carrier and user k g k l is the value of the linear equalization coefficient associated with the l th sub carrier and with the user k u0125 l is the estimate of the coefficient of the transmission channel for the l th sub carrier u03c3 noise 2 is the variance of the noise and u03c3 mai is the variance of the complex multiple access interference s q q 0 and s q q 1 are two complementary partitions of complex symbols containing respectively the symbols of the constellation with a u201c 0 u201d in position q q and the symbols of the constellation with a u201c 1 u201d in position q q from equation 24 can be obtained the exact formula for the llr for a 4 qam modulation generalized to the case of different powers where y k i corresponds to the real part of the complex symbol received after equalization and despreading the same relation applies for the imaginary part namely where y k q corresponds to the imaginary part of the complex symbol received after equalization and despreading however the exact formula for the llr given by equation 24 and even its application to the 4 qam modulation given by equation 25 may turn out to be difficult to implement in practice indeed the two terms complex multiple access interference and noise need to be estimated and to do this the receiver must be aware of all the active cdma codes moreover these equations use the law of large numbers to calculate the mathematical expectations this possibly no longer being valid when the length of the spreading codes becomes relatively small this is why the.