Method and apparatus using pseudo-inverses of linear transformations in multi-carrier modulation receivers and transceivers
First Claim
1. A system processing a sample list of at least two digitized samples based upon at least one electromagnetic receptor using a truncated pseudo-inverse B1 of a linear transform A1, comprising:
- at least one processing engine receptively coupled to said electromagnetic receptors to provide said digitized samples controlled by a program system comprising program steps residing in memory accessibly coupled to said processing engine;
wherein said program system comprising the program steps of;
receiving said sample list based upon said electromagnetic receptor to create a received sample list containing at least two received samples; and
processing said received sample list by using said truncated pseudo-inverse B1 on at least some of said received samples to create a received signal parameter list containing at least one received signal parameter;
wherein said sample list is based upon a transported version of a signal progression generated using at least part of linear transform A1; and
wherein said truncated pseudo-inverse B1 of said linear transform A1 is based upon a pseudo-inverse of A1 belonging to at least one member of the pseudo-inverse type collection comprising A1{1}, A1{2}, A1{3}, A1{4}, a Drazin inverse of A1, and a Moore-Penrose inverse A1{1,2,3,4}.
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Abstract
Many communications protocols involve a collection of communication channels collectively forming the dimensions of a finite dimensional vector space, of which at any point in time, only a subset of those channels or dimensions must be received. Messages on these channels are time progressions in at least the actively used dimensions of the vector space which have been linearly transformed to create a sample list transported across at least one physical transport layer to a receiver. The linear transform may further include an estimation of the effects of the transport of the sample list across the one or more physical layers to the receiver. This invention uses at least portions of pseudo-inverses of the linear transform in various ways within receivers and receiver portions of transceivers.
22 Citations
176 Claims
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1. A system processing a sample list of at least two digitized samples based upon at least one electromagnetic receptor using a truncated pseudo-inverse B1 of a linear transform A1, comprising:
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at least one processing engine receptively coupled to said electromagnetic receptors to provide said digitized samples controlled by a program system comprising program steps residing in memory accessibly coupled to said processing engine;
wherein said program system comprising the program steps of;
receiving said sample list based upon said electromagnetic receptor to create a received sample list containing at least two received samples; and
processing said received sample list by using said truncated pseudo-inverse B1 on at least some of said received samples to create a received signal parameter list containing at least one received signal parameter;
wherein said sample list is based upon a transported version of a signal progression generated using at least part of linear transform A1; and
wherein said truncated pseudo-inverse B1 of said linear transform A1 is based upon a pseudo-inverse of A1 belonging to at least one member of the pseudo-inverse type collection comprising A1{1}, A1{2}, A1{3}, A1{4}, a Drazin inverse of A1, and a Moore-Penrose inverse A1{1,2,3,4}. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30)
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31. A method of processing a sample list of at least two digitized samples based upon at least one electromagnetic receptor using a truncated pseudo-inverse B1 of a linear transform A1, comprising the steps of:
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receiving said sample list based upon said electromagnetic receptor to create a received sample list containing at least two received samples; and
processing said received sample list by using said truncated pseudo-inverse B1 on at least some of said received samples to create a received signal parameter list containing at least one received signal parameter;
wherein said sample list is based upon a transported version of a signal progression generated using at least part of linear transform A1; and
wherein said truncated pseudo-inverse B1 of said linear transform A1 is based upon a pseudo-inverse of A1 belonging to at least one member of the pseudo-inverse type collection comprising A1{1}, A1{2}, A1{3}, A1{4}, a Drazin inverse of A1, and a Moore-Penrose inverse A1{1,2,3,4}. - View Dependent Claims (32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67)
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68. A system determining availability of a first communications service based upon a third truncated pseudo-inverse B3 and of a second communications service based upon a fourth truncated pseudo-inverse B4 from a sample list of at least two digitized samples based upon at least one electromagnetic receptor, comprising:
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at least one processing engine receptively coupled to said electromagnetic receptors to provide said digitized samples controlled by a program system comprising program steps residing in memory accessibly coupled to said processing engine;
wherein said program system is comprised of the program steps of;
receiving said sample list based upon said electromagnetic receptor to create a received sample list containing at least two received samples; and
processing said second received sample list by using said third truncated pseudo-inverse B3 on at least some of said received samples to create a third received signal parameter list containing at least one third received signal parameter;
processing said second received sample list by using said fourth truncated pseudo-inverse B3 on at least some of said received samples to create a fourth received signal parameter list containing at least one fourth received signal parameter;
determining said first communications service availability based upon said third received signal parameter list to create a first communication service determination; and
determining said second communications service availability based upon said fourth received signal parameter list to create a second communication service determination;
wherein a truncated pseudo-inverse B3 is based upon a linear transform A1;
wherein said fourth truncated pseudo-inverse B4 is based upon a linear transform A2;
wherein said sample list is based upon a transported version of a signal progression generated using at least part of at least one member of a linear transform collection comprising said linear transform A1 and said linear transform A2; and
wherein said truncated pseudo-inverse B1 of said linear transform A1 is based upon a pseudo-inverse of A1 belonging to at least one member of the pseudo-inverse type collection comprising A1{1}, A1{2}, A1{3}, A1{4}, a Drazin inverse of A1, and a Moore-Penrose inverse A1{1,2,3,4}. - View Dependent Claims (69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91)
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92. A method of determining availability of a first communications service based upon a third truncated pseudo-inverse B3 and of a second communications service based upon a fourth truncated pseudo-inverse B4 from a sample list of at least two digitized samples based upon at least one electromagnetic receptor, comprising the steps of:
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receiving said sample list based upon said electromagnetic receptor to create a received sample list containing at least two received samples; and
processing said second received sample list by using said third truncated pseudo-inverse B3 on at least some of said received samples to create a third received signal parameter list containing at least one third received signal parameter;
processing said second received sample list by using said fourth truncated pseudo-inverse B3 on at least some of said received samples to create a fourth received signal parameter list containing at least one fourth received signal parameter;
determining said first communications service availability based upon said third received signal parameter list to create a first communication service determination; and
determining said second communications service availability based upon said fourth received signal parameter list to create a second communication service determination;
wherein a truncated pseudo-inverse B3 is based upon a linear transform A1;
wherein said fourth truncated pseudo-inverse B4 is based upon a linear transform A2;
wherein said sample list is based upon a transported version of a signal progression generated using at least part of at least one member of a linear transform collection comprising said linear transform A1 and said linear transform A2;
wherein said truncated pseudo-inverse B3 of said linear transform A3 is based upon a pseudo-inverse of A3 belonging to at least one member of the pseudo-inverse type collection comprising A3{1}, A3{2}, A3{3}, A3{4}Drazin inverse of A3, and a Moore-Penrose inverse A3{1,2,3,4}; and
wherein said truncated pseudo-inverse B4 of said linear transform A4 is based upon a pseudo-inverse of A4 belonging to at least one member of the pseudo-inverse type collection comprising A4{1}, A4{2}, A4{3}, A4{4}, a Drazin inverse of A4, and a Moore-Penrose inverse A4{1,2,3,4}. - View Dependent Claims (93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121)
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122. A system processing a sample list of at least two digitized samples based upon at least one electromagnetic receptor using a truncated pseudo-inverse B1 of a linear transform A1, comprising:
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at least one processing engine receptively coupled to said electromagnetic receptors to provide said digitized samples controlled by a program system comprising program steps residing in memory accessibly coupled to said processing engine;
wherein said program system comprising the program steps of;
receiving said sample list based upon said electromagnetic receptor to create a received sample list containing at least two received samples; and
processing said received sample list by using said truncated pseudo-inverse B1 on at least some of said received samples to create a received signal parameter list containing at least one received signal parameter;
wherein said sample list is based upon a transported version of a signal progression generated using at least part of linear transform A1;
wherein said linear transform A1 includes an IFFT of 64 points as specified in IEEE 802.11a; and
wherein said truncated pseudo-inverse B1 provides at least an approximation of the 52 active frequency bins of the IEEE 802.11a physical layer during data transmission. - View Dependent Claims (123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145)
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146. A method of processing a sample list of at least two digitized samples based upon at least one electromagnetic receptor using a truncated pseudo-inverse B1 of a linear transform A1, comprising the steps of:
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receiving said sample list based upon said electromagnetic receptor to create a received sample list containing at least two received samples; and
processing said received sample list by using said truncated pseudo-inverse B1 on at least some of said received samples to create a received signal parameter list containing at least one received signal parameter;
wherein said sample list is based upon a transported version of a signal progression generated using at least part of linear transform A1;
wherein said linear transform A1 includes an IFFT of 64 points as specified in IEEE 802.11a; and
wherein said truncated pseudo-inverse B1 provides at least an approximation of the 52 active frequency bins of the IEEE 802.11a physical layer during data transmission; and
wherein said truncated pseudo-inverse B1 of said linear transform A1 is based upon a pseudo-inverse of A1 belonging to at least one member of the pseudo-inverse type collection comprising A1{1}, A1{2}, A1{3}, A1{4}, a Drazin inverse of A1, and a Moore-Penrose inverse A1{1,2,3,4}. - View Dependent Claims (147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176)
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Specification