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The binary converted codeword c∈{0,1} n p is then binary phase shift keying (BPSK) modulated into an np dimensional modulated vector ({mathbf x}=left [x_{1},ldots,x_{np}right}right ]), where x j ∈{−1,1} for j∈[1,n p].
Denoting t ˜ the modulated vector corresponding to t ˜, the vectors t ˜ are transmitted during the next K time slot to the sensors using precoders W j).
We denote the corresponding quantized vector, modulated vector, channel noise vector, and received vector as b ′(t), c ′(t), e ′(t) and r ′(t), respectively.
Let r = [r1, r2, …,r n, rn+1, …] be a received soft-decision vector corresponding to the random modulated vector s = [s1, s2, …, s n, sn + 1, …].
The PAM channel input vector (in discrete-time baseband equivalent form) v=α F ε is superimposed on the L-dimensional digitally modulated vector u which is the result of applying entropy coding, channel coding, and modulation to M quantizer outputs whose errors are in ε.
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Combining the precoding, the user specific block-interleaved subcarrier mapping and the OFDM modulation, the elements,, of the modulated data vector in (6) can be written as (A.1).
In an SVD-based MIMO system, the relay RS i steers the modulated signal vector s i within the eigenspace spanned by the right singular vectors contained in E ̂ i t : s i t = E ̂ i t s i. (20).
In a SVD-based MIMO system, the R Si-1 steers the modulated signal vector, Si-1, within the eigenspace spanned by the right singular vectors contained in E ̂ i - 1 i t. S i - 1 t = E ̂ i - 1 i t S i - 1. (25).
The modulated signal vector is given by, where is a signal space mapper.
In the first hop, the modulated signal vector u s t ∈ C N s × 1 is transmitted to R1 relays.
Note that m b ζ ( l b ) ( l b = 1, 2,..., N M b ) represents a modulated chroma vector whose elements are shifted by amount ζ.
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