Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

MC-CDMA 792.1.8.1 Log-Likelihood Ratio for OFDM SystemsThe LLR is defined as( )p(w | b =+1)Ɣ = ln, (2.82)p(w | b =−1)which is the logarithm of the ratio between the likelihood functions p(w|b =+1) andp(w|b =−1). The LLR can take on values in the interval [−∞, +∞]. With flat fadingH l,l on the sub-carriers and in the presence of AWGN, the log-likelihood ratio for OFDMsystems results inƔ = 4| H l,l |σ 2 w. (2.83)2.1.8.2 Log-Likelihood Ratio for MC-CDMA SystemsSince in MC-CDMA systems a coded bit b (k) is transmitted in parallel on L sub-carriers,where each sub-carrier may be affected by both independent fading and multiple accessinterference, the LLR for OFDM systems is not applicable for MC-CDMA systems. TheLLR for MC-CDMA systems is presented in the next sub-section.Single-User DetectionA received MC-CDMA data symbol after single-user detection results in the soft decidedvalueL−1∑v (k) =l=0L−1∑= d (k) ∣⎛C (k)∗lG l,l∣C (k)ll=0∑⎝H l,lK−1g=0∣ 2 G l,l H l,l} {{ }desired symbold (g) C (g)l∑K−1+g≠kg=0+ N l⎞⎠∑d (g) L−1l=0G l,l H l,l C (g)lC (k)∗l} {{ }MAI∑L−1+l=0N l G l,l C (k)∗l} {{ }noise. (2.84)Since a frequency interleaver is applied, the L complex-valued fading factors H l,l affectingd (k) can be assumed to be independent. Thus, for sufficiently long spreading codes, themultiple access interference (MAI) can be considered to be additive zero-mean Gaussiannoise according to the central limit theorem. The noise term can also be considered asadditive zero-mean Gaussian noise. The attenuation of the transmitted data symbol d (k)is the magnitude of the sum of the equalized channel coefficients G l,l H l,l of the L subcarriersused for the transmission of d (k) , weighted with |C (k)l| 2 . The symbol de-mapperdelivers the real-valued soft decided value w (k) . According to Equation (2.83), the LLRfor MC-CDMA systems can be calculated as∣ L−1∑∣∣∣∣2|C (k)∣l| 2 G l,l H l,lƔ (k) l=0=σMAI 2 + σ noise2 w (k) . (2.85)