3.1 MC-CDMA System Analysis
CHAPTER 3
SYSTEM MODEL
3.1 MC-CDMA System model.
What is MC-CDMA: - MC-CDMA is a digital modulation technique where a single data symbol is transmitted at multiple narrowband subcarrier encoded with a phase offset of 0 and π instead based on a spreading code. The narrowband subcarrier are generated using BPSK modulated signals, each at different frequencies which at baseband are at multiples of a harmonic frequency, 1/T_b. Consequently, the subcarriers are orthogonal to each other at baseband, and the component at each subcarrier may be filtered out by modulating the received signal with the frequency corresponding to the particular subcarrier of interest and integrating over a symbol duration. The orthogonality between the subcarrier is maintained …show more content…
b_k (m)= m^th data bit
{C_(k,n) }_(n=1)^N= Spreading sequence θ_k= random carrier phase of user K. k_(T_b )= rectangular pulse defined in [0,T_b] ω_n=ω_c+2πnF/T_b is n^thsubcarrier, while ω_c= radio frequency, F = positive integer.
3.1.2 MC-CDMA Receiver Model:
When there is K active user, the received signal is:
r(t)=∑_(m=-∞)^∞▒√(2p/Nb) ∑_(k=1)^k▒〖b_k (m)〗 u_(T_b ) (t-m〖hT〗_b ) ∑_(n=1)^N▒〖β_(k,n) C〗_(k,n) cos(ω_n t+Ф_(k,n) )+n(t) (2)
Ф_(k,n)=θ_k+φ_(k,n) where, β_(k,n) and φ_(k,n)are assumed to be independent and identically distributed (i.i.d) for different k or n.
n(t)= AWGN with double sided power spectral density N_0/2.
2/T_b cos(2πf_c t+ϕ_0,0)c_0 [0] d_0,0
r(t)
2/T_b cos(2πf_c t+2πFt/T_b +ϕ_0,1)c_0 [1] 〖 d〗_0,1
2/T_b cos(2πf_c t+(2πF(N-1)t)/T_b +ϕ_(0,N-1))c_0 [N-1] 〖 d〗_(0,N-1)
Figure 3.2 MC-CDMA Receiver …show more content…
So, A_l=e^(-j∅_l )
Thus, (6) can be representing after some simplification as follows: d ̂_1 (u)=∑_(k=2)^K▒∑_(m=1)^M▒〖∑_(l=1)^M▒〖∑_(i=0)^∞▒√(2P/M) b_k (i+u) C_k (m) R_g^ml (iT_s ) C_1 (l) 〗 ∝_m e^(〖j∅〗_m ) A_l + ∑_(m=1)^M▒〖∑_(l=1)^M▒〖∑_(i=0)^∞▒√(2P/M) b_1 (i+u) C_1 (m) R_g^ml (iT_s ) C_1 (l) 〗 ∝_m e^(〖j∅〗_m ) A_l+〗 ∑_(l=1)^M▒〖∑_(i=1)^∞▒√(2P/M) b_1 (i+u) R_g^ml (iT_s ) 〗 ∝_d+∑_(l=1)^M▒√(2P/M) d_1 (u) α_1+ ∑_(l=1)^M▒〖C_1 (l) A_l 〗 ∫▒〖n(t)〖g_l〗^* (-uT_s)〗 (7)〗 d ̂_1 (u)=I_1+I_2+I_3+I_4+I_5
I_3=Interference from the same sub-channel l and the same user k=1.
I_2=Interference from the other subcarrier and same user.
I_1=Interference from the other user
SYSTEM MODEL
3.1 MC-CDMA System model.
What is MC-CDMA: - MC-CDMA is a digital modulation technique where a single data symbol is transmitted at multiple narrowband subcarrier encoded with a phase offset of 0 and π instead based on a spreading code. The narrowband subcarrier are generated using BPSK modulated signals, each at different frequencies which at baseband are at multiples of a harmonic frequency, 1/T_b. Consequently, the subcarriers are orthogonal to each other at baseband, and the component at each subcarrier may be filtered out by modulating the received signal with the frequency corresponding to the particular subcarrier of interest and integrating over a symbol duration. The orthogonality between the subcarrier is maintained …show more content…
b_k (m)= m^th data bit
{C_(k,n) }_(n=1)^N= Spreading sequence θ_k= random carrier phase of user K. k_(T_b )= rectangular pulse defined in [0,T_b] ω_n=ω_c+2πnF/T_b is n^thsubcarrier, while ω_c= radio frequency, F = positive integer.
3.1.2 MC-CDMA Receiver Model:
When there is K active user, the received signal is:
r(t)=∑_(m=-∞)^∞▒√(2p/Nb) ∑_(k=1)^k▒〖b_k (m)〗 u_(T_b ) (t-m〖hT〗_b ) ∑_(n=1)^N▒〖β_(k,n) C〗_(k,n) cos(ω_n t+Ф_(k,n) )+n(t) (2)
Ф_(k,n)=θ_k+φ_(k,n) where, β_(k,n) and φ_(k,n)are assumed to be independent and identically distributed (i.i.d) for different k or n.
n(t)= AWGN with double sided power spectral density N_0/2.
2/T_b cos(2πf_c t+ϕ_0,0)c_0 [0] d_0,0
r(t)
2/T_b cos(2πf_c t+2πFt/T_b +ϕ_0,1)c_0 [1] 〖 d〗_0,1
2/T_b cos(2πf_c t+(2πF(N-1)t)/T_b +ϕ_(0,N-1))c_0 [N-1] 〖 d〗_(0,N-1)
Figure 3.2 MC-CDMA Receiver …show more content…
So, A_l=e^(-j∅_l )
Thus, (6) can be representing after some simplification as follows: d ̂_1 (u)=∑_(k=2)^K▒∑_(m=1)^M▒〖∑_(l=1)^M▒〖∑_(i=0)^∞▒√(2P/M) b_k (i+u) C_k (m) R_g^ml (iT_s ) C_1 (l) 〗 ∝_m e^(〖j∅〗_m ) A_l + ∑_(m=1)^M▒〖∑_(l=1)^M▒〖∑_(i=0)^∞▒√(2P/M) b_1 (i+u) C_1 (m) R_g^ml (iT_s ) C_1 (l) 〗 ∝_m e^(〖j∅〗_m ) A_l+〗 ∑_(l=1)^M▒〖∑_(i=1)^∞▒√(2P/M) b_1 (i+u) R_g^ml (iT_s ) 〗 ∝_d+∑_(l=1)^M▒√(2P/M) d_1 (u) α_1+ ∑_(l=1)^M▒〖C_1 (l) A_l 〗 ∫▒〖n(t)〖g_l〗^* (-uT_s)〗 (7)〗 d ̂_1 (u)=I_1+I_2+I_3+I_4+I_5
I_3=Interference from the same sub-channel l and the same user k=1.
I_2=Interference from the other subcarrier and same user.
I_1=Interference from the other user