g n (t)s n (t) N(t) (noise) S (t) X Spreading function [g 1 (t)] Correlator & bandpass filter g 1 (t) g 1 (t)s 1 (t) g 1 (t) g 2 (t)s 2 (t). g 1 (t) g n (t)s n (t) g 1 (t) N(t) g 1 (t) S (t) S 1 (t) To demodulator Property of R. Struzak 61

62 SS-receiver s Input W/Hz Wanted (spread) signal: g 1 (t)s 1 (t) Unwanted signals SS s.: g 2 (t)s 2 (t); ; g n (t)s n (t) Other s. : S (t) Noise: N(t) Hz Bc Signal-to-interference ratio (S/ I) in = S/ [I(ω)*Bc] Bc = Input correlator bandwidth I(ω) = Average spectral power density of unwanted signals in Bc S = Power of the wanted signal Property of R. Struzak 62

63 SS-correlator/ filter output Wanted (correlated) signal: de-spread to its original bandwidth as g 1 (t) g 1 (t)s 1 (t) = S 1 (t) with g 1 (t) g 1 (t) = 1 Bm Uncorrelated (unwanted) signals spread & rejected by correlator + noise g 1 (t) S (t); g 1 (t) N(t); g 1 (t) g j (t)s j (t) = 0 as g i (t) g j (t) = 0 for i j Signal-to-interference ratio (S/ I) out = S/ [I(ω)*Bm] Bc Bc = Input correlator bandwidth Bm = Output filter bandwidth I(ω) = Average spectral power density of unwanted signals & noise in Bm S = power of the wanted signal at the correlator output Spreading = reducing spectral power density Property of R. Struzak 63

64 SS Processing Gain = = [(S/ I) in / (S/ I) out ] = ~Bc/ Bm Example: GPS signal RF bandwidth Bc ~ 2MHz Filter bandwidth Bm ~ 100 Hz Processing gain ~ (+43 db) Input S/N = -20 db Output S/N = +23 db (signal power = 1% of noise power) (signal power = 200 x noise power) (GPS = Global Positioning System) Property of R. Struzak 64

65 Outline Radiocommunication channel Modulation Spreading spectrum Nonlinearities & intermodulation Summary Property of R. Struzak 65

66 Sources of undesired nonlinear effects: Receiver RF input/ mixing stage Transmitter output stages Vicinity of the equipment (usually of the transmitter) Property of R. Struzak 66

67 Types of undesired nonlinear effects: Receiver blocking Transmitter spurious radiations & intermodulation Receiver spurious responses & intermodulation Note: Several nonlinear interactions may occur simultaneously» (Source: ITU/ CCIR Rep , Vol. 1, p. 30, 1986) Property of R. Struzak 67

68 X(t) 2 3 n Y = a + a X + a X + a X a X Y(t) n Non-ideal wideband memory-less linear devices are often treated by expressing the output (Y) of the system as a power series of the total input signal X: X(t) = A 1 sin(w 1 t) + A 2 sin(w 2 t) + The coefficients a are presumed to be real and independent on X. Property of R. Struzak 68

69 In practice, one focus only on those impairments that fall in the desired frequency channel The lowest from these (and often the dominant one) is the third-order nonlinearity Y = a + a X + a X The second-order nonlinearity may also be a critical performance parameter for a receiver. The approach presented here can easily be extended to the evaluation of the second-order and other nonlinearities of a receiver. 3 Property of R. Struzak 69

70 Blocking dynamic range (BDR) y = a + a x+ a x + a x MDS = Minimum Detectable Signal (Output Noise Floor) Output power (dbm) MDS P 1dB-out BDR (Blocking Dynamic Range) 1dB Noise Floor Input power (dbm) P 1dB-in Property of R. Struzak 70

71 IP1dB_b Two-signal Input Referred Blocking 1 db Gain Compression Point Refers to the condition when there are 2 singlefrequency input signals x(t) = [A 1 cos(ω 1 t) + A 2 cos(ω 2 t) and one of them (the blocker) is significantly stronger than the other, that is A 2 >> A yt ( ) = a0 + a1+ aa 3 2 A1cos ( ω1 t) Property of R. Struzak 71

72 If a 3 < 0, the weaker signal A 1 cos(ω 1 t) experiences progressively less gain as the stronger signal A 2 cos(ω 2 t) gets stronger. The gain drops by 1 db from its ideal value when the blocker amplitude reaches A IP1 db _ b = a a 1 3 Property of R. Struzak 72

73 Assume a small signal test, i.e. A small enough such that a 9 a A The input level for which the output components at ω 1 and ω 2 have the same amplitude as those at (2ω 1 ω 2 ) and (2ω 2 ω 1 ) is the input referred thirdorder intercept point: 4 a1 A 3 IIP3 = 3 a 3 2 Property of R. Struzak 73

74 Intermodulation Intermodulation spurious signals can be generated when two or more RF signals are applied to a nonlinear device They could produce interference The magnitude of the spurious signals depends on the power of the original signals and on the degree of device nonlinearity Technical standards and RR impose limits on outof-band (spurious) radiations Property of R. Struzak 74

75 Intermodulation products The frequency (Fi) of an intermodulation product Fi = C1*F1+C2*F2+.. +Cn*Fn {C1, C2,...,Cn} are positive or negative integers or zero, and {F1, F2,..., Fn} are the frequencies of the signals applied to the device The order of the intermodulation product is the sum: { C1 + C Cn } Property of R. Struzak 75

76 IIP3 Two-signal Input-Referred Third-order Intercept Point A third-order intermodulation component (IM3) due to two sinusoidal input signals of equal amplitude (Acosω 1 t, Acosω 2 t) [ ω ω ] [ ω ω ] yt ( ) = a + a Acos( t) + Acos( t) + a Acos( t) + Acos( t) = = a + a+ aa A t + A t + aa + aa [ cos( ω ) cos( ω )] cos( 2ω ω ) cos( 2ω ω ) Property of R. Struzak 76

77 Example: 3rd order intermodulation Two real signals of frequencies F1 and F2 when applied to a nonlinearity, produce six false signals (3-rd order intermodulation products) at the following frequencies: Fia = 2*F1 -F2 Fib = 2*F2 -F1 Fic = 2*F1 + F2 Fid = 2*F2 + F1 Fie = 3F1 Fif = 3F2 Even if F1 and F2 do not interfere one with another, intermodulation products can interfere with one or another. Frequencies Fia, Fib, can be close to F1 or F2. More real signals, more the number of false signals Property of R. Struzak 77

78 2F1-F2 2F2-F1 2F1+F2 2F2+F1 2F1 2F2 3F1 3F2 F1 F2 Property of R. Struzak 78

79 All above parameters are defined under assumptions of small-signal and systems with third-order nonlinearity IP1dB and IP1dB_b can be directly measured IIP3 and IIP3_h cannot be directly measured: they can only be extrapolated from small signal measurements as they are defined under small signal assumptions. The numerical values of the parameters are inter-related: IP1dB = IIP3 9.6 db IP1dB_b = IIP db IIP3_h = IIP3 + 5 db Property of R. Struzak 79

80 Summary Radiocommunication channel Modulation Spreading spectrum Nonlinearities & intermodulation Property of R. Struzak 80

81 References Campbell AT. Untangling the Wireless Web Radio Channel Issues, Lecture Notes E6951, comet.columbia.edu/~campbell Proakis J. Digital Communications, McGraw & Hill Int. Rappaport TS. Wireless Communications, Prentice Hall PTR Property of R. Struzak 81

82 Any question? Thank you for your attention Property of R. Struzak 82

83 Copyright note Copyright 2005 Ryszard Struzak. This work is licensed under the Creative Commons Attribution License These materials may be used freely for individual study, research, and education in not-for-profit applications. Any other use (and/or displaying the material in the WWW) requires the written author s permission If you cite these materials, please credit the author. If you have comments or suggestions, please send these directly to the author at r.struzak@ieee.org. Property of R. Struzak 83