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

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

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

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

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

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 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 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

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

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

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

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

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

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

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

U NIVERSITY of N EW H AMPSHIRE I NTER O PERABILITY L ABORATORY VDSL MCM Simulation DMT Modulation  Discrete Multi-Tone  Uses 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 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

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

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

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

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

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

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  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  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

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

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

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

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

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