Complex Block FloatingPoint Format with Box Encoding For
Complex Block Floating-Point Format with Box Encoding For Wordlength Reduction in Communication Systems Yeong Foong Choo, Brian L. Evans and *Alan Gatherer Embedded Signal Processing Laboratory Wireless Networking & Communications Group The University of Texas at Austin, Texas USA *Huawei Technologies, Plano, Texas, USA http: //www. wncg. org
Background on IEEE-754 format Components u Complex exponent pair of 32 -bit floating -point 2
Problem Statement u Intuition Increase information sharing at Bits level u Exploit magnitude and phase correlation u Approach 3
Exponent Box Encoding Components Complex-valued exponent pairs X ∼ N(130, 122 ) and potential candidate for common
Exponent Box Encoding/ Decoding Perform at the entry point from IEEE 754 Perform at block arithmetic units Exponent Box Encoding and Decoding Algorithms 5
32 -bit Equivalent SIMD ALU Perform arithmetic operations on blocks of samples at time u Single-Instruction Multiple-Data (SIMD) operation increases instruction sets efficiency u Example Block Arithmetic Units: u Complex Block Add u Complex Block Multiply u Complex Multiply. Accumulate Example ALU diagram on complex block 32 -bit format 6
32 -bit Equivalent SIMD ALU Dark solid arrow shows mantissa vectors prescale in simplified Adder ALU Complex Block Add: u Box Shift Vectors used to pre-scale Mantissa Vectors u No obvious advantage of phase resolution u Expect no improvement! Dark solid arrow shows exponent vectors prescale in simplified Multiply ALU Complex Block Multiply: u Box Shift Vectors used to pre-scale Shared Exponents Vectors u 2 Input Shared Exponents & 2 Box Shift Vectors 4 possible Intermediate Shared Exponents 7
Validation: 32 -bit Equivalent SIMD ALU EVM Plot on Complex Block Arithmetic Outputs 8
Case Study: Single-carrier QAM 9
Case Study: Single-carrier QAM 10
Block Diagram for Simulating Single-Carrier QAM Complex Baseband Chain of Single-Carrier QAM Transmitter Simulation Parameters Values Complex Baseband Chain of Single-Carrier QAM Receiver Root-Raised Cosine (RRC) Filter Impulse Response 11
Validation: Single-carrier QAM EVM Plot on Single-Carrier 1024 Single-Carrier QAM Transceiver: Ø Similar EVM performance due to DR requirement in pulse shaping filter and matched filter 12
Conclusion 13
Thank you! Any questions ?
Appendix Derivation: I. Maximum Exponent Difference under Exponent Box Encoding II. Pre/ Post Processing Complexity of Complex-valued Convolution Table: I. Processing Complexity for Complex Block ALU II. Memory Input/ Output and Computational Rates 15
Derivation of Maximum Exponent Difference 16
Pre / Post Processing Complexity Of Complex-valued Convolution 17
Pre / Post Processing Complexity Of Complex-valued Convolution 18
Pre / Post Processing Complexity Of Complex-valued Convolution 19
Processing Complexity for Complex Block ALU 20
Memory Input/ Output and Computational Rates 21
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