On the linear complexity of Sidel'nikov sequences over nonprime fields

We introduce a generalization of Sidel'nikov sequences for arbitrary finite fields. We show that several classes of Sidel'nikov sequences over arbitrary finite fields exhibit a large linear complexity. For Sidel'nikov sequences over F-8 we provide exact values for their linear complexity

Finite Fields: Theory and Applications

Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation

A Discrete-Time Technique for Linearity Enhancement of Wideband Receivers

A new signal processing technique is introduced to enhance the linearity performance of wideband radio frequency (RF) receivers. The proposed technique combines the advancements in mixer first architectures with a library of binary sequences as local oscillator signals to enable wide instantaneous bandwidth and high linearity for the RF receiver. To do so, N-bit pseudo-random-binary-sequences (PRBS) are used as local oscillator signals. The RF input signal is multiplied with the PRBS at the mixer and then averaged over the full sequence. This in effect reduces the amplitude of the signal and improves the overall linearity of the system. In order to enable full reconstruction of the input signal N channels are used with each employing a shifted version of a PRBS. The effect of the proposed technique on different aspects of the system performance such as noise and linearity is discussed. In addition, the effect of nonidealities stemming from hardware implementation on the overall performance are studied. A prototype integrated circuit (IC) is implemented in 130\,nm CMOS technology to demonstrate the feasibility of the proposed technique. The design procedure of each circuit block is described and simulation results are used to evaluate the performance. The device is fabricated and characterized using a custom data acquisition system. Measurement results show good agreement with the expected values from simulation and analytical analysis. Calibration techniques are introduced to minimize the effect of DC offsets, gain mismatches, and timing skews. Modifications to the implemented CMOS circuit are proposed to enable such calibrations and further enhance the overall performance of the system. The requirements for the precision of calibration techniques are derived and used to find the specifications of circuit block that are designed to enable these techniques. Calibration of DC offsets along with gain mismatches is carried out for the fabricated IC and results are shown. A digitally assisted technique is proposed to enable the calibration of timing skews. In addition, a review of additional implementation shortcomings that can affect the system performance are reviewed. Finally, a conclusion of the dissertation is presented along with potential future work for further enhancement of the system performance