Wireless CommunicationChapter: Analog and Digital
Transmission

As is seen from the BER expression and (36), the MMSE cancellation of the MUI leads to a noise penalty. Two terms occur in the denominator, one is due to imperfect cancellation of MUI, the other is due to noise. The ICI is not actively cancelled, so its behaviour is similar to the noise. Figure 4, plots z and also the individual effects from MUI and noise, relative to the SNR per subcarrier. That is, it plots (M_{11}/ (M_{22}M_{11}^{2})) / (P_{T}T_{s}/N_{0} ) and (M_{11}T_{s}/ M_{02}N_{0}) / (P_{T}T_{s}/N_{0} ). It is seen that the noise penalty increases monotonically with the localmean SNR.
Figure 4: MCCDMA figure of merit z in dB versus the localmean SNR on Rayleigh channel. MATLAB
Figure 5 plots the localmean BER for BPSK versus the signaltonoise ratio (SNR) in a veryslowly changing Rayleighfading channel, without Doppler spread and ICI (v = 0). Curves (AWGN), (OFDM) and (3  MCCDMA) are theoretical results. Curve (AWGN) depicts the BER of BPSK in a channel without fading, using erfcÖ (E_{N}/N_{0}). Curve (OFDM) gives the BER for a narrowband Rayleigh fading channel (N = 1) which is the same as the localmean BER for OFDM, before any error correction. Moreover, it models MCCDMA with N = 1. Curve (3) is the localmean BER for MCCDMA for N ® ¥ . Curve (1) and (2) are Monte Carlo simulations for a system with N is 8 and 64 subcarriers, respectively.
Curves (4) and (5) for correlated Rayleigh fading have been simulated in the frequency domain. All subcarrier amplitudes are known to be zeromean complex Gaussian with covariance matrix G [1726
(37)
with
_{, (38)}
where T_{RMS} is the delay spread of the radio channel. In a MonteCarlo simulation we generated channels from an i.i.d vector of complex Gaussian random variables G, with unity variance and length N. This vector was then multiplied by an NbyN matrix A, such that AA^{H} = G , to create diag(H) = [b _{0,0} b _{1,1 }, .. ,b _{n,n }] = A G, and b _{m,n} = 0 for n ¹ m (no Doppler). Then, the weight vector diag(W) was determined from diag(H). This results in amplitudes for the wanted signal (x_{0}), amplitudes for the MUI and a noise amplification term. So the BER for this particular channel can be calculated. Average BER's have been obtained by repeating this process for different channels G.
Figure 5: Localmean average BER versus SignaltoNoise ratio. Theory: (3, AWGN, OFDM) and simulations (1, 2, 4, 5). ("AWGN"): BPSK, nofading, AWGN ("OFDM"): (1): N = 8, uncorrelated fading, (2): N = 8, highly correlated fading, (3): Infinitely many subcarriers, (4) N = 8, highly correlated fading, (4) N = 8, lightly correlated fading
The average BER versus the SNR for correlated fading was also simulated for
the case of N = 8with T_{RMS}/T_{s}.= 0.001 and 0.125, in curve (4) and (5), respectively. Results show that the assumption of I.I.D. fading at the subcarriers is optimistic.
The differences amoung the curves (3) and those for finite N are due to the fact that the SNR after despreading still contains fading. The slope of the curve for large SNR is determined mainly by the 'resolvable' number of independently fading channel components, which is approximately equal to min(N, T_{RMS}/T_{s}.+1).
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The effect of Doppler spreading at 4 GHz is introduced in Figure 7. Here we consider a system with (infinitely) many subcarriers. We inserted typical values for DTTB but modified it to MCCDMA instead of the standardized OFDM. The frame duration is 896 microseconds, with an FFT size of 8192. This corresponds to a subcarrier spacing of f_{s} = 1.17 kHz and a data rate of 9.14 Msymbols/s. Figure 7 shows the localmean BER versus antenna speeds v for E_{b}/N_{0} of 10, 20 and 30 dB. While MCCDMA appears to largely outperform uncoded OFDM.