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The evolution of third generation mobile communications toward high-speed packet access and long-term evolution is ongoing and will substantially increase the throughput with higher spectral efficiency. This paper presents the system architecture of an LTE modem based on a programmable baseband processor. The architecture includes a baseband processor that handles processing time and frequency synchronization, IFFT/FFT (up to 2048-p), channel estimation and subcarrier de-mapping. The throughput and latency requirements of a Category four User Equipment (CAT4 UE) is met by adding a MIMO symbol detector and a parallel Turbo decoder supporting H-ARQ, which brings both low silicon cost and enough flexibility to support other wireless standards. The complexity demonstrated by the modem shows the practicality and advantage of using programmable baseband processors for a single-chip LTE solution.