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**Wideband Communications**

Lecture 8-9: DMT Aliazam Abbasfar

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Outline DMT examples Channel estimation Noise estimation

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**ADSL/VDSL ADSL : The most popular broadband Internet service**

Over telephone lines ITU .G992.1 DMT : T = 250 usec Down stream 256 tones, KHz spacing, real baseband (ADSL2+ /VDSL -> 512/4096 tones) 1/T’ = MHz ( BW = MHz) N + v = (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 = (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)

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**Isaksson’s Zipper Bidirectional communication (full duplex)**

N = 10, v=2, D = 3 Suffix = 2 D Suffix = D Time advance at TX

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**WiFi Wireless LAN 802.11a/g @ 5/2.4 GHz COFDM : T = 4 usec**

64 tones, KHz spacing, complex baseband 1/T’ = 20 MHz BW = 20 MHz (15.56) N + v = 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

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**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’ = 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 Mbps Carries 2-8 TV channels

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**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]

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**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

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**FEQ Frequency domain equalizer Adaptive methods Yn x Wn = Xn Wn = 1/Pn**

Zero Forcing MMSE

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**Noise estimation Noise variance estimator 0.1 dB accuracy L=3200**

Mean = true estimate Variance 0.1 dB accuracy L=3200 %10 chance of more deviation %1 12,800 %0.1 28,800 Noise tracking First order update L = 6400 m’ = 6x10-4 Note : 1/gn = k s2

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**Windowing DMT/OFDM has a windowing for each symbol Windowing in time =**

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

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Reading Cioffi Ch. 4.7, 4.9

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