Abstract: A system for evaluating the convergence to a solution for a matrix equation comprises at least one reconfigurable computing device such as a field programmable gate array (FPGA), an update storage element, a conversion element, a summation unit, and a comparator. The FPGA includes a plurality of configurable logic elements and a plurality of configurable storage elements, which are utilized to form the update storage element, the conversion element, the summation unit, and the comparator. The update storage element is configured to store a plurality of updates. The conversion element determines the absolute value of the updates. The summation unit accumulates the absolute values of the updates to produce a total sum, which is compared to a convergence factor by the comparator. Convergence is signaled when the total sum is less than the convergence factor.

Abstract: A system for a conjugate gradient iterative linear solver that calculates the solution to a matrix equation comprises a plurality of gamma processing elements, a plurality of direction vector processing elements, a plurality of x-vector processing elements, an alpha processing element, and a beta processing element. The gamma processing elements may receive an A-matrix and a direction vector, and may calculate a q-vector and a gamma scalar. The direction vector processing elements may receive a beta scalar and a residual vector, and may calculate the direction vector. The x-vector processing elements may receive an alpha scalar, the direction vector, and the q-vector, and may calculate an x-vector and the residual vector. The alpha processing element may receive the gamma scalar and a delta scalar, and may calculate the alpha scalar. The beta processing element may receive the residual vector, and may calculate the delta scalar and the beta scalar.

Abstract: RF sampling receivers are disclosed that employ multiple sampling clocks to produce multiple projections. In operation, a Nyquist folded receiver (NYFR) may be implemented that utilizes at least one modulated sampling clock in combination with one or more other modulated or non-modulated sampling clocks to identify received signals. In such an embodiment, one or more clock modulations may be used to induce frequency modulations that are Nyquist zone dependent, and multiple Nyquist zones may be aliased together while still allowing for signals from different Nyquist zones to be separated and identified.

Abstract: Problem solution speed may be increased by dynamically changing processing device computational hardware configuration in concert with respective mathematical phases of an algorithm to match accuracy demands at various phases of computation. Smaller but faster hardware structures may be increased in size using real-time partial or full reconfiguration of a processing device to apply the smallest and fastest possible computational structure for the needed accuracy during each of multiple computational phases.

Abstract: Systems and methods for interference cancellation in which a first signal having a first frequency may be cancelled with a second frequency having a second and different (e.g., lower) frequency by employing sampling to cancel the first signal with the separate signal at the sample instances.

Abstract: Problem solution speed may be increased by dynamically changing processing device computational hardware configuration in concert with respective mathematical phases of an algorithm to match accuracy demands at various phases of computation. Smaller but faster hardware structures may be increased in size using real-time partial or full reconfiguration of a processing device to apply the smallest and fastest possible computational structure for the needed accuracy during each of multiple computational phases.

Abstract: A system for evaluating the convergence to a solution for a matrix equation comprises at least one reconfigurable computing device such as a field programmable gate array (FPGA), an update storage element, a conversion element, a summation unit, and a comparator. The FPGA includes a plurality of configurable logic elements and a plurality of configurable storage elements, which are utilized to form the update storage element, the conversion element, the summation unit, and the comparator. The update storage element is configured to store a plurality of updates. The conversion element determines the absolute value of the updates. The summation unit accumulates the absolute values of the updates to produce a total sum, which is compared to a convergence factor by the comparator. Convergence is signaled when the total sum is less than the convergence factor.

Abstract: A system for a conjugate gradient iterative linear solver that calculates the solution to a matrix equation comprises a plurality of gamma processing elements, a plurality of direction vector processing elements, a plurality of x-vector processing elements, an alpha processing element, and a beta processing element. The gamma processing elements may receive an A-matrix and a direction vector, and may calculate a q-vector and a gamma scalar. The direction vector processing elements may receive a beta scalar and a residual vector, and may calculate the direction vector. The x-vector processing elements may receive an alpha scalar, the direction vector, and the q-vector, and may calculate an x-vector and the residual vector. The alpha processing element may receive the gamma scalar and a delta scalar, and may calculate the alpha scalar. The beta processing element may receive the residual vector, and may calculate the delta scalar and the beta scalar.

Abstract: Systems and methods for interference cancellation in which a first signal having a first frequency may be cancelled with a second frequency having a second and different (e.g., lower) frequency by employing sampling to cancel the first signal with the separate signal at the sample instances.