DSP Systems Implementation Course Seminar Tehran University Electrical And Computer Engineering Department Spring 2004

DSP Systems Implementation2 A Practical Example Of DSP System Design, ADSL Modem DMT Engine

DSP Systems Implementation3 Outline  A Glance At ADSL Modems Structure  Digital System Design Methodology  Design Flow  Finite Precision Arithmetic Libraries  ADSL Modulator/Demodulator Design  ADSL Time Equalizer Design

DSP Systems Implementation4 A Glance At ADSL Modems Structure ADSL Modem Modulation  Discrete Multi Tone (DMT) Modulation  Simple Digital Implementation By FFT, IFFT  Uses FDM  256 Sub-Channels  QAM In All Channels  Simultaneous Voice Transmission

DSP Systems Implementation5 A Glance At ADSL Modems Structure ADSL Modem Block Diagram  ADSL DMT Engine Block Diagram

DSP Systems Implementation6 Digital System Design Methodology Design Flow- All Steps Together  General Methodology  Much Human Brain Work  Less Automatic Procedures  Test & Verification Importance

DSP Systems Implementation7 Digital System Design Methodology Design Flow Step One: Simulation  High Precision Modeling  Using C Or MATLAB  Converting High Level Protocol Or Standard To A Software Model  System Environment Modeling  Engineering Modeling  Quantization Noise And Other Finite Precision Effects Modeling  Parametric Modeling To Find Noise-Parameter(s) relations  Wide Simulation And Parameter Extraction

DSP Systems Implementation8 Digital System Design Methodology Design Flow Step One: Simulation- Important Notes  For High Precision Modeling:  “MATLAB” Is Preferred Because Of Its Friendly Interfaces, Ready Modules And Visual Capabilities  “C” Is Preferred Because Of Its High Simulation Speed  For None-Ideal Engineering Modeling  Finite-Precision-Arithmetic Libraries  Fixed-Floating Point Support  Different Round-Off, Saturation, … Strategies Support

DSP Systems Implementation9 Digital System Design Methodology Design Flow Step One: Simulation- Important Notes  Common Parameter Extraction Method  Finding (Output Error- Parameter(s)) Curves Using The Below Scheme  Common Output Error Criterions: BER, SNR And MSE  Finding Optimal Point On The Curve(s) To Satisfy Defined Error Conditions With The Lowest Possible Cost

DSP Systems Implementation10 Digital System Design Methodology Design Flow Step Two: Hardware Modeling  Golden Model Creation  For Test Purpose  Behavioral Modeling  Component Modeling  Interfacing Considerations  Model Synthesizability  Structural Modeling  System Modeling  Components Wiring

DSP Systems Implementation11 Digital System Design Methodology Design Flow Step Two: Hardware Modeling- Important Notes  Golden Model Creation  Simplifies Test Of The Final Model  Functionally Same As C Or MATLAB Model  Not Necessarily Synthesizable Or Efficient  Component Modeling  Common Design Strategy: Top-Down Design, Bottom- Up wiring  Extracted Parameters From Simulation Step, Inserted Into Components

DSP Systems Implementation12 Digital System Design Methodology Design Flow Step Three: Implementation  FPGA Implementation  FPGA Specific HDL Languages Such As AHDL  Usually Better Performance When Lower Level Components RTL Level  Hardware Emulation Systems  ASIC Implementation

DSP Systems Implementation13 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  C Does Not Have Sufficient Capabilities Needed For Bit- True Modeling  Special Libraries Need To Be Developed That Support  Different Finite-Length Number Representations (Fixed, Float,…)  Different Finite-Length Sign Representations (2’s Complement, Sign And Magnitude, …)  Basic Arithmetic Operations With Finite Precision (Sum, Sub,…)  Different Round-Off Strategies (Truncation, Rounding,…)  Different Overflow Strategies (Maximum Saturation, Zero Saturation, Wrap Around,…)

DSP Systems Implementation14 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Using The Libraries, The System Should Be Modeled And Simulated With Different Library Options  All Trade-Offs And Strategies Are Extracted  Number Representation Method (Fixed, Float, …)  Sign Representation  Round-Off Strategy  Overflow Strategy  Each Trade-Off Or Strategy Corresponds To A Different Hardware Implementation

DSP Systems Implementation15 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  “ACOLADE” Library  C Language  Parameters  Word_width (Fixed Or Float Selection)  Precision (Precision Selection)  RND_CHR (Round-Off Strategy)  OVL_CHR (Overflow Strategy)

DSP Systems Implementation16 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  C Finite Length Arithmetic Modeling Extension, C_FLAME Library  Developed In UT VLSI Lab  Support Truncation And Rounding Round-Off Strategies  Library Interface Functions: Dec2bin, Bin2dec  Negation Function: Negate

DSP Systems Implementation17 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  C Finite Length Arithmetic Modeling Extension (C_FLAME) Library  Arithmetic Functions  Fixed Point  Scaling Functions: Sum, Sub, Sum_wa, Multiply  Saturation Functions: Sum_sat, Sub_sat, Sub_wa  Block Floating Point  Sum_bfp, Sub_bfp  Special Purpose Function: Multiply_ideal

DSP Systems Implementation18 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  C_FLAME Library Data Structure  High precision input data for library must be scaled, -1≤ Inputs < 1  Fixed point is aligned after the most significant bit of the numbers (MSB of each number, represents sign)  High precision scaled input data should be converted to finite precision data for C_FLAME functions by library interface functions

DSP Systems Implementation19 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  C_FLAME Library Data Structure (Cntd.)  Inside C_FLAME, all binary finite precision numbers treated as integer numbers  Numbers representation inside C_FLAME struct binary{ long int number; int length;}

DSP Systems Implementation20 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Example of input preparation for C_FLAME library  r1=0.625; r2=0.9999; r3=-1; //Real Input Data To Library  Int Wordlength=8; //Determining Finite Precision  Struct binary b1,b2,b3; //Library Internal Data Structures  //void dec2bin(double a, int wordlength, binary *num)  Dec2bin(r1,wordlength,&b1); //b1={ 80, 8 } 80=(0101,0000)  Dec2bin(r2,wordlength,&b2); //b2={ 127, 8 } 127=(0111,1111)  Dec2bin(r3,wordlength,&b3); //b3={ 128, 8 } 128=(1000,0000)

DSP Systems Implementation21 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Another example of data manipulation by C_FLAME library functions  r1= ; //Real Input Data  Int Wordlength=8; //Determining Finite Precision  Struct Binary b; //library Internal data structure  Dec2bin(r1,wordlength,b); // b= { 84, 8 } 84 =(0101,0100)  Negate(&b) // b= { 172, 8 } 172=(1010,1100)

DSP Systems Implementation22 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Different C_FLAME Summation Functions  Saturated Fixed Point Summation  Void Sum_Sat (binary a, binary b, binary *k)  Scaling Fixed Point Summation  Void Sum (int round_truncate, binary a, binary b, int resultlength, binary *k)  Block Floating Point Summation  void Sum_bfp(int round_truncate, binary a, binary b, int resultlength, binary *k)  Wrap Around Summation  Void Sum_wa(binary a, binary b, binary *k);

DSP Systems Implementation23 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Illustration of functionality of different Add functions in C_FLAME library  Sum_sat Function  Output length=input length  No round-off strategy needed  When Not Overflow The function returns Result(N-1,0)  When Overflow The function saturates and returns Maximum and minimum representable numbers

DSP Systems Implementation24 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Illustration of functionality of different Add functions in C_FLAME library  Sum Function  If Output length=input length +1 function returns (C & Result(N-1,0)) Round-off strategy not needed  If output length= input length function returns (C & Result(N-1,1)) considering round-off strategy

DSP Systems Implementation25 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Illustration of functionality of different Add functions in C_FLAME library  Sum_bfp Function  If Output length=input length +1 function returns (C & Result(N-1,0)) Round-off strategy not needed  If output length= input length  When Not Overflow function returns (Result(N-1,0))  When Overflow function returns (C & Result(N-1,1))

DSP Systems Implementation26 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Illustration of functionality of different Add functions in C_FLAME library  Sum_wa Function  Output length=input length  No round-off strategy needed  No Saturation Strategy

DSP Systems Implementation27 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  A finite precision complex multiply Finite_precision_complex_multiply (double: Ra,Ia,Rb,Ib, int r_t) { Struct Binary: Rab,Iab,Rbb,Ibb,partialmul1,partialmul2; dec2bin(Ra,8,Rab); dec2bin(Ia,8,Iab); dec2bin(Rb,8,Rbb); dec2bin(Ib,8,Ibb); Multiply(r_t, Rab, Rbb, 8, &Partialmul1); Multiply(r_t, Iab, Ibb, 8, &Partialmul2); sub(r_t, partialmul1, partialmul2, 9, &resultreal); Multiply(r_t, Rab, Ibb, 8, &Partialmul1); Multiply(r_t, Iab, Rbb, 8, &Partialmul2); sum(r_t, partialmul1, partialmul2, 9, &resultimag); realpart=bin2dec(resultreal); imagpart=bin2dec(resultimag);}

DSP Systems Implementation28 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Block Floating Point  Extra Hardware  A Solution Between Fixed And Floating Point  Wide range Representation Capability  Simple Hardware Implementation  Low Quantization Noise Sensitivity  Low Delay

DSP Systems Implementation29 Digital System Design Methodology Finite-Precision-Arithmetic Libraries  Example Of C Finite Length Arithmetic Modeling Extension (C_FLAME) Library Functions  Block Floating Point Illustration

DSP Systems Implementation30 Digital System Design Methodology ADSL Modulator/Demodulator Design  IFFT/FFT Used For Modulation/Demodulation  The Most Complicated And Most Important Block Of An ADSL Modem  Hardware Structure  Operation Count  Quantization Noise  Design Constraints (Speed, Area, Power)

DSP Systems Implementation31 Digital System Design Methodology ADSL Mo/Dem- Implementation Method Selection Space  A Multi-Dimensional Space  Different Algorithms  Radix 2, Radix 4, Radix 8, Split Radix, Mixed Radix  Different Algorithm Versions  Decimation In Time (DIT), Decimation In Frequency (DIF)  Different Butterfly Structures  Symmetric Structures, Asymmetric Structures  Different Implementations  Full Parallel Structure, Column Structure, FFT Processor Structure, Pipeline Structure

DSP Systems Implementation32 Digital System Design Methodology ADSL Mo/Dem- Choosing Suitable Structure  Selection Criteria  Maximum Delay Constraint (250 µs)  Hardware Cost (# of Adders, Multipliers,…)  Maximum Quantization Noise Acceptable  Implementation Complexity (VLSI Layout,…)

DSP Systems Implementation33 Digital System Design Methodology ADSL Mo/Dem- Choosing Suitable Structure  So Many Trade-Offs Must Be Considered And Resolved  # Of Operations (~Quantization Noise Error)  Register Word Lengths  Butterfly Hardware Complexity  Symmetric Or Asymmetric Butterfly Hardware  Delay  Hardware Component Count  Hardware Utilization  Input Output Sequence  Final Chip Size

DSP Systems Implementation34 Digital System Design Methodology ADSL Mo/Dem- Choosing Suitable Structure  Important Results Of Browsing Selection Space  Result#1: Hardware Complexity Decreases as the Radix Increases !  Result#2: Operations Count Decreases as the Radix Increases!  Result#3: Mixed-Radix Algorithms are Hardware Optimized Solutions!  Result#4: Implementation Complexity Increases as the Radix Increases (More Than 4 or 8)!  Result#5: Hardware Utilization Decreases as the Radix Increases (Generally)!

DSP Systems Implementation35 Digital System Design Methodology ADSL Mo/Dem- The Chosen Algorithm  Mixed-Radix 2^2 +2 Algorithm  Hardware Complexity of Radix-4 Algorithms!  Operation Count of Radix-4 Algorithms!  Mixed-Radix Hardware Optimized With a Very Simple Controller!  Implementation Complexity of Radix-2 Algorithms!  Hardware Utilization of Radix-2 Algorithms!

DSP Systems Implementation36 Digital System Design Methodology ADSL Mo/Dem- The Chosen Algorithm  Mixed-Radix 2^2 +2 Algorithm DFG

DSP Systems Implementation37 Digital System Design Methodology ADSL Mo/Dem- The Selected Implementation Method  Different Implementations  Fully Parallel FFTs  Column FFTs  Pipeline FFTs  FFT Processors  The Selected Implementation Method  Pipeline FFT Implementation

DSP Systems Implementation38 Digital System Design Methodology ADSL Mo/Dem- FFT Block C Simulation Results  Change Of “Output Error” Due To Increase Of “Constant Length” Word Length=16 Constant Length Error Word Length=12 Constant Length Error

DSP Systems Implementation39 Digital System Design Methodology ADSL Mo/Dem- FFT Block C Simulation Results  Change Of “Output Error” Due To Increase Of “Word Length” Constant Length=12 Word Length Error Constant Length=16 Word Length Error

DSP Systems Implementation40 Digital System Design Methodology ADSL Mo/Dem- FFT Block C Simulation Results  Change Of “Output Error” Due To Using “Rounding” Instead Of “Truncation” Constant Length=16 Word Length Error Truncation Rounding

DSP Systems Implementation41 Digital System Design Methodology ADSL Mo/Dem- Components Implementation  Butterfly Structures Of The Algorithm BF IBF II

DSP Systems Implementation42 Digital System Design Methodology ADSL Mo/Dem- Components Implementation  Design Multipliers Enhancement To Do Rounding Instead Of Truncation On Output

DSP Systems Implementation43 Digital System Design Methodology ADSL Mo/Dem- Components Implementation  Design Adders/Subtractors Enhancement To Do Unbiased Rounding Instead Of Truncation On Output

DSP Systems Implementation44 Digital System Design Methodology ADSL Time Equalizer Design  A Digital Filter To Cancel Line Distortion  Implemented As A 16 Tap Adaptive FIR Filter (Changeable Coefficients)

DSP Systems Implementation45 Digital System Design Methodology ADSL Time Equalizer - Choosing A Suitable Structure  Constant Length = Filter Word Length  Selection Criteria  Maximum Delay Constraint  Hardware Cost (# Of Adders, Multipliers, …)

DSP Systems Implementation46 Digital System Design Methodology ADSL Time Equalizer – TEq C Simulation Results  Change Of “Output Error” Due To Increase Of “Word Length”  Output Error Is Negligible With Respect To FFT

DSP Systems Implementation47 Digital System Design Methodology ADSL Time Equalizer – TEq C Simulation Results  Change Of “Output Error” Due To Using “Rounding” Instead Of “Truncation”

DSP Systems Implementation48 Digital System Design Methodology ADSL Time Equalizer – Implementation  Block Floating Point Method