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During the next time slot, the modulated symbol of XOR version will then be transmitted.
∀k l ∈Θ, where (x_{i,k_{l}}) being the corresponding modulated symbol of (c_{i,k_{l}}).
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This block yields d ̂ ∈ C K ~ N o = vec D ̂ eq ( O ) T, row vector carrying the received version of the digitally modulated symbol vector d, of size K ~ N o.
A parallel-to-serial operation is performed on D ̂ eq ( C ) to yield d ̂ = vec D ̂ eq ( C ) T ∈ C J ~ L, row vector carrying the received version of the digitally modulated symbol vector d, of size J ~ L, ready to be fed to the constellation demapper.
In coded SM-MIMO systems, the soft information consists of two parts, i.e., the soft information of antenna index bits and the soft information of modulated symbol bits.
Considering the code rate R c and the number of bits per modulated symbol M, the relation between the number of double binary coded symbols (NCSymb) and the corresponding number of modulated symbols (NMSymb) can be written as follows.
where is the index of the OFDM symbol, is the frequency domain th modulated symbol,, and is the total number of subcarriers.
where v l is the lth bit of each received modulated symbol.
In order to gain resilience against error bursts, the resulting sequence is interleaved using an S-random interleaver π2 with S = N / 4. Punctured and interleaved bits denoted by v i are then gray mapped to complex channel symbols s q chosen from a 2 M -ary constellation X, where M is the number of bits per modulated symbol.
Without loss of generality, we define ({Lambda _{p}^{A}}) and ({Lambda _{p}^{S}}) as the a posterior LLRs of antenna index bits and modulated symbol bits, respectively.
The th user data-modulated symbol vector is represented by for.
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