Wideband Communications

Wideband Communications Lecture 8-9:

DMT

Aliazam Abbasfar

OutlineDMT examples

Channel estimation

Noise estimation

ADSL/VDSL ADSL : The most popular broadband Internet service

Over telephone lines ITU .G992.1 DMT : T = 250 usec Down stream

256 tones, 4.3125 KHz spacing, real baseband (ADSL2+ /VDSL -> 512/4096 tones) 1/T’ = 2.208 MHz ( BW = 1.104 MHz) N + v = 512 + 40 (Hermitian symmetry ) 2-3 tones are not used (phone line) Tone 64 is pilot ( known QPSK data), Tone 256 not used Pmax = 20.5 dBm

Up stream Upstream transmission uses 32 tones to frequency 138 KHz 1/T’ = 276 KHz ( BW = 138 KHz) N + v = 64 + 5 (Hermitian symmetry ) 1st tone not used (phone line) Pmax = 14.5 dBm

Upto 12/1.5 Mbps down/upstream Bit loading to optimize data rate bmax = 15 (per tone)

Isaksson’s Zipper Bidirectional communication (full duplex)

N = 10, v=2, D = 3

Suffix = 2 D

Suffix = D Time advance at TX

WiFiWireless LAN

802.11a/g @ 5/2.4 GHz COFDM : T = 4 usec

64 tones, 312.5 KHz spacing, complex baseband 1/T’ = 20 MHz BW = 20 MHz (15.56) N + v = 64 + 16 Tones : -31 to 31 (48 tones for data ) -31 to -27, 0, 27 to 32 are not used -27, -7, 7, and 21 are pilot Data rate = k * 48 * 250 KHz = 12k Mbps k = bn : bits/tone Upto 54 Mbps

Variable coding No bit loading bn is constant for all tones

Pmax = 16/23/29 dBm

Digital Video Broadcast (DVB) Digital TV broadcast

Single frequency network (SFN) Improves coverage Creates ISI

COFDM 2048 or 8192 tones, 4.464/1.116 KHz spacing complex baseband 1/T’ = 9.142 MHz BW = 20 MHz (15.56)

N T’ = 8192 T’ = 896 usec (1/1.116 KHz) (N+v) T’ = 924/952/1008/1120 usec

N T’ = 2046 T’ = 224 usec (1/4.464 KHz) (N+v) T’ = 231/238/252/280 usec

4/16/64 QAM Coding : 172/204 * 1/2, 2/3, 3/4, 5/6, or 7/8

Data rates : 4.98 31.67 Mbps Carries 2-8 TV channels

Channel estimation Channel model (n=0, 1,.., N-1)

yn = xn * pn + un Yn = Pn Xn + Un P = Q p

Time/Freq. domain estimates and errors pn , Pn en = yn – xn * pn En = Yn - Pn Xn

MSE = E[|e|2] /N = E[|E|2] /N MSE = E[|u|2] /N + E[|p-p|2] Ex MSE = E[|U|2] /N + E[|P-P|2] Ex

MSEch = E[|p-p|2] Ex = E[|P-P|2] Ex

SNR = E[|x|2 ] /N |p|2 / E[|u|2] /N = Ex |p|2 / s2u

SNRn = |Pn|2 E[|Xn|2] / E[|Un|2] = |Pn|2 E[|Xn|2]/ s2n

SNRch,n >> SNRn E[|Un|2] >> E[|Pn - Pn|2]

Channel estimation (2) Estimation method

Average over L trials

Estimation error

E[ |En|2] = E[|Un|2] + E[|P-P|2] /N

= E[|Un|2] (1+ 1/L)

SNRch,n = L SNRn

L = 40 1/L = 0.1 dB 0.1 dB accuracy

Time–domain constraint improves the estimation

FEQFrequency domain equalizer

Yn x Wn = Xn Wn = 1/Pn

Adaptive methodsZero Forcing

MMSE

Noise estimationNoise variance estimator

Mean = true estimate Variance

0.1 dB accuracy L=3200%10 chance of more deviation

%1 12,800%0.1 28,800

Noise trackingFirst order update

L = 6400 m’ = 6x10-4

Note : 1/gn = k s2

Windowing DMT/OFDM has a windowing for each symbol

Duration = T Rectangular/Raised cosine

Needs extra guard time excess bandwidth

Windowing in time =Convolution in frequency

At TX Reduces out of band emission

At RX Reduces narrowband noise

Lower sidelobes improves gn

ReadingCioffi Ch. 4.7, 4.9