ItIntersymb blol ItfInterference
• Any signal can be decomposed as the sum of orthogonal waveforms (basis functions) ()t ()t dt 0 xt() xi i () t and ij for i j i Modulation : mapping constellation symbols x i to waveforms • Signa l transmi tted over non-ideal ch annel h(t)(t)
rt() xt ()*() ht xi ( ht ()*ii ()) t xhti () i i
In general, ht i () are not orthogonal Success ive transmitt ed symblbols int erf ere with each oth er Transmit Filter (Modulation Basis Function) • Most common choice for basis
function i (t) (t iT ) where T is symbol period • Analog transmitted waveform is generated by modulating the transmit (t) filter byyy the symbols xi 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) 2 Scatter Diagram
3 Time-Domain View
t kT t For LTI channel, received noisy & match-filtered analog signal n(t) 0
x j r()t xjht ( jT )nt () h(t) r(t) j rk Note that matched filter t kT t Sampldled at ti me 0 ( t 0 is sampling offset) is absorbed in h (t) def rk r(t0 kT) xkh(t0 T) xjh(t0 (k j)T) n(t0 kT) jk 0 is decision delay
Desired ISI Noise Signal Cursor ( j = k- ) pre-cursor post-cursor ISI ISI (j > k- ) (j < k- )
4 Freqqyuency-Domain View
• Ideal (Memory-less or ISI-f)free) ChChlannel
• Constant Magnitude Response ht() K (tt 0 ) j 2ft • Linear Phase Response H( f ) Ke 0 • T-spaced sampling replicated spectrum at in teger mu ltip les o f 2 (radi an frequency) T • Nyquist’s Criterion for No ISI
2n H ( w ) Constant n T 5 Nyquist Pulses
• Satisfyyyq Nyquist’s condition for no ISI • Impulse response is zero for all sampling instants except desired one, hence, hk 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 Raised-Cosine Filter
t t cos( ) ht() sinc ( ) T T 2 t 1 ()2 T T ||w (1 ) T H (w) 0 ()||1 w T
T T (1 si(in( (|w| ))) 2 2 T ()||()11 w T T
7 Causes of ISI
• Rece ive Filter ing (t(out-of-bdband noise rejection, desired channel selection) • Transm it pulse shap ing (e.g. to reduce sid e- lobes, narrow main-lobe) • MliMultipat h propagation -chlhannel frequency selectivity • Higher transmission rates (using wider transmission bandwidth)
8 Transmitted Waveform
Received Waveform
9 ISI Distortion Criteria
Peak Distortion Criterion D p | hk x j k | | x |max | hk | k k • Represents worst-case distance loss between signal points
• Worst-case ISI (rare in practi ce) - ifllinput pattern of all xmax
Mean Squ are Distortion 2 2 Dms S x | hk | E[( xi hk i ) ] k k i • Assumes zero-mean I.I.D. input sequence
• Dms is added to noise v ariance in probability of error Q-function calculations (only accurate if ISI is Gaussian)
10 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 Eye Diagrams
BPSK Constellation 4-PAM Constellation
Rece ive d wavef orms superi mposed and fold ed over durati on of 2 symb ol peri od s
12 Simple Example
2-Tap ISI Channel ykkk x x 1 n k
^
k xk nk yk xk -1 -3 -3 -1 1 3 0 -3 0.35 -5.65 -3 1 -1 0.05 -3.95 -3 232 3 -010.1 1 19.9 1 4-PAM 3 1 0.25 4.25 3
Symbol-by-symbol detection is sub-optimum in presence of ISI because it does not exploit channel memory
13 ISI Channel Model
• Received analoggg signal is p assed throug h 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 km h x km n k m 0
14 15 Examples of ISI Channels
• Wire less TiiTransmission ChlChannels • Digital Cellular Radio (2G,3G,4G) • Dig ita l Video Broad cast (DVB-T, DVB-H) • Local Area Network (IEEE802.11x)
• Wireline Transmission Channels • TitdTwisted-Pa ir Copper Lines (XDSL) • Coaxial Cable (DOCSIS) • Power Line Communi cati ons (PLC) Mobile Digital Cellular Radio • Frequency band : around 1-2 GHz • Coverage area divided into cells (eac h w ith it s own b ase st ati on)
• 2G Standards : IS-136, GSM, IS-95, EDGE,.. f7 • 3G standards : CDMA based f6 f2 f2f1 f6 • 4G standards : OFDM based (LTE) f5 f3 f4 Impairments : • Path loss (proportional to R : 2 . 5 5 ) • Resolvable multipath reflections (in-band nulls), frequency –selective channel • SiSignal fdifading : f ast small-scale fa ding d ue t o multi pa th , and sl ow large-scale fading (shadowing) due to obstacles in direct path v • Doppler shift (mobility f ), time-selective channel d • Co-channel interference (a.k.a. inter-cell interference) frequency re-use factor) • Thermal Noise (modeled as additive white Gaussian noise (AWGN)) Wireless Channels : Challenges
Remote Dominant Reflector
Local Scatterers to Base Co-Channel Mobile
Base Station Local Scatterers to Mobile Local Scattering Fading Multipath Propagation Intersymbol Interference MbilMtiMobil e Motion Time VVary iing Ch Ch anne l l Local Scatterers Cellular Spectrum Reuse Co-channel Interference to Base Remote Dominant 18 Reflecto r Signal Level in Wireless Channels Short Term Fading
Mean Path Loss dB) ((
Signal Level Long Term Fading
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 Signal Fading
• Long-term (l(slow ) fdifading (k(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 • 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 Multipppgath 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 Frequen cy no n-sel ecti ve ch ann el (m em or yl ess, IS I-free, no n-ddspesve)ispersive) Signal Bandwidth << Coherence Bandwidth (negligible delay spread narrow-band signaling) Symbol period >> Delay Spread 22 Typical Numbers • IdIndoor environmen t (e.g. cubi c le o ffices ) 100nano -sec Bc 10MHz • Outdoor environment (e.g. urban cellular) 5 micro -sec Bc 200kHz 23 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 Cond itio n fo r S low l y Tim e Var yin g Ch anne l Transmission Block Duration << Coherence Time 1/(Block Length * Symbol period) >> Doppler Frequency 1 v fd v 24 NTs NTs Example fc 3GHz 0.1m fd 10 • Pedestrian Speed : 3m / sec fd 30Hz Tc 33msec • Highway Speed : 120Km / hr 33.3m / sec fd 333.3Hz Tc 3msec Guidelines for choosing block length : Doppler, complexity, memory, overhead 25 Narrowband vs. Wideband • If a signal u(t) propagates distance “d” experiencing attenuation of “A”, then the ppggyassband received signal is given by y(t) {A.u(t )e j2 fc (t )} 2 j d {A.u(t )e j2 fcte } d d where f f c c c Therefore, the transfer function of the 2 j d equivalent baseband channel is Ae j2 f e 26 Narrowband vs. Wideband In narrowband transmission,,pp channel appears to have constant gain & delay for all frequencies 2 2 jd jd jf2 1 jf2 2 2-path model 1 2 A12e e A e e Using superposition 2 2 jd jd jf2 1 A 2 jf2 1 Ae1 e ()1 ee A 1 wavelength delay spreadd path length diff. Condition for Narrow-band transmission Onlyyq frequency -dependent term in channel magnitude response is 1 e j2 f Non-resolvable where is complex const. multipath ||f max 1 1 transmission BW | f | coherence BW max Example 2−path channel, 1 microsec delay spread 2−path channel, 1 microsec delay spread 1 5 10 10 0 10 −5 10 −10 10 −15 10 −20 gnitude Response agnitude Response 10 Mag Magn −25 10 −30 10 −35 0 10 10 0 1 2 3 4 5 6 7 8 9 10 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Frequency (Hz) 6 Frequency (Hz) x 10 jf2 Hf() 1 e 1 sec 2 2 | H ( f ) | 4cos ( f ) Coherence BW = 1MHz Indoor/Outdoor Wireless Standards WWAN/WMAN/WRAN (few Km) 2.5/3G/4G Channel is time (GPRS/WCDMA/LTE/DVB-H) and frequency Long delay spreads Large selective, wider (10 micro) # users coverage WLAN (100M) 802.11a/b/g/n/ad Medium delay Medium spreads # users (1 micro) WPAN (10M) Bluetooth, Zigbee 802Short.11 delay spreads Low mobility (0.05-0.1 micro) Shorter Coverage Small # users Range 10m 100m 1km+ 29 A single technology may not be ‘optimal’ for all spheres source : Intel 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 Design Tradeoffs IlImplementati iCon Comp lilexity Rate Reliability 31 Copper Twisted-Pair Channel (a.k .a . Telephone lines) • Used for connecting phone equipment to central office • Channel Model Subscriber bridged tap Central Office 2 f |H( f )| e TX RX • Impairments RX TX FEXT NEXT - ISI TX RX - Crosstalk (NEXT + FEXT) RX TX - In-band nulls (bridged taps, gauge changes) - Thermal noi se ( el ectroni cs) -Impulse noise (switching) - External Radio Freqqyuency Interference ()(RFI) - Loading Coils : low-pass filters which limit broadband transmission and must be removed for DSL service 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 Asymmetric Digital Subscriber Lines (ADSL) digital ItInternet Service G Provider ADSL analog A modem Split Mux ADSL T modem ter or E . Splitter Demux . W ADSL ADSL A modem Voice Y analog Service S 00--44 miles DSLAM Provider POTS digital customer premises Telephone company office • Upstream : 26 kHz to 137 kHz, rates up to 1.4 Mbps • Downstream : 138 kHz to 2.2 MHz, rates up to 24 Mbps 34 Other Noises • Radio Noise, AM, HAM • narrowband • must reject HAM by 70-90 dB (VDSL) and AM by 20-40 dB (ADSL) • Impulse Noise • 10’s millivolts strength • 100’s microseconds duration 35 Very High Speed DSL (VDSL) To 100 Mbps ONU fiber S VDSL p l i S t p l i POTS t .1- 2 km VDSL Hyyppbrid 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 VDSL Loops Shorter loops loops with bridge taps 37 Crosstalk in Digital Subscriber Lines (VDSL) f 3/ 2 lf 2 | H ( f ) |2 FDD is used in VDSL to eliminate NEXT Next-generation VDSL modems use adddvanced FEXT Cancellation Algorithms g.Vector standard Approved in 2010 38