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Wireless CommunicationChapter: Analog and Digital
Transmission
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Comparison of MC-CDMA with uncoded OFDM is unfair in the sense that OFDM can exploit channel state information about fading subcarriers in its error correction decoder. In a MC-CDMA downlink, any user symbol is spread over all subcarriers. After despreading from many subcarriers, all symbols see a relatively fixed, non-fading channel. It is beyond the intentions of this paper to exhaustively evaluate practical coding strategies for OFDM and MC-CDMA. Instead we compare the potential of the systems based on "capacity" per subcarrier. Formally, the Shannon capacity of OFDM and MC-CDMA are identical because the weighting operation W and the inverse code matrix C-1 are invertable operations. This is understood from the Data Processing Theorem [26]: In order to achieve the full capacity of the link, the receiver must jointly detect MC-CDMA symbols and address the fact on the noise for the various user symbols is correlated if W uses different weights per subcarrier. However, practical receiver would not consider this. A loss of performance occurs (relative to ideally coded OFDM) in a system that extracts N MC-CDMA symbols and processes these as if they were transmitted over an AWGN, Linear Time Invariant, dispersion-free channel. It is reasonable to estimate the capacity per dimension of such system as 1/2 log2(1 + V P0Ts/N0). MATLAB
Lee [27] proposed to estimate the capacity of the Rayleigh fading channel as
Which can be expressed as [20, eq 4.331.2]
This expression assumes that the transmitter does not adapt is power per subcarrier to the instantaneous fades. It was later confirmed that this capacity can be achieved in a (broadcast) system where the transmitter also cannot adapt its coding strategy based on knowledge of the individual subcarrier states [28]. It is easy to understand that OFDM can achieve the same capacity as this Rayleigh fading channel.
Figure 7: Capacity per dimension versus EN/N0, no Doppler. MATLAB
For large SNR, we use E1(z) @ - g - lnz, so COFDM @ - g /(2 ln2) + 1/2 log2 (2 P0 Ts / N0), thus asymptotically, it has approximately 0.4 bit per dimension less capacity than for a fixed channel with the same SNR.
Figure 8: Capacity in bits per dimension for OFDM and MC-CDMA versus antenna speed. MATLAB
Figure 8 plots the capacity under Doppler spreads, using the same system parameters as Figure 6.
