FPGA-based tracking for the CMS Level-1 trigger using the tracklet algorithm

The high instantaneous luminosities expected following the upgrade of the Large Hadron Collider (LHC) to the High Luminosity LHC (HL-LHC) pose major experimental challenges for the CMS experiment. A central component to allow efficient operation under these conditions is the reconstruction of charged particle trajectories and their inclusion in the hardware-based trigger system. There are many challenges involved in achieving this: a large input data rate of about 20--40\,Tb/s; processing a new batch of input data every 25\,ns, each consisting of about 15,000 precise position measurements and rough transverse momentum measurements of particles (``stubs''); performing the pattern recognition on these stubs to find the trajectories; and producing the list of trajectory parameters within $4\,\mu$s. This paper describes a proposed solution to this problem, specifically, it presents a novel approach to pattern recognition and charged particle trajectory reconstruction using an all-FPGA solution. The results of an end-to-end demonstrator system, based on Xilinx Virtex-7 FPGAs, that meets timing and performance requirements are presented along with a further improved, optimized version of the algorithm together with its corresponding expected performance.