Any signal can be decomposed as the sum of orthogonal waveforms (basis functions) Successive transmitted symbols bl interfere with each other

Transcription

1 Intersymbol Interference Any signal can be decomposed as the sum of orthogonal waveforms (basis functions) x ( t ) x i i ( t ) i and () t () t dt 0 for i j Modulation : mapping constellation symbols to waveforms Signal transmitted over non-ideal channel h t t rt () xt ()* ht () x( ht ()* ()) t xh() t In general, h () i t are not orthogonal i i i i j x i i i i ( ) ( ) Successive transmitted symbols bl interfere with each other

2 Transmit Filter (Modulation Basis Function) Most common choice for basis function ( t) ( t it ) i where T is symbol period Analog transmitted waveform is generated by modulating the transmit filter (t) by the symbols Throughput this course, unless otherwise stated, transmit filter is lumped with channel filter and receiver front-end continuous matched filter into one filter h(t) x i 2

3 Scatter Diagram 3

4 Time-Domain View For LTI channel, received noisy & match-filtered analog signal r() t x ht ( jt) nt () Sampled ldat time t kt t r k def r j j 0 ( is sampling offset) ( k j 0 jk t0 kt) x h( t0 T ) x h( t0 ( k j) T) n( t kt) x j h(t) Desired ISI Noise Signal Cursor ( j = k- ) pre-cursor ISI t 0 post-cursor ISI (j > k- ) (j < k- ) n(t) t kt t 0 r(t) r k Note that matched filter is absorbed in h (t) 0 is decision delay 4

5 Frequency-Domain View Ideal (Memory-less or ISI-free) Channel Constant Magnitude Response Linear Phase Response H f Ke j ( ) ft ht () K ( t t ) T-spaced sampling replicated spectrum at l 2 integer multiples of (radian frequency) Nyquist s Criterion for No ISI T n 2n H ( w ) T Constant 5

6 Nyquist Pulses Satisfy Nyquist s condition for no ISI Impulse response is zero for all sampling instants except desired one, hence, h k k h(t) = sinc (t/t) is only Nyquist pulse w/ minimum bandwidth equal to (sensitive to timing errors and T difficult to realize in practice) Most popular choices in practice are raised-cosine and square-root raised cosine pulses with 15-35% excess BW, implemented as FIR digital filters (for 30% excess factor, 37 filter taps needed and the first sidelobe is 40 db down) 6

7 Raised-Cosine Filter t h( t) sinc( ) T t cos( ) T 2 t 2 1 ( ) T H ( w ) T w ( 1) T 0 ( 1 ) w T T T ( 1 sin( ( w ))) 2 2 T ( 1 ) w ( 1 ) T T 7

8 Causes of ISI Receive Filtering i (out-of-band noise rejection, desired channel selection) Transmit pulse shaping (e.g. to reduce sidelobes, narrow main-lobe) Multipath propagation -channel frequency selectivity Higher transmission rates (using wider transmission bandwidth) 8

9 Transmitted Waveform Received Waveform 9

10 ISI Distortion Criteria k j k max Peak Distortion Criterion D h x x h p k k Represents worst-case distance loss between signal points Worst-case ISI (rare in practice)- input pattern of all x max k 2 2 Mean Square Distortion D S h E[( x h ) ] ms x k k k i Assumes zero-mean I.I.D. input sequence D ms is added to noise variance in probability of error Q-function calculations (only accurate if ISI is Gaussian) i k i 10

11 Graphical Display of ISI Channel Impulse Response Single impulse for ideal channel. ISI results in scaled & delayed impulses. Channel Frequency Response Flat magnitude response and linear phase response for ideal channel. Nulls indicate severe ISI Eye Diagrams Generated using oscilloscope to observe received signal when symbol timing is used as a trigger Scatter Diagram For ideal channels looks like input signal constellation

12 Eye Diagrams BPSK Constellation 4-PAM Constellation Received waveforms superimposed and folded d over duration of 2 symbol periods 12

13 Simple Example 2-Tap ISI Channel y x x n 1 k k k k k x k n k y k ^ x k PAM Symbol-by-symbol detection is sub-optimum in presence of ISI because it does not exploit channel memory 13

14 ISI Channel Model Received analog signal is passed through an analog matched filter and sampled at the symbol rate T-spaced samples at matched filter output are sufficient statistics (i.e. no loss of information as far as data detection is concerned) for representing the ISI channel (Forney 72) Without loss of generality, the combined effects of transmit filter, channel, and receive filter are modeled as FIR filter w/ memory y h x n k m 0 m k m k 14

15 15

16 Examples of ISI Channels Wireless Transmission i Channels Digital Cellular Radio (2G,3G,4G) Digital it Video Broadcast (DVB-T, DVBH) DVB-H) Local Area Network (IEEE802.11x) Wireline Transmission Channels Twisted-Pair i Copper Lines (XDSL) Coaxial Cable (DOCSIS) Power Line Communications (PLC)

17 Mobile Digital Cellular Radio Frequency band : around 1-2 GHz Coverage area divided into cells (each with its own base station) ti 2G Standards : IS-136, GSM, IS-95, EDGE,.. 3G standards : CDMA based 4G standards : OFDM based (LTE) Impairments : Path loss (proportional to R : ) Resolvable multipath reflections (in-band nulls), frequency selective channel Signal fdi fading : fast small-scale l fading due to multipath th, and slow large-scale l fading (shadowing) due to obstacles in direct path v Doppler shift (mobility ), time-selective channel f d Co-channel interference (a.k.a. inter-cell interference) frequency re-use factor) Thermal Noise (modeled as additive white Gaussian noise (AWGN)) f2 f6 f5 f7 f1 f4 f2 f3 f6

18 Wireless Channels : Challenges Remote Dominant Reflector Local Scatterers to Base Co-Channel Mobile Base Station Local Scatterers to Mobile Local Scatterers to Base Remote Dominant Reflector Local Scattering Multipath Propagation Mbil Mobile Mti Motion Cellular Spectrum Reuse Fading Intersymbol Interference Time Varying Channel Co-channel Interference 18

19 Signal Level in Wireless Channels Short Term Fading (db) Signal Level ( Long Term Fading Mean Path Loss Distance (db) Slow fading (shadowing) caused by large obstructions between transmitter and receiver Fast fading is due to reflection and scattering of the signal by objects near transmitter Path loss proportional to 1/r <5 19

20 Signal Fading Long-term (slow) fading (a.k.a. shadowing) occurs over long distances and is log-normal distributed (i.e. Gaussian in db) about the mean path loss (which is inversely proportional to nth power of propagation distance where 2.5<n<5 Short-term (fast) fading is Rayleigh- distributed relative to local mean P Pr[ P received P] 1 e P ( ) P 20

21 Cell Planning Typical reuse factors are K= 4,7, and 12 Tradeoffs : for small cells, transmitted signals encounter smaller propagation loss which translates into transmit power savings. Also, smaller cells allow for more frequency re-use which translates into capacity increase (assuming effective interference cancellation). However, more base stations are needed (infrastructure cost) 21

22 Multipath Propagation Multipath Delay Spread of Channel Range of time delays over which an impulse transmitted at time 0 is received with non-zero energy (also called memory of channel) Coherence Bandwidth of Channel Frequency range over which two transmitted sinusoids are affected the same (in magnitude & phase) by the channel Delay Spread = 1 / Coherence Bandwidth Frequency non-selective ec channel (memoryless, ess, ISI-free, non-dispersive) dspesve) Signal Bandwidth << Coherence Bandwidth Symbol period >> Delay Spread (negligible delay spread narrow-band signaling) 22

23 Typical Numbers Indoor environment (e.g. cubicle offices) 100nano -sec B c 10MHz Outdoor environment (e.g. urban cellular) 5 micro -sec B c 200kHz 23

24 Multipath Propagation Doppler Spread of Channel Range of frequencies over which a tone transmitted at time 0 is received with non-zero energy Coherence Time of Channel Time range over which two transmitted impulses are affected the same (in magnitude & phase) by the channel Doppler Frequency = 1 / Coherence Time Condition o for Slowly Time Varying Channel Transmission Block Duration << Coherence Time 1/(Block Length * Symbol period) >> Doppler Frequency 1 v fd v NT NT s s 24

25 f c Example 3GHz 0.1m f 10 d Pedestrian Speed : 3m / sec f 30Hz T 33msec d c Highway Speed : 120Km / hr 33.3m / sec f 333.3Hz T 3msec d c Guidelines for choosing block length : Doppler, complexity, memory, overhead 25

26 Narrowband vs. Wideband If a signal u(t) propagates distance d experiencing attenuation of A, then the passband received signal is given by j2fc ( t ) y ( t ) { Au. ( t ) e { Au. ( t ) e j2f t c 2 j d d d where fc fc c Therefore, the transfer function of the e } } equivalent baseband channel is Ae j2f e 2 j d 26

27 Narrowband vs. Wideband In narrowband transmission, channel appears to have constant gain & delay for all frequencies 2-path model 2 j d 1 j2 f 1 j2 f 2 A e e A e e 1 2 Ae 1 j2 f 1 e 2 j d 2 A A e j f e j d 2 2 ( 1 ) 2 j d Using superposition wavelength delay spread d path length diff. Condition for Narrow-band transmission Non-resolvable multipath transmission BW f 1 max fmax 1 coherence BW Only frequency-dependent term in channel magnitude j f response is 1 e 2 where is complex const.

28 Example 2 path channel, 1 microsec delay spread path channel, 1 microsec delay spread Mag gnitude Response Mag gnitude Response Frequency (Hz) Frequency (Hz) x 10 6 H ( f ) 1 e j f H ( f ) 2 4cos 2 ( f ) 2 1 sec Coherence BW = 1MHz

29 Indoor/Outdoor Wireless Standards Channel is time and frequency selective, wider coverage WWAN/WMAN/WRAN (few Km) 2.5/3G/4G (GPRS/WCDMA/LTE/DVB-H) Long delay spreads (10 micro) Large # users WLAN (100M) a/b/g/n/ad Medium delay spreads (1 micro) WPAN (10M) Bluetooth, Zigbee Medium # users Low mobility Shorter Coverage Short delay spreads ( micro) Small # users 10m 100m 1km+ A single technology may not be optimal for all spheres source : Intel Range 29

30 Wireless Comm. Challenges Reliability impaired by fading, frequency selectivity, noise, interference (co-channel, adjacent channel), mobility (Doppler) Shared medium : interference management (TDMA/FDMA/CDMA/SDMA) Scarcity & Cost of suitable RF spectrum (licensed vs. unlicensed transmissions) Low power/form factor terminal constraints (battery lifetime, high circuit integration) 30

31 Design Tradeoffs Implementation Complexity Rate Reliability 31

32 Copper Twisted-Pair Channel (a.k.a. a Telephone lines) Used for connecting phone equipment to central office Channel Model H ( f ) Impairments e Subscriber 2 f TX RX bridged tap FEXT NEXT - ISI TX RX - Crosstalk (NEXT + FEXT) - In-band nulls (bridged taps, gauge changes) - Thermal noise (electronics) -Impulse noise (switching) - External Radio Frequency Interference (RFI) - Loading Coils : low-pass filters which limit broadband transmission and must be removed for DSL service Central Office RX TX RX TX

33 Unshielded Twisted Pair (UTP) Channel Attenuation increases exponentially w/ frequency and length of loop Different frequency components of signal attenuated differently (dispersion) Connecting several UTP s w/o proper termination results in frequency nulls A.G. Bell patented twisting and differential signaling on telephone lines to reduce electromagnetic radiation and cancel external common-mode noise 33

34 Asymmetric Digital Subscriber Lines (ADSL) digital Internet t Service Provider Voice Service Provider G A T E W A Y S Mux or Demux ADSL modem ADSL modem.. ADSL modem DSLAM analog Split ter analog 0-4 miles Splitter ADSL digital POTS customer premises Telephone company office Upstream : 26 khz to 137 khz, rates up to 1.4 Mbps Downstream : 138 khz to 2.22 MHz, rates up to 24 Mbps 34

35 Other Noises Radio Noise, AM, HAM narrowband must reject HAM by db (VDSL) and AM by db (ADSL) Impulse Noise 10 s millivolts strength 100 s microseconds duration 35

36 Very High Speed DSL (VDSL) ONU To 100 Mbps fiber VDSL POTS S p l i t S p l i t.1-2 km VDSL Hybrid Fiber/copper Downstream bandwidth up to 30 MHz Rates : 100 Mbps at 0.5 km and 50 Mbps at 1 km Example : AT&T U-verse System 36

37 VDSL Loops Shorter loops loops with bridge taps 37

38 Crosstalk in Digital Subscriber Lines (VDSL) FDD is used in VDSL to eliminate NEXT lf H ( f 3/ f ) Next-generation VDSL modems use advanced d FEXT Cancellation Algorithms g.vector standard Approved in