Bit interleaved chirp spread spectrum coded modulations with iterative decoding based on LDPC codes for coherent and non-coherent regimes

In this paper, we investigate on bit-interleaved chirp spread spectrum (CSS) coded modulations with iterative decoding (ID) based on low-density parity-check (LDPC) codes. First, we study coded modulation (CM) and bit-interleaved coded modulation (BICM) capacities of CSS based LoRa-like waveforms over Gaussian and Rayleigh fading channels for both coherent and non-coherent receivers. LoRa-like waveforms being by essence nonlinear nonbinary memoryless continuous-phase modulations, this study shows that optimized BICM schemes with iterative decoding are mandatory to close the non negligible gap to the CM capacity when outer binary error-correcting schemes are used. Then, we design LDPC codes, optimized for BICM-ID CSS modulation schemes using both coherent and non coherent receivers. In particular, we show that one has to be careful when using optimized codes for the different regimes. Indeed, unstructured LDPC codes optimized for the coherent regime may be asymptotically non stable when used in the non coherent regime. On the contrary, optimized codes for the non coherent case are always stable in the coherent regime with negligible to fair loss of performance. Finally, designed sparse-graph based BICM-ID CSS modulation schemes show significant performance improvement over classical or advanced LoRa legacy CSS waveforms at finite length.