In recent years, LoRa has been deployed in countless Internet of Things (IoT) applications across the globe. However, as LoRa is a proprietary technology, research into its physical-layer performance has been challenging. Implementing LoRa on software-defined radio (SDR) platforms yields valuable insight into the physical layer of the LoRa standard and paves the way for improvements in packet reception capabilities for LoRa receivers. This article presents an independently developed packet reception algorithm, which drastically improves the physical performance of LoRa communication links. The advanced signal presence detection, synchronization, and symbol detection strategies are shown to significantly increase packet reception ratios in extremely adverse noise conditions. Multiple algorithm variations are presented and compared in terms of bit error rate (BER) performance and computational cost. In comparison to a theoretical system with perfect channel state information, the simulated BER performance of the best performing algorithm only requires an increase of 1.6 dB in signal-to-noise ratio (SNR) to exhibit the same performance. Finally, SDR implementations of the algorithms exhibit average SNR performance gains up to 4.7 dB when compared to commercially available hardware.