  A systematic analysis of the advantages and challenges associated with the
satellite-based implementation of the high dimensional extended B92
(HD-Ext-B92) and high-dimensional BB84 (HD-BB84) protocol is analyzed. The
method used earlier for obtaining the key rate for the HD-Ext-B92 is modified
here and subsequently the variations of the key rate, probability distribution
of key rate (PDR), and quantum bit error rate (QBER) with respect to dimension
and noise parameter of a depolarizing channel is studied using the modified key
rate equation. Further, the variations of average key rate (per pulse) with
zenith angle and link length in different weather conditions in day and night
considering extremely low noise for dimension d=32 are investigated using
elliptic beam approximation. The effectiveness of the HD-(extended) protocols
used here in creating satellite-based quantum key distribution links (both
up-link and down-link) is established by appropriately modeling the atmosphere
and analyzing the variation of average key rates with the probability
distribution of the transmittance (PDT). The analysis performed here has
revealed that in higher dimensions, HD-BB84 outperforms HD-Ext-B92 in terms of
both key rate and noise tolerance. However, HD-BB84 experiences a more
pronounced saturation of QBER in high dimensions.
