Abstract: In MIMO millimeter-wave (mmWave) systems, while the hybrid digital/analog precoding structure provides the ability to increase the reach rate, it also faces the challenge of reducing the channel time limit due to the large number of horns on both sides of the Tx / Rx. . In this paper, channel measurement is done by searching with multiple beams, and a new hierarchical multi-beam search system is proposed, using a pre-designed analog codebook. Performance tests show that, compared to a highperformance system, the proposed system not only achieves a high level of success in getting multiple beams under normal system settings but also significantly reduces channel estimation time Keywords: Massive MIMO, Channel Estimation, precoding
This paper studies the equality generalized symmetric traveling salesman problem (EGSTSP). A salesman has to visit a predefined set of countries. S/he must determine exactly one city (of a subset of cities) to visit in each country and the sequence of the countries such that s/he minimizes the overall travel cost. From an academic perspective, EGSTSP is very important. It is NP-hard. Its relaxed version TSP is itself NP-hard, and no exact technique solves large difficult instances. From a logistic perspective, EGSTSP has a broad range of applications that vary from sea, air, and train shipping to emergency relief to elections and polling to airlines’ scheduling to urban transportation. During the COVID-19 pandemic, the roll-out of vaccines further emphasizes the importance of this problem. Pharmaceutical firms are challenged not only by a viable production schedule but also by a flawless distribution plan especially that some of these vaccines must be stored at extremely low temperatures. This paper proposes an approximate tree-based search technique for EGSTSP . It uses a beam search with low and high level hybridization. The low-level hybridization applies a swap based local search to each partial solution of a node of a tree whereas the high-level hybridization applies 2-Opt, 3-Opt or Lin-Kernighan to the incumbent. Empirical results provide computational evidence that the proposed approach solves large instances with 89 countries and 442 cities in few seconds while matching the best known cost of 8 out of 36 instances and being less than 1.78% away from the best known solution for 27 instances.