Pulse shaping and spectrum in LTE

RF engineering is a trade off between: required radio spectrum (bandwidth), speed of data transmission (bit rates) and complexity of implementation. The pulse form used to modulate complex data symbols to the radio carrier frequency is the major element of this story.

Over the years several pulse forms and their associated pulse shaping filters have been studied and used in private and commercial radio systems. GSM for instance uses GMSK (Gaussian Minimum Shift Keying) filter that produces pulses that are close to sin/cosine waveforms with a Gaussian curve as amplitude, WCDMA uses root raised cosine roll off pulse shaping filters.

Two characteristics are important for a pulse: the time domain presentation and the frequency domain presentation. In the time domain one can recognize “how long the symbol pulses on air” will be and in the frequency domain the required spectrum in terms of bandwidth can be studied. One of the most simple time-domain pulses is the rectangular pulse. It simply jumps at time t=0 to its maximum amplitude and after the pulse duration TS it jumps back to 0. This pulse form has two major advantages.

First it is simple to implement, there is no complex filter system required to detect such pulses and to generate them. Second the pulse has a clearly defined duration. After TS the signal amplitude is zero, this is a major advantage in case of multi-path propagation environments as it simplifies handling of inter-symbol interference. Furthermore if the next symbol starts after the first pulse finished, there will be no inter-symbol interference in a non-multi-path environment.

For a receiver this means, that there are no complicated and expensive inter-symbol interference cancellation mechanisms required. A disadvantage of the rectangular pulse is, that it allocates a quite huge spectrum.

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