The complex baseband receive signal r(t) corresponds to the complex transmit signal x t), which is given as a weighted sum of time shifted transmit pulses h(t), disturbed by additive white Gaussian noise n(t).
We consider a special case with the transmit pulse h(t)=hcos(t), a receive filter with g(t)=δ(t) and n(t)=0, such that the input signal of the ADC is x t), which is a weighted sum of time shifted transmit pulses h(t).
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In these systems, different PN sequences (which are orthogonal to one another or cyclically shifted) are transmitted at each transmit antenna for channel estimation, which are modulated by BPSK in the same phase angle.
Recently, research studies on 2 × 1 multi input-single output (MISO) TDS-OFDM systems have been conducted, and different PN sequences (which are orthogonal to one another or cyclically shifted) are transmitted at each transmit antenna for channel estimation, which are modulated by binary phase shift keying in the same phase angle.
At each transmit antenna, the PN sequences, which are orthogonal to one another or cyclically shifted, are transmitted by BPSK modulation in the same phase angle for MISO channel estimation [5 7].
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In fact, J r time-shifts the transmitted signals and extends them up to the maximum received signal duration (by zero-padding) and it is defined as {boldsymbol{J}}_r=left[begin{array}{c}hfill {0}_{left( r-1right times r-1right times {boL}symbol{I}}_L hfill hfill {boldsymbol{}_r- rrI}ht)times L}_Lill end{array}righfill
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