Wideband is a booming technology in the field of wireless communications. The receivers in wideband communication systems are expected to cover a very wide spectrum and adaptively extract the parts of interest. The literature has focused on mixing the input spectrum to baseband using a pseudorandom sequence modulation and recovering the received signals from linearly independent measurements by parallel branches to mitigate the pressures from required extreme high sampling frequency. However, a pseudorandom sequence provides no rejection for the strong interferers received together with weak signals from distant sources. The interferers cause significant distortion due to the nonlinearity of the subsequent amplifier and mask the weak signals.
In this dissertation, we optimize the modulation sequences with a specific spectrum shape to mitigate interferers while preserving messages; the sequences have binary entries to simplify hardware implementation. Though the resulting sequence design problems are NP-hard, we solve them approximately by semidefinite relaxation and randomized projection.
First, we formulate the design algorithm for a single spectrally shaped binary sequence base on a randomized convex optimization method. We analyze the performance of the algorithm in obtaining binary sequences and show its advantages compared with method available in the literature. And, we show a comparison between the proposed sequence design method with the exhaustive approaches when feasible. Additionally, we propose several custom sequence scoring functions that allow for an improved selection of binary sequences for message preservation and interference rejection.
Second, we propose an algorithm to design a multi-branch set of binary sequences one by one by introducing the constrains on the orthogonality between pairs of sequences. Numerical results show the proposed algorithm obtains sequences with a small search size compared with the exhaustive search.
Finally, we extend the randomized method to multi-branch sequence design. In order to avoid the unstable performance and high complexity of designing multi-branch sequence iteratively, the whole branch sequences will be obtained directly via matrix randomized projection from the relaxed problems
