For LS channel estimation, we used two different rectangular pilot constellations, i.e., selected uniformly 6.5% and 12.5% of all symbols for pilots, respectively.
The expressions in Equations (40) and (41) apply to a rectangular QAM constellation when k is even and k is odd, respectively.
For non-rectangular QAM signal constellations (b i ∈ 3, 5, 7,...), the SNR gap is given by (19) without the equality [45].
Here, the -ary rectangular QAM signal constellation is assumed to be formed by drawing the inphase and quadrature components from the independent -ary pulse amplitude modulation (PAM) and -ary PAM, respectively, where,,,, and.
Traditionally, in point-to-point systems the decoding complexity is reduced by using suboptimal constellations such as rectangular QAM.
This is an extension of our previous work only valid for 2×2 MIMO system and 4-QAM modulation [21], using the pdf statistic of minimum Euclidean distance of the received constellation of a precoded MIMO system with rectangular QAM modulations.
The PAPR reduction is performed here via expanding the constellation points, the so-called polar or rectangular mapping and accordingly the corresponding de-mapping is required at the receiver [6].
Assuming equi-probable symbol transmission of a rectangular M-QAM consisting of direct product of M i -PAM constellation M = M1·M2, the average power is E s = ( M 1 2 + M 2 2 − 2 ) d 2 / 12.
Its vast, tall rectangular block of space is framed by high windows, a ceiling embellished with constellations, and double staircases at either end.
where a l = 0.2 and c l is a constellation specific constant defined as[4] c l = 6 5 · 2 l − 4 for rectangular QAM ( odd l ) 3 2 ( 2 l − 1 ) for square QAM ( even l ).
