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© UNIVERSITY of NEW HAMPSHIRE INTEROPERABILITY LABORATORY VDSL MCM Simulation Tim Clark VDSL Consortium Tim Clark VDSL Consortium

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Presentation Content Simulation Overview Constellation Encoding and Multi-Carrier Modulation Reed-Solomon Forward Error Correction Convolutional Interleaving Channel Model Equalization (TEQ and FEQ) Bit Allocation Training Simulation Overview Constellation Encoding and Multi-Carrier Modulation Reed-Solomon Forward Error Correction Convolutional Interleaving Channel Model Equalization (TEQ and FEQ) Bit Allocation Training

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Simulation Overview Simulation done with code in MATLAB Simulates a DSLAM transmitter, twisted-pair channel, and remote receiver Simulation process: *Generate a frame of random binary data *Encode and modulate at the transmitter *Apply channel attenuation and add crosstalk to signal *Equalize, demodulate, and decode at the receiver *Compare binary data and CRC *Calculate BER and FER Simulation done with code in MATLAB Simulates a DSLAM transmitter, twisted-pair channel, and remote receiver Simulation process: *Generate a frame of random binary data *Encode and modulate at the transmitter *Apply channel attenuation and add crosstalk to signal *Equalize, demodulate, and decode at the receiver *Compare binary data and CRC *Calculate BER and FER

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Block Diagram

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Fast and Slow Data Paths Data is split evenly between an interleaved (slow) path and a non-interleaved (fast) path Interleaving provides resistance to burst errors but introduces latency Each path has a separate CRC, scrambler, and FEC Data is joined together before modulation Data is split evenly between an interleaved (slow) path and a non-interleaved (fast) path Interleaving provides resistance to burst errors but introduces latency Each path has a separate CRC, scrambler, and FEC Data is joined together before modulation

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Cyclic Redundancy Check (CRC) CRC Generation Algorithm: 1.Left-shift the input by 8 bits 2.Divide by the CRC generator polynomial G(D) = D 8 + D 4 + D 3 + D 2 + 1 3.The remainder is the checksum and is appended to the frame CRC Check Algorithm 1.Remove checksum from received frame 2.Use same algorithm to calculate checksum for received frame 3.If the two agree, set the syndrome to 0 Otherwise, set the syndrome to 1 CRC Generation Algorithm: 1.Left-shift the input by 8 bits 2.Divide by the CRC generator polynomial G(D) = D 8 + D 4 + D 3 + D 2 + 1 3.The remainder is the checksum and is appended to the frame CRC Check Algorithm 1.Remove checksum from received frame 2.Use same algorithm to calculate checksum for received frame 3.If the two agree, set the syndrome to 0 Otherwise, set the syndrome to 1

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Scrambler/DescramblerScrambler/Descrambler Scrambler output is the sum of the current bit and the 18 th and 23 rd delayed bits: x(n) = m(n) + m(n-18) + m(n-23) Addition is modulo-2, equivalent to exclusive-OR Scrambler output is the sum of the current bit and the 18 th and 23 rd delayed bits: x(n) = m(n) + m(n-18) + m(n-23) Addition is modulo-2, equivalent to exclusive-OR

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Forward Error Correction VDSL uses Reed-Solomon coding for FEC A RS codeword contains N=K+R bytes: *N = codeword length *K = message length *R = redundancy length RS code parameters are specified as (N,K) *The simulation uses either (240,224) or (144,128) *RS coding can correct R/2 byte errors per codeword VDSL uses Reed-Solomon coding for FEC A RS codeword contains N=K+R bytes: *N = codeword length *K = message length *R = redundancy length RS code parameters are specified as (N,K) *The simulation uses either (240,224) or (144,128) *RS coding can correct R/2 byte errors per codeword

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Reed-Solomon Coding R redundant bytes are calculated by dividing the K message bytes by a generator polynomial over the Galois Field GF(256) MATLAB has built-in functions for encoding and decoding RS codewords R redundant bytes are calculated by dividing the K message bytes by a generator polynomial over the Galois Field GF(256) MATLAB has built-in functions for encoding and decoding RS codewords

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation InterleavingInterleaving VDSL uses a convolutional interleaving algorithm to protect data against burst errors by spreading them out over multiple Reed-Solomon codewords Interleaving parameters: *I = number of interleaver branches *M = incremental delay *D = interleaving depth = M x I + 1 Can correct byte errors Introduces a delay of M x I x (I-1) bytes VDSL uses a convolutional interleaving algorithm to protect data against burst errors by spreading them out over multiple Reed-Solomon codewords Interleaving parameters: *I = number of interleaver branches *M = incremental delay *D = interleaving depth = M x I + 1 Can correct byte errors Introduces a delay of M x I x (I-1) bytes

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Convolutional Interleaving (1) Interleaver has I branches of length M x (I-1) + 1 Algorithm: 1.Interleaver memory is initialized with zeros 2.Input data is read into interleaver I bytes at a time 3.Each interleaver branch is delayed in increments of M 4.Data is output from front of interleaver 5.Left-shift interleaver memory Interleaver has I branches of length M x (I-1) + 1 Algorithm: 1.Interleaver memory is initialized with zeros 2.Input data is read into interleaver I bytes at a time 3.Each interleaver branch is delayed in increments of M 4.Data is output from front of interleaver 5.Left-shift interleaver memory

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Convolutional Interleaving (2)

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation QAM Constellations A sequence of bits is mapped to a complex number representing a constellation point Can use 1 to 15 bits per constellation point Corresponds to constellation size of 2 1 to 2 15 = 2 to 32K A sequence of bits is mapped to a complex number representing a constellation point Can use 1 to 15 bits per constellation point Corresponds to constellation size of 2 1 to 2 15 = 2 to 32K

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation DMT Modulation Discrete Multi-Tone Uses 4095 4-kHz bands Each band can carry a different number of bits Construct an array of 4096 complex numbers Take IFFT Result is the DMT signal Demodulated by the FFT, reverse-mapping Discrete Multi-Tone Uses 4095 4-kHz bands Each band can carry a different number of bits Construct an array of 4096 complex numbers Take IFFT Result is the DMT signal Demodulated by the FFT, reverse-mapping

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Cyclic Extension (1) Eliminates inter-symbol interference Simplifies equalizers Beginning samples are added to the end, last samples are added to the beginning, then whole thing is windowed At receiver, cyclic extension is stripped from received symbol Eliminates inter-symbol interference Simplifies equalizers Beginning samples are added to the end, last samples are added to the beginning, then whole thing is windowed At receiver, cyclic extension is stripped from received symbol

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Cyclic Extension (2)

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Channel Model Channel transfer function is calculated using ABCD modeling IFFT transfer function to get channel impulse response Convolve DMT signal with impulse response to get attenuated signal Add crosstalk Channel transfer function is calculated using ABCD modeling IFFT transfer function to get channel impulse response Convolve DMT signal with impulse response to get attenuated signal Add crosstalk

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation CrosstalkCrosstalk VDSL self-crosstalk is added to signal Simulates up to 20 other VDSL modems using the same spectrum operating in the same binder group VDSL self-crosstalk is added to signal Simulates up to 20 other VDSL modems using the same spectrum operating in the same binder group

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation TrainingTraining At beginning of simulation, modems perform a training session that involves discovery of the channel and bit allocation Channel discovery for calculating equalizer coefficients Channel equalizers designed to negate channel effects Bit allocation determines how many bits are carried on each tone At beginning of simulation, modems perform a training session that involves discovery of the channel and bit allocation Channel discovery for calculating equalizer coefficients Channel equalizers designed to negate channel effects Bit allocation determines how many bits are carried on each tone

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Bit Allocation Shannon Capacity formula: Number of bits on each tone is calculated from the SNR corresponds to a BER of 10 -7 Bits are adjusted such that total number of bits fits an integer number of Reed-Solomon codewords Creates a bit allocation profile that tells both receivers how many bits are modulated on each tone, i.e. what constellation size to map to Shannon Capacity formula: Number of bits on each tone is calculated from the SNR corresponds to a BER of 10 -7 Bits are adjusted such that total number of bits fits an integer number of Reed-Solomon codewords Creates a bit allocation profile that tells both receivers how many bits are modulated on each tone, i.e. what constellation size to map to

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Frequency-Division Duplexing Upstream and Downstream are multiplexed by assigning each tone to a direction Although 4096 tones extend beyond 17 MHz, current frequency plans only allocate transmission up to 12 MHz Upstream and Downstream are multiplexed by assigning each tone to a direction Although 4096 tones extend beyond 17 MHz, current frequency plans only allocate transmission up to 12 MHz

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Spectrum Allocation Plans

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Time-domain equalization (TEQ) Designed to reduce the impulse response of the channel Eliminates ISI Send a signal known to both modems Wiener filter block-data formulation Result is an FIR filter Designed to reduce the impulse response of the channel Eliminates ISI Send a signal known to both modems Wiener filter block-data formulation Result is an FIR filter

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation Frequency-domain equalization (FEQ) Negates combination of the channel and TEQ filter Channel attenuation for each tone is calculated by sending a known signal and comparing to the received signal Negates combination of the channel and TEQ filter Channel attenuation for each tone is calculated by sending a known signal and comparing to the received signal

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U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation ReferencesReferences ANSI / T1E1 *T1.424 Trial Standard Multi Carrier Modulation: Part III ANSI / T1E1 *T1.424 Trial Standard Multi Carrier Modulation: Part III

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