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The half symbol delay applied on the imaginary branch is compensated so that both the real and imaginary signals are received synchronously when downsampling by M to reach back the symbol rate 1/T s.
Saltzberg in [16] showed that by designing a transmit pulse-shape in a multichannel QAM system, and by introducing a half symbol space delay between the in-phase and quadrature components of QAM symbols, it is possible to achieve a baud-rate spacing between adjacent subcarrier channels and still recover the information symbol free of ISI and ICI.
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An introduced orthogonality condition between subcarriers guarantees that the transmitted symbols arrive at the receiver free of ISI and ICI, which is achieved through time staggering the in-phase and quadrature components of the subcarrier symbols by half a symbol period.
First, we introduce an intentional half-symbol delay between the two users.
The receiver structure proposed in [8] is tailored towards implementation of the half-symbol spaced fractionally spaced equalizers.
The best performance would be obtained with just the half-symbol delay and no random delays; however, this is not a realistic case.
Next, to show the advantage of the intentional half-symbol delay, we consider a case without intentional delay, with random user delays only.
However, with the introduction of OQAM modulation, also the half-symbol shifts of the pulse shaping filter shall not produce an abrupt signal change and hence the pulse shaping filter is required to vanish at every half-subsymbol time.
The product TF is set to 1.07 for the first two waveforms, and K=1.07 is used for pulse-shaped OFDM, while OFDM with subband-filtering employs a half-symbol length FIR filter.
As before, one user is delayed by a half-symbol interval, and in addition, a random delay is added to both users to model random delays introduced at the transmitter.
The real symbol values, obtained alternatingly as real and imaginary parts of complex QAM symbols, are denoted as ak,l and τ0, respectively, is the corresponding half-symbol duration.
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