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Then M is additive.
We say that M is additive if (M varnothing) = { 0 }) and M(A cup B) = M(A),dot, M B) for all disjoint sets A, B in (mathfrak{A}).
Note that in this section, the time-discrete transmitted OFDM signal is s(m), which is usually composed of a number of consecutive OFDM symbols, and z(m) is additive Gaussian white noise while r(m) is the received signal sequence.
This issue can be described as recovering an unknown signal x of a high-dimension from a low-dimensional signal y having a limited set of measurements: boldsymbol{y}=boldsymbol{Mx}+boldsymbol{e} (1 where M ∈ ℜ m × d is a known linear operator and e ∈ ℜ m is additive noise bounded by ( parallel boldsymbol{e}{parallel}_2^2le {varepsilon}^2 ).
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where (mathbf {y} in mathbb {C}^{M}) is the measurement vector, (mathbf {A} in mathbb {R}^{M times N}) is the fixed sensing matrix, and (mathbf {w} in mathbb {C}^{M}) is additive measurement noise.
With the chosen relay, the m th user receives y m II = P BS h BS, m x s A + P RS h l ⋆, m β y l ⋆ + w m II in the second phase, where w m II is additive noise of variance σ w 2. The interfering symbols sBat users in cluster A can be cancelled using the symbols decoded in the first phase [11].
where s l (t) is the lth signal source, n m (t) is additive white Gaussian noise at the mth antenna, v m =(m−1)d/c, where d is the distance between adjacent antennas, and c is the speed of light.
where the nonzero entries of (mathbf {x}in mathbb {C}^{N}) store the complex-valued channel coefficients and dictate which columns in S are selected, and with (mathbf {w}in mathbb {C}^{M}) being additive Gaussian measurement noise with i.i.d.i.d
where C m,k [t,n] is the channel frequency response, s k [ t,n] is the transmitted (quadrature amplitude modulation (QAM)) pilot tone corresponding to user k, and v m [ t,n] is additive white Gaussian noise (AWGN).
{ c i } i = 1 F are complex amplitudes and e(m) is an additive noise.
and n(m) is the additive white Gaussian noise (AWGN) with zero mean and covariance matrix σ n 2 I V.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com