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Signal Flow

Figure 20.1: Signal Flow Block Diagram

(data->symbols->samples, frequencies and all) The raw data bits are grouped to form message symbols in the mapper. Each such symbol can be regarded as a member of a finite alphabet set containing M members. For every two raw data bits, we map them to a symbol in the QPSK signal space as shown in Figure 20.2.

Figure 20.2: QPSK signal space

The symbols are then spread by means of a spreading sequence which is independant of the data. The symbols are thus coded over more signaling coordinates. This operation involves multiplying each symbol with a predetermined sequence of $\pm$1. The length of the $\pm$1 sequence is the spreading factor($SF$). So, when we are finished spreading, we have $SF$ times the number of symbols we started out with.

Then a midamble (training-sequence) is inserted into the signal. This sequence is known from the receiver that uses it to estimate the channel and to create the matched-filter.

Next a synchronisation sequence is added to the signal. This sequence is formed such as to be extracted at the receiver end with as less calculations as possible. Next, we upsample the symbols by four and pass them through a transmit filter. A root-raised cosine filter is used, whose Fourier transform is the square root of the commonly used raised-cosine spectrum. If a root-raised cosine filter is used at both the transmitter and the receiver, the product of the transfer functions will be a raised cosine that will give rise to an output having a minimal inter-symbol interference at the receiver.

The final step before transmission is to take the real part of the transmit filter output, since we can only transmit real values through a real-life channel.

For an application involving RF transmission, the next important step is bandpass modulation; it is required whenever the transmission medium will not support the propagation of pulse-like waveforms. The term bandpass is used to indicate that the baseband waveform is translated by a carrier wave to a frequency that is much larger than the spectral content waveform. The Figure 20.3 illustrates the upsampling, filtering and taking the real part operations.

Figure 20.3: Illustration of the upsampling and bandpass conversion in the Frequency Domain

At the receiver end, the demodulator provides frequency down-conversion for each bandpass waveform. Then the received samples are passed through a matched filter, which is matched to a cascade composed of the spreading sequence and the channel estimate. The matched filter produces points on the QPSK signal space in Figure 20.2. Due to channel effects, theses points will not likely lie exactly on one of the four signal points. Instead we will need to perform some sort of detection or demapping to guess which signal point was transmitted. This is done by the slicer, which output we want to be as close as possible to the raw data that we wanted to send at the beginning of the chain.