The Fourier Transform is often used in Communication and Signal Processing to find the spectral content of a time-domain signal. The most common example is that of a sinusoid in the time domain, resulting in a sharply peaked signal in the frequency domain, also known as a delta function. A rectangular pulse in the time domain has a more complicated frequency domain equivalent, a sinc function. A rectangular pulse may be thought of as a combination of many sinusoids, hence its frequency domain equivalent is not that straightforward.

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# LTE Resource Allocation in Time-Frequency Plane

The LTE standard defines a resource allocation structure in time and frequency domains. If the spatial domain is also considered the resource allocation structure actually becomes a 3-dimensional arrangment. We will ignore the spatial domain for now and focus on the time-frequency plane.

In the time domain the LTE transmissions are organized into frames of 10 msec length. Each frame is composed of 10 subframes of 1 msec duration. Each subframe is made up of two equal sized slots of 0.5 msec each. Each slot is composed of 7 or 6 OFDM symbols depending upon whether a short or long Cyclic Prefix (CP) has been used. In the case of a short CP the CP has a duration of 5.21 usec for the first symbol and 4.69 usec for the remaining 6 symbols such that the total slot duration is 0.5 msec. For the long CP the CP has a duration of 16.67 usec for all 6 symbols. The useful symbol duration is fixed at 66.67 usec.

Short CP

1*(5.21+66.67)+6*(4.69+66.67)=500 usec

Long CP

6*(16.67+66.67)=500 usec

In the frequency domain the subcarriers are spaced at 15kHz giving a useful symbol duration of 1/15000=66.67 usec after the IFFT operation. A group of 12 subcarriers (12*15=180 kHz) over one time slot (0.5 msec) is referred to as a Resource Block (RB). With 1200 subcarriers available over a 20 MHz bandwidth the LTE transmitter has 100 RBs available over one time slot.

The smallest unit of resource is termed as the Resource Element which is composed of one subcarrier and one OFDM symbol. Thus an RB has 12×7=84 and 12×6=72 Resource Elements for short and long CP respectively.

Note:

1. The total number of subcarriers over a 20 MHz bandwidth is calculated as 20000 kHz/15 kHz = 1333 subcarriers, which is much greater than 1200. This is because all subcarriers are not used and some subcarriers act as guard carriers at the edges.

2. Longer CP is useful in environments with long delay spread.