  This paper presents a comprehensive analysis and performance enhancement of
short block length channel detection incorporating training information. The
current communication systems' short block length channel detection typically
consists of least squares channel estimation followed by quasi-coherent
detection. By investigating the receiver structure, specifically the
estimator-correlator, we show that the non-coherent term, often disregarded in
conventional detection metrics, results in significant losses in performance
and sensitivity in typical operating regimes of 5G and 6G systems. A comparison
with the fully non-coherent receiver in multi-antenna configurations reveals
substantial losses in low spectral efficiency operating areas. Additionally, we
demonstrate that by employing an adaptive DMRS-data power adjustment, it is
possible to reduce the performance loss gap, which is amenable to a more
sensitive quasi-coherent receiver. However, both of the aforementioned ML
detection strategies can result in substantial computational complexity when
processing long bit-length codes. We propose an approach to tackle this
challenge by introducing the principle of block or segment coding using
First-Order RM Codes, which is amenable to low-cost decoding through
block-based fast Hadamard transforms. The Block-based FHT has demonstrated to
be cost-efficient with regards to decoding time, as it evolves from quadric to
quasi-linear complexity with a manageable decline in performance. Additionally,
by incorporating an adaptive DMRS-data power adjustment technique, we are able
to bridge/reduce the performance gap with respect to the conventional maximum
likelihood receiver and attain high sensitivity, leading to a good trade-off
between performance and complexity to efficiently handle small payloads.
