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

Signal Constellation, Mapping, De-Mapping, and Equalization 18964-QAMQ4-QAMQ7111011 110011 100011 101011001011 000011 010011 01101110100I5111010 110010 100010 101010001010 000010 010010 01101011−1−113111000 110000 100000 101000001000 000000 010000 01100016-QAM1101 10011100 1000−3 −131Q0001 01010000 01001 3I1111001 110001 100001 101001−3111100 110100 100100 101100−5111110 110110 100110 101110001001 000001 010001 011001 I−7 −5 −3 −1 1 3 5 7−1111101 110101 100101 101101 001101 000101 010101 011101001100 000100 010100 011100001110 000110 010110 0111101110 10101111 1011−1−30010 01100011 0111b 0 b 1 b 2 b 3111111−7110111 100111 10111101 b0 b 1b 0 b 1 b 2 b 3 b 4 b 5001111 000111 010111 011111Figure 4-50M-QAM signal constellation (4-, 16- and 64-QAM)Table 4-7 Modulation-dependentnormalization factor K MODModulationK MOD4-QAM 116-QAM 1/ √ 564-QAM 1/ √ 214.5.2 Equalization and De-MappingThe channel estimation unit in the receiver provides for each sub-carrier n an estimate ofthe channel transfer function H n = a n e jϕ n. In mobile communications, each sub-carrieris attenuated (or amplified) by a Rayleigh or Ricean distributed variable a n =|H n | and isphase distorted by ϕ n . Therefore, after FFT operation a correction of the amplitude andthe phase of each sub-carrier is required. This can be done by a simple channel inversion,i.e. multiplying each sub-carrier by 1/H n . Since each sub-carrier suffers also from noise,this channel correction leads to a noise amplification for small values of a n . To counteractthis effect, the SNR value γ n = 4|H n | 2 /σn 2 of each sub-carrier (where σ n 2 is the noisevariance at sub-carrier n) should be considered for soft metric estimation. Moreover,in order to provide soft information for the channel decoder, i.e. Viterbi decoder, thereceived channel corrected data (after FFT and equalization with CSI coefficients) should