# US 6,418,164 B1 · Adaptive equalizer with enhanced error quantization > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 6,418,164 B1 - Document ID: US6418164B1 - Status: Granted - Kind: B1 - Application number: 09/231,888 - Filed: 1999-01-14 - Granted: 2002-07-09 - Earliest claimed: 1999-01-14 - Assignees: Nxtwave Communications, Inc. - Inventors: Thomas J Endres; Samir N Hulyalkar; Christopher H Strolle; Troy A Schaffer - Web page: https://patentgrep.com/patent/US6418164B1 ## CPC - H04L 27/01: Equalisers {(baseband equalizers at the transmitter end H04L25/03343; in analogue transmission systems H04B3/04, H04B7/005)} - H04L 2025/0342: {QAM} - H04L 2025/03624: {Zero-forcing} - H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M) ## Abstract An adaptive equalizer for use in blind equalization systems to compensate for transmission channel distortion and noise in a digital communication system uses multiple quantization levels for implementation of the Constant Modulus Algorithm (CMA). Different quantization levels are used in different regions of the CMA error function for both passband and baseband equalizers. In one embodiment, a quantizer with a step rise having logarithmic scale is used to digitize the CMA error function. In particular, a quantizer with a step rise in which each level of the quantizer step rise is a power of 2 is used to digitize the CMA error function. In another embodiment, a quantizer with a step rise in which each level of the quantizer step rise is the sum of two or more logarithmic scales is used to digitize the CMA error function. In particular, a quantizer with a step rise wherein each level of the quantizer step rise is the sum of two or more numbers each of which is a power of 2 is used to digitize the CMA error function. The use of logarithmic scales, the sum of logarithmic scales, powers of 2, or the sum of powers of 2 for the quantizer step rise size to digitize the CMA error function make efficient use of shift and add operations to achieve multiplication in the adaptation process. ## Claims ### Claim 1 In a digital communications receiver including an equalization filter having a plurality of adjustable parameters, and an error term calculator for updating said plurality of adjustable parameters, said error term calculator responsive to a received digital signal and the error in said received digital signal, said error being proportional to an error function, a quantization method comprising: determining first and second regions of said error function; quantizing said first region of said error function using a first step rise size; and quantizing said second region of said error function using a second step rise size. ### Claim 2 (depends on 1) A method in accordance with claim 1, further including: selecting said error function responsive to said received digital signal; and determining the roots of said error function, wherein said roots define the boundaries of said first and second regions of said error function. ### Claim 3 (depends on 1) A method in accordance with claim 1, wherein said first region of said error function using said first step rise size is quantized using a logarithmic scale. ### Claim 4 (depends on 3) A method in accordance with claim 3, wherein said second region of said error function using said second step rise size is quantized using a logarithmic scale. ### Claim 5 (depends on 1) A method in accordance with claim 1, wherein said first step rise size is selected to be a power of 2. ### Claim 6 (depends on 5) A method in accordance with claim 5, wherein said second step rise size is selected to be a power of 2. ### Claim 7 (depends on 1) A method in accordance with claim 1, wherein said first step rise size is selected to be the sum of at least two numbers, each of which numbers is a power of 2. ### Claim 8 (depends on 7) A method in accordance with claim 7, wherein said second step rise size is selected to be the sum of at least two numbers, each of which numbers is a power of 2. ### Claim 9 (depends on 1) A method in accordance with claim 1, wherein said first step rise size is equal to 40. ### Claim 10 (depends on 1) A method in accordance with claim 1, wherein said second step rise size is equal to 128. ### Claim 11 (depends on 1) A method in accordance with claim 1, wherein the boundary between said first and second regions of said error function is the square root of Godard's radius. ### Claim 12 In a digital communications receiver including an equalization filter having a plurality of adjustable parameters, and an error term calculator for updating said plurality of adjustable parameters, said error term calculator responsive to a received digital signal and the error in said received digital signal, said error being proportional to an error function, a quantization apparatus comprising: means for determining first and second regions of said error function; means for quantizing said first region of said error function using a first step rise size; and means for quantizing said second region of said error function using a second step rise size. ### Claim 13 (depends on 12) An apparatus in accordance with claim 12, further including: means for selecting said error function responsive to said received digital signal; and means for determining the roots of said error function, wherein said roots define the boundaries of said first and second regions of said error function. ### Claim 14 (depends on 12) An apparatus in accordance with claim 12, wherein said first region of said error function using said first step rise size is quantized using a logarithmic scale. ### Claim 15 (depends on 14) An apparatus in accordance with claim 14, wherein said second region of said error function using said second step rise size is quantized using a logarithmic scale. ### Claim 16 (depends on 12) An apparatus in accordance with claim 12, wherein said first step rise size is selected to be a power of 2. ### Claim 17 (depends on 16) An apparatus in accordance with claim 16, wherein said second step rise size is selected to be a power of 2. ### Claim 18 (depends on 12) An apparatus in accordance with claim 12, wherein said first step rise size is selected to be the sum of at least two numbers, each of which numbers is a power of 2. ### Claim 19 (depends on 18) An apparatus in accordance with claim 18, wherein said second step rise size is selected to be the sum of at least two numbers, each of which numbers is a power of 2. ### Claim 20 (depends on 12) An apparatus in accordance with claim 12, wherein said first step rise size is equal to 40. ### Claim 21 (depends on 12) An apparatus in accordance with claim 12, wherein said second step rise size is equal to 128. ### Claim 22 (depends on 13) An apparatus in accordance with claim 13, wherein the boundary between said first and second regions of said error function is the square root of Godard's radius. ### Claim 23 In a digital communications receiver including an equalization filter having a plurality of adjustable parameters, and an error term calculator for updating said plurality of adjustable parameters, said error term calculator responsive to a received digital signal and the error in said received digital signal, said error being proportional to an error function, a quantization method comprising: quantizing said error function using a step rise size according to a logarithmic scale to provide a quantized error function; and updating said plurality of adjustable parameters using said quantized error function. ### Claim 24 (depends on 23) A method in accordance with claim 23, wherein said step rise size is selected to be a power of 2. ### Claim 25 (depends on 23) A method in accordance with claim 23, wherein said step rise size is selected to be the sum of at least two numbers, each of which numbers is a power of 2. ### Claim 26 In a digital communications receiver including an equalization filter having a plurality of adjustable parameters, and an error term calculator for updating said plurality of adjustable parameters, said error term calculator responsive to a received digital signal and the error in said received digital signal, said error being proportional to an error function, a quantization apparatus comprising: means for quantizing said error function using a step rise size according to a logarithmic scale to provide a quantized error function; and means for updating said plurality of adjustable parameters using said quantized error function. ### Claim 27 (depends on 26) An apparatus in accordance with claim 26, wherein said step rise size is selected to be a power of 2. ### Claim 28 (depends on 26) An apparatus in accordance with claim 26, wherein said step rise size is selected to be the sum of at least two numbers, each of which numbers is a power of 2. ### Claim 29 An equalizer for a digital communications receiver for receiving digital symbols, said equalizer comprising: an equalization filter having a plurality of adjustable parameters, and an output terminal providing said received digital symbols; a slicer having a respective input and output, the input of said slicer being coupled to the output of said equalization filter, said slicer being set for the nominal decision threshold levels corresponding to each of said digital symbols; an error term calculator for updating said plurality of adjustable parameters of said equalization filter, said error term calculator responsive to said received digital symbols and to the output of said slicer to determine an error function; said error term calculator further responsive to said received digital symbols to determine first and second regions of said error function; and a quantizer having a respective input and output, said quantizer further having a first step rise size to digitize said error function in said first region and a second step rise size to digitize said error function in said second region, wherein the output of said quantizer is used in said error term calculator to update said plurality of adjustable parameters of said equalization filter. ### Claim 30 (depends on 29) An equalization filter in accordance with claim 29, wherein at least one of said first and second regions of said error function are respectively quantized using a logarithmic scale. ### Claim 31 (depends on 29) A method in accordance with claim 29, wherein at least one of said first and second step rise size is selected to be a power of 2. ### Claim 32 (depends on 29) A method in accordance with claim 29, wherein at least one of said first and second step rise size is selected to be the sum of at least two numbers, each of which numbers is a power of 2. ### Claim 33 An equalizer for a digital communications receiver for receiving digital symbols, said equalizer comprising: an equalization filter having a plurality of adjustable parameters, and an output terminal providing said received digital symbols; a slicer having a respective input and output, the input of said slicer being coupled to the output of said equalization filter, said slicer being set for the nominal decision threshold levels corresponding to each of said digital symbols; an error term calculator for updating said plurality of adjustable parameters of said equalization filter, said error term calculator responsive to said received digital symbols and to the output of said slicer to determine an error function; and a quantizer having a respective input and output, said quantizer further having a step rise size to digitize said error function, said step rise size being a logarithmic scale, wherein the output of said quantizer is used in said error term calculator to update said plurality of adjustable parameters of said equalization filter. ### Claim 34 (depends on 33) A quantizer in accordance with claim 33, wherein said step rise size is selected to be a power of 2. ### Claim 35 (depends on 34) A method in accordance with claim 34, wherein said step rise size is selected to be the sum of at least two numbers, each of which numbers is a power of 2. ### Claim 36 (depends on 5) A method in accordance with claim 5, wherein said error term calculator for updating said plurality of adjustable parameters includes at least one multiply operation, said method further comprising performing said multiply operation by only one shift operation. ### Claim 37 (depends on 24) A method in accordance with claim 24 wherein said error term calculator for updating said plurality of adjustable parameters includes at least one multiply operation, said method further comprising performing said multiply operation by only one shift operation. ### Claim 38 (depends on 7) A method in accordance with claim 7, wherein said error term calculator for updating said plurality of adjustable parameters includes at least one multiply operation, said method further comprising performing said multiply operation by only two shift operations and one add operation. ### Claim 39 (depends on 25) A method in accordance with claim 25, wherein said error term calculator for updating said plurality of adjustable parameters includes at least one multiply operation, said method further comprising performing said multiply operation by only two shift operations and one add operation. ### Claim 40 (depends on 16) An apparatus in accordance with claim 16, wherein said error term calculator for updating said plurality of adjustable parameters includes at least one multiply operation, said apparatus further comprising means for performing said multiply operation by only one shift operation. ### Claim 41 (depends on 27) An apparatus in accordance with claim 27, wherein said error term calculator for updating said plurality of adjustable parameters includes at least one multiply operation, said apparatus further comprising means for performing said multiply operation by only one shift operation. ### Claim 42 (depends on 18) An apparatus in accordance with claim 18, wherein said error term calculator for updating said plurality of adjustable parameters includes at least one multiply operation, said apparatus further comprising means for performing said multiply operation by only two shift operations and one add operation. ### Claim 43 (depends on 28) An apparatus in accordance with claim 28, wherein said error term calculator for updating said plurality of adjustable parameters includes at least one multiply operation, said apparatus further comprising means for performing said multiply operation by only two shift operations and one add operation.