DSP Builder for Intel® FPGAs (Advanced Blockset): Handbook

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ID 683337
Date 5/01/2023
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Document Table of Contents
Document Table of Contents x
1. Answers to Top FAQs 2. About DSP Builder for Intel® FPGAs 3. DSP Builder for Intel FPGAs Advanced Blockset Getting Started 4. DSP Builder Design Flow 5. Primitive Library Blocks Tutorial 6. IP Tutorial 7. DSP Builder for Intel FPGAs (Advanced Blockset) Design Examples and Reference Designs 8. DSP Builder Design Rules, Design Recommendations, and Troubleshooting 9. About DSP Builder for Intel FPGAs Optimization 10. About Folding 11. Floating-Point Data Types 12. Design Configuration Library 13. IP Library 14. Interfaces Library 15. Primitives Library 16. Utilities Library 17. Simulink Supported Blocks 18. Document Revision History for DSP Builder for Intel FPGAs (Advanced Blockset) Handbook
2. About DSP Builder for Intel® FPGAs x
2.1. DSP Builder for Intel® FPGAs Features 2.2. DSP Builder for Intel® FPGAs Design Structure 2.3. DSP Builder for Intel® FPGAs Libraries 2.4. DSP Builder for Intel® FPGAs Device Support 2.5. FPGA Architecture Features for DSP Designs 2.6. DSP Design Flow in FPGAs 2.7. Software and Hardware DSP Design Flows in FPGAs
3. DSP Builder for Intel FPGAs Advanced Blockset Getting Started x
3.1. Installing DSP Builder for Intel® FPGAs 3.2. Licensing DSP Builder for Intel® FPGAs 3.3. Starting DSP Builder in MATLAB* 3.4. Browsing DSP Builder Libraries and Adding Blocks to a New Model 3.5. Browsing and Opening DSP Builder Design Examples 3.6. Creating a New DSP Builder Design with the DSP Builder New Model Wizard 3.7. Simulating, Verifying, Generating, and Compiling Your DSP Builder Design
3.6. Creating a New DSP Builder Design with the DSP Builder New Model Wizard x
3.6.1. DSP Builder Menu Options 3.6.2. DSP Builder New Model Wizard Setup Script Parameters
4. DSP Builder Design Flow x
4.1. Implementing your Design in DSP Builder Advanced Blockset 4.2. Verifying your DSP Builder Advanced Blockset Design in Simulink and MATLAB 4.3. Exploring DSP Builder Advanced Blockset Design Tradeoffs 4.4. Verifying your DSP Builder Design with C++ Software Models 4.5. Verifying your DSP Builder Advanced Blockset Design in the ModelSim Simulator 4.6. Verifying Your DSP Builder Design in Hardware 4.7. Integrating Your DSP Builder Advanced Blockset Design into Hardware
4.1. Implementing your Design in DSP Builder Advanced Blockset x
4.1.1. Dividing your DSP Builder Design into Subsystems 4.1.2. Connecting DSP Builder Subsystems 4.1.3. Creating a New Design by Copying a DSP Builder Design Example 4.1.4. Vectorized Inputs
4.1.2. Connecting DSP Builder Subsystems x
4.1.2.1. DSP Builder Block Interface Signals 4.1.2.2. Periods 4.1.2.3. Sample Rate 4.1.2.4. Building Multichannel Systems 4.1.2.5. Channelization for Two Channels with a Folding Factor of 3 4.1.2.6. Channelization for Four Channels with a Folding Factor of 3 4.1.2.7. Synchronization and Scheduling of Data with the Channel Signal 4.1.2.8. Simulink vs Hardware Design Representations
4.1.2.1. DSP Builder Block Interface Signals x
4.1.2.1.1. Multichannel Systems with IP Library Blocks 4.1.2.1.2. Valid, Channel, and Data Examples
4.1.2.4. Building Multichannel Systems x
4.1.2.4.1. Multichannel Systems with IP Library Blocks
4.1.3. Creating a New Design by Copying a DSP Builder Design Example x
4.1.3.1. Creating a New Design From the DSP Builder FIR Design Example and Changing the Namespaces
4.2. Verifying your DSP Builder Advanced Blockset Design in Simulink and MATLAB x
4.2.1. Verifying your DSP Builder Advanced Blockset Design with a Testbench 4.2.2. Running DSP Builder Advanced Blockset Automatic Testbenches 4.2.3. Using DSP Builder Advanced Blockset References 4.2.4. Setting Up Stimulus in DSP Builder Advanced Blockset 4.2.5. Analyzing your DSP Builder Advanced Blockset Design
4.2.1. Verifying your DSP Builder Advanced Blockset Design with a Testbench x
4.2.1.1. Visualization Features
4.2.2. Running DSP Builder Advanced Blockset Automatic Testbenches x
4.2.2.1. dspba.runModelsimATB 4.2.2.2. Running All Automatic Testbenches 4.2.2.3. The command run_all_atbs Command Syntax 4.2.2.4. Testbench Error Messages
4.3. Exploring DSP Builder Advanced Blockset Design Tradeoffs x
4.3.1. Bit Growth 4.3.2. Managing Bit Growth in DSP Builder Advanced Blockset Designs 4.3.3. Using Rounding and Saturation in DSP Builder Advanced Blockset Designs 4.3.4. Scaling with Primitive Blocks 4.3.5. Changing Data Type with Convert Blocks and Specifying Output Types
4.3.5. Changing Data Type with Convert Blocks and Specifying Output Types x
4.3.5.1. The Convert Block and Real-world Values 4.3.5.2. Output Data Types on Primitive Blocks
4.4. Verifying your DSP Builder Design with C++ Software Models x
4.4.1. Software Model Options 4.4.2. Software Model Generated Files 4.4.3. Software Model Compilers 4.4.4. Compiling Testbenches and Model Libraries 4.4.5. Testing the Software Model 4.4.6. MATLAB MEX Function Wrapper for a Generated Software Model
4.4.5. Testing the Software Model x
4.4.5.1. Linking to External Libraries
4.4.6. MATLAB MEX Function Wrapper for a Generated Software Model x
4.4.6.1. Driving the Model 4.4.6.2. MEX Model Code 4.4.6.3. Complete the MEX Function 4.4.6.4. Compile, Run, and Test the MEX Function
4.5. Verifying your DSP Builder Advanced Blockset Design in the ModelSim Simulator x
4.5.1. Automatic Testbench 4.5.2. DSP Builder Advanced Blockset ModelSim Simulations
4.5.1. Automatic Testbench x
4.5.1.1. DSP Builder Advanced Blockset Automatic Testbench Files
4.6. Verifying Your DSP Builder Design in Hardware x
4.6.1. Hardware Verification
4.6.1. Hardware Verification x
4.6.1.1. Hardware Verification Design Example
4.7. Integrating Your DSP Builder Advanced Blockset Design into Hardware x
4.7.1. DSP Builder Generated Files 4.7.2. DSP Builder Designs and the Quartus Prime Project 4.7.3. Interfaces with a Processor Bus 4.7.4. DSP Builder Designs in Platform Designer
4.7.2. DSP Builder Designs and the Quartus Prime Project x
4.7.2.1. Adding a DSP Builder Advanced Blockset Design to an Existing Quartus Prime Project
4.7.3. Interfaces with a Processor Bus x
4.7.3.1. Assigning Base Addresses in DSP Builder Designs 4.7.3.2. Updating Registers with the Nios II Processor
4.7.4. DSP Builder Designs in Platform Designer x
4.7.4.1. Integrating a DSP Builder Design to a Platform Designer System 4.7.4.2. Modifying Avalon Streaming Blocks 4.7.4.3. Restrictions for DSP Builder Designs with Avalon Streaming Interface and AXI4-Stream Blocks 4.7.4.4. Connecting Conduit Interfaces
5. Primitive Library Blocks Tutorial x
5.1. Creating a Fibonacci Design from the DSP Builder Primitive Library 5.2. Setting the Parameters on the Testbench Source Blocks 5.3. Simulating the Fibonacci Design in Simulink 5.4. Modifying the DSP Builder Fibonacci Design to Generate Vector Signals 5.5. Simulating the RTL of the Fibonacci Design
6. IP Tutorial x
6.1. Creating an IP Design 6.2. Simulating the IP Design in Simulink 6.3. Viewing Timing Closure and Viewing Resource Utilization for the DSP Builder IP Design 6.4. Reparameterizing the DSP Builder FIR Filter to Double the Number of Channels 6.5. Doubling the Target Clock Rate for a DSP Builder IP Design
7. DSP Builder for Intel FPGAs (Advanced Blockset) Design Examples and Reference Designs x
7.1. DSP Builder Design Configuration Block Design Examples 7.2. DSP Builder FFT Design Examples 7.3. DSP Builder DDC Design Example 7.4. DSP Builder Filter Design Examples 7.5. DSP Builder Finite State Machine Design Example 7.6. DSP Builder Folding Design Examples 7.7. DSP Builder Floating Point Design Examples 7.8. DSP Builder Flow Control Design Examples 7.9. DSP Builder HDL Import Design Example 7.10. DSP Builder Host Interface Design Examples 7.11. DSP Builder Fixed-Point Matrix Multiply Engine Design Example 7.12. DSP Builder Platform Design Examples 7.13. DSP Builder Primitive Block Design Examples 7.14. DSP Builder Reference Designs 7.15. DSP Builder Waveform Synthesis Design Examples
7.1. DSP Builder Design Configuration Block Design Examples x
7.1.1. Scale 7.1.2. Local Threshold
7.2. DSP Builder FFT Design Examples x
7.2.1. FFT 7.2.2. FFT without BitReverseCoreC Block 7.2.3. IFFT 7.2.4. IFFT without BitReverseCoreC Block 7.2.5. Floating-Point FFT 7.2.6. Floating-Point FFT without BitReverseCoreC Block 7.2.7. Floating-Point iFFT 7.2.8. Floating-Point iFFT without BitReverseCoreC Block 7.2.9. Multichannel FFT 7.2.10. Multiwire Transpose 7.2.11. Parallel FFT 7.2.12. Parallel Floating-Point FFT 7.2.13. Single-Wire Transpose 7.2.14. Switchable FFT/iFFT 7.2.15. Variable-Size Fixed-Point FFT 7.2.16. Variable-Size Fixed-Point FFT without BitReverseCoreC Block 7.2.17. Variable-Size Fixed-Point iFFT 7.2.18. Variable-Size Fixed-Point iFFT without BitReverseCoreC Block 7.2.19. Variable-Size Floating-Point FFT 7.2.20. Variable-Size Floating-Point FFT without BitReverseCoreC Block 7.2.21. Variable-Size Floating-Point iFFT 7.2.22. Variable-Size Floating-Point iFFT without BitReverseCoreC Block 7.2.23. Variable-Size Low-Resource FFT 7.2.24. Variable-Size Low-Resource Real-Time FFT 7.2.25. Variable-Size Supersampled FFT
7.3. DSP Builder DDC Design Example x
7.3.1. DDC Design Example Subsystem 7.3.2. Building the DDC Design Example
7.3.2. Building the DDC Design Example x
7.3.2.1. DDC Design Example Generated Files
7.4. DSP Builder Filter Design Examples x
7.4.1. Complex FIR Filter 7.4.2. Decimating CIC Filter 7.4.3. Decimating FIR Filter 7.4.4. Filter Chain with Forward Flow Control 7.4.5. FIR Filter with Exposed Bus 7.4.6. Fractional FIR Filter Chain 7.4.7. Fractional-Rate FIR Filter 7.4.8. Half-Band FIR Filter 7.4.9. IIR: Full-rate Fixed-point 7.4.10. IIR: Full-rate Floating-point 7.4.11. Interpolating CIC Filter 7.4.12. Interpolating FIR Filter 7.4.13. Interpolating FIR Filter with Multiple Coefficient Banks 7.4.14. Interpolating FIR Filter with Updating Coefficient Banks 7.4.15. Root-Raised Cosine FIR Filter 7.4.16. Single-Rate FIR Filter 7.4.17. Super-Sample Decimating FIR Filter 7.4.18. Super-Sample Fractional FIR Filter 7.4.19. Super-Sample Interpolating FIR Filter 7.4.20. Variable-Rate CIC Filter
7.6. DSP Builder Folding Design Examples x
7.6.1. Position, Speed, and Current Control for AC Motors 7.6.2. Position, Speed, and Current Control for AC Motors (with ALU Folding) 7.6.3. About FOC 7.6.4. Folded FIR Filter
7.7. DSP Builder Floating Point Design Examples x
7.7.1. Black-Scholes Floating Point 7.7.2. Double-Precision Real Floating-Point Matrix Multiply 7.7.3. Fine Doppler Estimator 7.7.4. Floating-Point Mandlebrot Set 7.7.5. General Real Matrix Multiply One Cycle Per Output 7.7.6. Newton Root Finding Tutorial Step 1—Iteration 7.7.7. Newton Root Finding Tutorial Step 2—Convergence 7.7.8. Newton Root Finding Tutorial Step 3—Valid 7.7.9. Newton Root Finding Tutorial Step 4—Control 7.7.10. Newton Root Finding Tutorial Step 5—Final 7.7.11. Normalizer 7.7.12. Single-Precision Complex Floating-Point Matrix Multiply 7.7.13. Single-Precision Real Floating-Point Matrix Multiply 7.7.14. Simple Nonadaptive 2D Beamformer
7.8. DSP Builder Flow Control Design Examples x
7.8.1. Avalon-ST Interface (Input and Output FIFO Buffer) with Backpressure 7.8.2. Avalon-ST Interface (Output FIFO Buffer) with Backpressure 7.8.3. Kronecker Tensor Product 7.8.4. Parallel Loops 7.8.5. Primitive FIR with Back Pressure 7.8.6. Primitive FIR with Forward Pressure 7.8.7. Primitive Systolic FIR with Forward Flow Control 7.8.8. Rectangular Nested Loop 7.8.9. Sequential Loops 7.8.10. Triangular Nested Loop
7.9. DSP Builder HDL Import Design Example x
7.9.1. Performing a Cosimulation
7.10. DSP Builder Host Interface Design Examples x
7.10.1. Memory-Mapped Registers
7.12. DSP Builder Platform Design Examples x
7.12.1. 16-Channel DDC 7.12.2. 16-Channel DUC 7.12.3. 2-Antenna DUC for WiMAX 7.12.4. 2-Channel DUC 7.12.5. Super-Sample Rate Digital Upconverter
7.13. DSP Builder Primitive Block Design Examples x
7.13.1. 8×8 Inverse Discrete Cosine Transform 7.13.2. Automatic Gain Control 7.13.3. Bit Combine for Boolean Vectors 7.13.4. Bit Extract for Boolean Vectors 7.13.5. Color Space Converter 7.13.6. CORDIC from Primitive Blocks 7.13.7. Digital Predistortion Forward Path 7.13.8. Fibonacci Series 7.13.9. Folded Vector Sort 7.13.10. Fractional Square Root Using CORDIC 7.13.11. Fixed-point Maths Functions 7.13.12. Gaussian Random Number Generator 7.13.13. Hello World 7.13.14. Hybrid Direct Form and Transpose Form FIR Filter 7.13.15. Loadable Counter 7.13.16. Matrix Initialization of LUT 7.13.17. Matrix Initialization of Vector Memories 7.13.18. Multichannel IIR Filter 7.13.19. Quadrature Amplitude Modulation 7.13.20. Reinterpret Cast for Bit Packing and Unpacking 7.13.21. Run-time Configurable Decimating and Interpolating Half-Rate FIR Filter 7.13.22. Square Root Using CORDIC 7.13.23. Test CORDIC Functions with the CORDIC Block 7.13.24. Uniform Random Number Generator 7.13.25. Vector Sort—Sequential 7.13.26. Vector Sort—Iterative 7.13.27. Vector Initialization of Sample Delay 7.13.28. Wide Single-Channel Accumulators
7.14. DSP Builder Reference Designs x
7.14.1. 1-Antenna WiMAX DDC 7.14.2. 2-Antenna WiMAX DDC 7.14.3. 1-Antenna WiMAX DUC 7.14.4. 2-Antenna WiMAX DUC 7.14.5. 4-Carrier, 2-Antenna W-CDMA DDC 7.14.6. 1-Carrier, 2-Antenna W-CDMA DDC 7.14.7. 4-Carrier, 2-Antenna W-CDMA DUC 7.14.8. 4-Carrier, 4-Antenna DUC and DDC for LTE 7.14.9. 1-Carrier, 2-Antenna W-CDMA DDC 7.14.10. 4-Carrier, 2-Antenna High-Speed W-CDMA DUC at 368.64 MHz with Total Rate Change 32 7.14.11. 4-Carrier, 2-Antenna High-Speed W-CDMA DUC at 368.64 MHz with Total Rate Change 48 7.14.12. 4-Carrier, 2-Antenna High-Speed W-CDMA DUC at 307.2 MHz with Total Rate Change 40 7.14.13. Cholesky-based Matrix Inversion Parameters Performance and Resource Usage 7.14.14. Cholesky Solver Multiple Channels 7.14.15. Crest Factor Reduction 7.14.16. Direct RF with Synthesizable Testbench 7.14.17. Dynamic Decimating FIR Filter 7.14.18. Multichannel QR Decompostion 7.14.19. QR Decompostion 7.14.20. QRD Solver 7.14.21. Reconfigurable Decimation Filter 7.14.22. Single-Channel 10-MHz LTE Transmitter 7.14.23. STAP Radar Forward and Backward Substitution 7.14.24. STAP Radar Steering Generation 7.14.25. STAP Radar QR Decomposition 192x204 7.14.26. Time Delay Beamformer 7.14.27. Transmit and Receive Modem 7.14.28. Variable Integer Rate Decimation Filter
7.15. DSP Builder Waveform Synthesis Design Examples x
7.15.1. Complex Mixer 7.15.2. Four Channel, Two Banks NCO 7.15.3. Four Channel, Four Banks NCO 7.15.4. Four Channel, Eight Banks, Two Wires NCO 7.15.5. Four Channel, 16 Banks NCO 7.15.6. IP 7.15.7. NCO 7.15.8. NCO with Exposed Bus 7.15.9. Real Mixer 7.15.10. Super-sample NCO
8. DSP Builder Design Rules, Design Recommendations, and Troubleshooting x
8.1. DSP Builder Design Rules and Recommendations 8.2. Troubleshooting DSP Builder Designs
8.2. Troubleshooting DSP Builder Designs x
8.2.1. About Loops 8.2.2. Closing Timed feedback Loops 8.2.3. Loops, Clock Cycles, and Data Cycles
9. About DSP Builder for Intel FPGAs Optimization x
9.1. Associating DSP Builder with MATLAB 9.2. Setting Up Simulink for DSP Builder Designs 9.3. The DSP Builder Windows Shortcut 9.4. Setting DSP Builder Design Parameters with MATLAB Scripts 9.5. Managing your Designs 9.6. How to Manage Latency 9.7. Flow Control in DSP Builder Designs 9.8. Reset Minimization 9.9. About Importing HDL
9.2. Setting Up Simulink for DSP Builder Designs x
9.2.1. Setting Up Simulink Solver 9.2.2. Setting Up Simulink Signal Display Option
9.4. Setting DSP Builder Design Parameters with MATLAB Scripts x
9.4.1. Running Setup Scripts Automatically 9.4.2. Defining Unique DSP Builder Design Parameters 9.4.3. Example DSP Builder Custom Scripts
9.5. Managing your Designs x
9.5.1. Managing Basic Parameters 9.5.2. Creating User Libraries and Converting a Primitive Subsystem into a Custom Block 9.5.3. Revision Control
9.6. How to Manage Latency x
9.6.1. Reading the Added Latency Value for an IP Block 9.6.2. Zero Latency Example 9.6.3. Implicit Delays in DSP Builder Designs 9.6.4. Distributed Delays in DSP Builder Designs 9.6.5. Latency and fMAX Constraint Conflicts in DSP Builder Designs 9.6.6. Control Units Delays
10. About Folding x
10.1. ALU Folding 10.2. Removing Resource Sharing Folding
10.1. ALU Folding x
10.1.1. ALU Folding Limitations 10.1.2. ALU Folding Parameters 10.1.3. ALU Folding Simulation Rate 10.1.4. Using ALU Folding 10.1.5. Using Automated Verification 10.1.6. Ready Signal 10.1.7. Connecting the ALU Folding Ready Signal 10.1.8. About the ALU Folding Start of Packet Signal
11. Floating-Point Data Types x
11.1. DSP Builder Floating-Point Data Type Features 11.2. DSP Builder Supported Floating-Point Data Types 11.3. DSP Builder Round-Off Errors 11.4. Trading Off Logic Utilization and Accuracy in DSP Builder Designs 11.5. Upgrading Pre v14.0 Designs 11.6. Floating-Point Sine Wave Generator Tutorial 11.7. Newton-Raphson Root Finding Tutorial 11.8. Forcing Soft Floating-point Data Types with the Advanced Options
11.6. Floating-Point Sine Wave Generator Tutorial x
11.6.1. Creating a Sine Wave Generator in DSP Builder 11.6.2. Using Data Type Variables to Parameterize Designs 11.6.3. Using Data-Type Propagation in DSP Builder Designs 11.6.4. DSP Builder Testbench Verification
11.6.4. DSP Builder Testbench Verification x
11.6.4.1. Tuning ATB Thresholds 11.6.4.2. Writing Application Specific Verification 11.6.4.3. Performing Bit-Accurate Simulation 11.6.4.4. Adder Trees and Scalar Products 11.6.4.5. Creating Floating-Point Accumulators for Designs that Use Iteration
11.7. Newton-Raphson Root Finding Tutorial x
11.7.1. Implementing the Newton Design 11.7.2. Improving DSP Builder Floating-Point Designs
12. Design Configuration Library x
12.1. Avalon Memory-Mapped Agent Settings (AvalonMemoryMappedAgentSettings) 12.2. Control 12.3. Device 12.4. LocalThreshold
12.2. Control x
12.2.1. DSP Builder Memory and Multiplier Trade-Off Options
13. IP Library x
13.1. Channel Filter and Waveform Library 13.2. Dependent Delay Library 13.3. FFT IP Library
13.1. Channel Filter and Waveform Library x
13.1.1. DSP Builder FIR and CIC Filters 13.1.2. DSP Builder FIR Filters 13.1.3. Channel Viewer (ChanView) 13.1.4. Complex Mixer (ComplexMixer) 13.1.5. Decimating CIC 13.1.6. Decimating FIR 13.1.7. Fractional Rate FIR 13.1.8. Interpolating CIC 13.1.9. Interpolating FIR 13.1.10. NCO 13.1.11. Real Mixer (Mixer) 13.1.12. Scale 13.1.13. Single-Rate FIR
13.1.1. DSP Builder FIR and CIC Filters x
13.1.1.1. Common CIC and FIR Filter Features 13.1.1.2. Updated Help 13.1.1.3. Half-Band and L-Band Nyquist FIR Filters 13.1.1.4. Parameterization of CIC and FIR Filters 13.1.1.5. Setting and Changing FIR Filter Coefficients at Runtime in DSP Builder
13.1.2. DSP Builder FIR Filters x
13.1.2.1. FIR Filter Avalon-MM Interfaces 13.1.2.2. Reconfigurable FIR Filters
13.1.10. NCO x
13.1.10.1. NCO Block Phase Increment and Inversion 13.1.10.2. NCO Block Phase Increment Memory Registers 13.1.10.3. NCO Block Frequency Hopping
13.3. FFT IP Library x
13.3.1. Bit Reverse Core C (BitReverseCoreC and VariableBitReverse) 13.3.2. FFT (FFT, FFT_Light, VFFT, VFFT_Light)
14. Interfaces Library x
14.1. Memory-Mapped Library 14.2. Streaming Library
14.1. Memory-Mapped Library x
14.1.1. Bus Slave (BusSlave) 14.1.2. Bus Stimulus (BusStimulus) 14.1.3. Bus Stimulus File Reader (Bus StimulusFileReader) 14.1.4. External Memory, Memory Read, Memory Write 14.1.5. Register Bit (RegBit) 14.1.6. Register Field (RegField) 14.1.7. Register Out (RegOut) 14.1.8. Shared Memory (SharedMem)
14.2. Streaming Library x
14.2.1. Avalon-ST Input (AStInput) 14.2.2. Avalon-ST Input FIFO Buffer (AStInputFIFO) 14.2.3. Avalon-ST Output (AStOutput) 14.2.4. AXI4-Stream Blocks (AXI4StreamReceiver and AXI4StreamTransmitter)
15. Primitives Library x
15.1. Vector and Complex Type Support 15.2. DFT Design Elements Library 15.3. FFT Design Elements Library 15.4. Primitive Basic Blocks Library 15.5. Primitive Configuration Library 15.6. Primitive Design Elements Library
15.1. Vector and Complex Type Support x
15.1.1. Vector Type Support 15.1.2. Complex Support
15.1.1. Vector Type Support x
15.1.1.1. Element by Element Mode 15.1.1.2. Mathematical Vector Mode 15.1.1.3. Interactions with Simulink
15.1.2. Complex Support x
15.1.2.1. Interactions with Simulink
15.2. DFT Design Elements Library x
15.2.1. DFT (DFT) 15.2.2. Reorder (ReorderBlock) 15.2.3. Reorder and Rescale (ReorderAndRescale)
15.3. FFT Design Elements Library x
15.3.1. About Pruning and Twiddle for FFT Blocks 15.3.2. Bit Vector Combine (BitVectorCombine) 15.3.3. Butterfly Unit (BFU) 15.3.4. Butterfly I C (BFIC) (Deprecated) 15.3.5. Butterfly II C (BFIIC) (Deprecated) 15.3.6. Choose Bits (ChooseBits) 15.3.7. Crossover Switch (XSwitch) 15.3.8. Dual Twiddle Memory (DualTwiddleMemoryC) 15.3.9. Edge Detect (EdgeDetect) 15.3.10. Floating-Point Twiddle Generator (TwiddleGenF) (Deprecated) 15.3.11. Fully-Parallel FFTs (FFT2P, FFT4P, FFT8P, FFT16P, FFT32P, and FFT64P) 15.3.12. Fully-Parallel FFTs with Flexible Ordering (FFT2X, FFT4X, FFT8X, FFT16X, FFT32X, and FFT64X) 15.3.13. General Multitwiddle and General Twiddle (GeneralMultiTwiddle, GeneralMultVTwiddle, GeneralTwiddle, GeneralVTwiddle) 15.3.14. Hybrid FFT (Hybrid_FFT, HybridVFFT, HybridVFFT_btb) 15.3.15. Multiwire Transpose (MultiwireTranspose) 15.3.16. Parallel Pipelined FFT (PFFT_Pipe) 15.3.17. Pulse Divider (PulseDivider) 15.3.18. Pulse Multiplier (PulseMultiplier) 15.3.19. Single-Wire Transpose (Transpose) 15.3.20. Split Scalar (SplitScalar) 15.3.21. Streaming FFTs (FFT2, FFT4, VFFT2, and VFFT4) 15.3.22. Stretch Pulse (StretchPulse) 15.3.23. Twiddle Angle (TwiddleAngle) 15.3.24. Twiddle Generator (TwiddleGenC) Deprecated 15.3.25. Twiddle and Variable Twiddle (Twiddle and VTwiddle) 15.3.26. Twiddle ROM (TwiddleRom, TwiddleMultRom and TwiddleRomF (deprecated))
15.4. Primitive Basic Blocks Library x
15.4.1. Absolute Value (Abs) 15.4.2. Accumulator (Acc) 15.4.3. Add 15.4.4. Add SLoad (AddSLoad) 15.4.5. AddSub 15.4.6. AddSubFused 15.4.7. AND Gate (And) 15.4.8. Bit Combine (BitCombine) 15.4.9. Bit Extract (BitExtract) 15.4.10. Bit Reverse (BitReverse) 15.4.11. Compare (CmpCtrl) 15.4.12. Complex Conjugate (ComplexConjugate) 15.4.13. Compare Equality (CmpEQ) 15.4.14. Compare Greater Than (CmpGE) 15.4.15. Compare Less Than (CmpLT) 15.4.16. Compare Not Equal (CmpNE) 15.4.17. Constant (Const) 15.4.18. Constant Multiply (Const Mult) 15.4.19. Convert 15.4.20. CORDIC 15.4.21. Counter 15.4.22. Count Leading Zeros, Ones, or Sign Bits (CLZ) 15.4.23. Dual Memory (DualMem) 15.4.24. Demultiplexer (Demux) 15.4.25. Divide 15.4.26. Fanout 15.4.27. FIFO 15.4.28. Floating-point Classifier (FloatClass) 15.4.29. Floating-point Multiply Accumulate (MultAcc) 15.4.30. ForLoop 15.4.31. Load Exponent (LdExp) 15.4.32. Left Shift (LShift) 15.4.33. Loadable Counter (LoadableCounter) 15.4.34. Look-Up Table (Lut) 15.4.35. Loop 15.4.36. Math 15.4.37. Minimum and Maximum (MinMax) 15.4.38. MinMaxCtrl 15.4.39. Multiply (Mult) 15.4.40. Multiplexer (Mux) 15.4.41. NAND Gate (Nand) 15.4.42. Negate 15.4.43. NOR Gate (Nor) 15.4.44. NOT Gate (Not) 15.4.45. OR Gate (Or) 15.4.46. Polynomial 15.4.47. Ready 15.4.48. Reinterpret Cast (ReinterpretCast) 15.4.49. Round 15.4.50. Sample Delay (SampleDelay) 15.4.51. Scalar Product 15.4.52. Select 15.4.53. Sequence 15.4.54. Shift 15.4.55. Sqrt 15.4.56. Subtract (Sub) 15.4.57. Sum of Elements (SumOfElements) 15.4.58. Trig 15.4.59. XNOR Gate (Xnor) 15.4.60. XOR Gate (Xor)
15.5. Primitive Configuration Library x
15.5.1. Channel In (ChannelIn) 15.5.2. Channel Out (ChannelOut) 15.5.3. General Purpose Input (GPIn) 15.5.4. General Purpose Output (GPOut) 15.5.5. Synthesis Information (SynthesisInfo)
15.5.5. Synthesis Information (SynthesisInfo) x
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15.6. Primitive Design Elements Library x
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16. Utilities Library x
16.1. Analyze and Test Library 16.2. HDL Import Library
16.1. Analyze and Test Library x
16.1.1. Capture Values 16.1.2. Dechannelizer 16.1.3. Channelizer 16.1.4. Display Resources 16.1.5. Edit Params 16.1.6. Pause
16.2. HDL Import Library x
16.2.1. HDL Import 16.2.2. HDL Import Config
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7.14.13. Cholesky-based Matrix Inversion

Matrix inversion has many applications in wireless communications, e.g. digital predistortion (DPD) for RF linearization and multiple-input multiple-output (MIMO) detection. Matrix inversion algorithms typically require high-resolution numerics to guarantee accuracy and numerical stability. The implementation is normally resource demanding in particular if the matrix dimension grows. The DSP Builder Cholesky-based Matrix Inversion reference design offers an efficient implementation of matrix inversion for minimized resource utilization and improved latency and throughput. The Cholesky decomposition technique inverts a positive-definite real or complex square matrix. Cholesky decomposition-based matrix inversion is more efficient than direct matrix inversion.
Figure 79. Matrix inversion based on Cholesky decompositionThe figure shows the three steps of implementing a Hermitian matrix inversion using Cholesky decomposition:
  1. Cholesky decomposition
  2. Triangular matrix inversion through forward substitution
  3. Triangular matrix multiplication

The Cholesky decomposition calculates the reciprocal values of the diagonal elements of L, which the triangular matrix inversion requires. The design propagates those values to the output interface of the Cholesky decomposition reducing resource usage and latency.

Assuming matrix A is an NxN positive-definite square matrix, Cholesky decomposition of A into lower and upper triangular matrices, L, and L H is given by:

A = LH

The inverse of Hermitian A, A -1 is:

The design performs Cholesky decomposition and calculates the inverse of L, , through forward substitution. J is a lower triangle matrix. The inverse of the input matrix requires a triangular matrix multiplication, followed by a Hermitian matrix multiplication:

The Cholesky-based matrix inversion reference design comprises a Cholseky decomposition design and a triangular matrix inversion design. Both designs are fully pipelined, with multichannel input and output streaming to maximize throughput. The size of dot-product engines in both designs are compile-time configurable according to the size of the input matrices. The datapath and control logic are split.

Figure 80. Cholesky Decomposition Top-level DesignInput = Size* (size +1)* channel/2
Figure 81. Triangular Matrix Inversion Top-level Design

This design supports single-precision floating-point Cholesky matrix inversion. DSP Builder requires a single-precision floating-point input for the floating point inversion.

Matrix inversion takes multiple matrices and interleaves the inverse computations for all matrices. This method hides the latency in computing each element by pipelining inversion of a completely different channel. Multichannel designs use the idle cycles in the computation chain to process the next channel. Two buffers at the input and output of the design create channels for streaming matrices into multichannel interfaces.

Table 19.  Top-level matrix inversion input and output portsThe input and output interfaces follow Avalon™ streaming (Avalon-ST) standard.
Signal Direction Type Width Description
Sink_Valid Input Boolean 1 Avalon streaming sink valid signal for the input matrix interface. Number of valid input = (matrix size*(matrix size + 1))/2
Sink_Channel Input unsigned integer 8 Avalon streaming sink channel bus for the input matrix interface.
Sink_Data Input Single floating-point complex 64 bit I/Q Avalon streaming sink data bus for the input matrix interface. Lower matrix elements are streamed in column major order.
Source_Valid Output Boolean 1 Avalon streaming source valid signal for output interface. This signal is asserted for (size*(size+1))/2 clocks
Source_Channel Output unsigned integer 8 Avalon streaming source channel bus for output interface.
Source_Data Output Single floating-point complex 64 bit I/Q Avalon streaming source data bus for output interface. Lower matrix elements are streamed in column major order.

Parameters

Table 20.  Parameters of the matrix inversion designThe parameters are compile-time configurable using the setup file. .
Parameter Description
Size of Matrix The size of matrix to invert.
Channels Number of matrices inverted in a burst. Minimum of 16 channel.
Latency The period in cycles the module waits before receiving the next set of matrices.

DSP Builder calculates the throughput of the design by setting the latency value and the system clock:

Throughput (matrix inversion per second) = System clock/Latency

Although elements of input matrices arrive in streaming format, the internal channelizer vectorizes the input matrices into several channels (the default is 16). This vectorization significantly improves the throughput.

Figure 82. Input streaming interface for 8x8 Hermitian input matrix

The figure shows the latency configuration parameter in the input interface including data, valid, and channel signals. In this example of 8x8 matrix inversion, the valid signal remains high for 36 clock cycles (total number of lower triangle elements of the Hermitian matrix of 8x8) and remains low for (latency – 36) cycles before inserting the next matrix elements. The minimum duration to remain low and hence the minimum latency period may vary depending on the matrix size and the pipelining required to meet timing constraints.

Table 21.  Recommended Values for the Minimum Latency (maximum throughput) In Intel Stratix 10 and Intel Arria 10 devices, speed grade –1 and –2, for three different matrix sizes.
Matrix Dimension Latency in clock cycles
Intel Arria 10 Devices Intel Stratix 10 Devices
4x4 ≥ 30 ≥ 30
8x8 ≥ 75 ≥ 74
16x16 ≥ 230 ≥ 220

Performance and Resource Usage

Table 22.  Floating-point implementation resource utilization targeting Intel® Stratix® 10 GX/SX/TX 280 FPGAThe table shows the resource count of the floating-point Cholesky-based matrix inversion design including the channelizing input and output buffers.
Matrix Dimension Number of channels Logic Elements (ALMs) DSP Blocks Memory bits RAM blocks Registers
4x4 16 8,236 55 548,448 55 22,066
8x8 16 16,665 103 2,001,664 194 45,463
16x16 16 35,025 199 7,085,088 521 95,079
Table 23.  Performance of the floating-point matrix inversion module for different matrix dimensionsThis table shows the fMAX performance of the floating-point design for different matrix sizes with a system clock of 368.64 MHz and targeting a Intel® Stratix® 10 FPGA device. The maximum throughput is in millions of matrix inversions per second.
Matrix Dimension Number of channels Target System clock (MHz) fMAX (MHz) ThroughputMAX
4x4 16 368.64 468.06 12.2
8x8 16 368.64 403.88 5.0
16x16 16 368.64 392.77 1.67
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