When
we talk about the cell size, we usually think of RF coverage first. The
cell radius is also related to the parameter configuration for the
random access procedure, such as the preamble format and cyclic shift.
Let's look at the preamble format here.
In
LTE, the random access procedure is nonsynchronized, which means the
UE which initiates the random access procedure is not uplink
synchronized yet (It is, however, already downlink synchronized). So
the random access procedure of this UE should not interfere the uplink
transmission of other already uplink synchronized UEs.
Figure
1 shows the mapping of the PRACH (Physical Random Access Channel) to
physical resources. The PRACH occupies 6 PRBs in the frequency domain
and spans 1 or 2 or 3 subframes in the time domain, depending on the
specific preamble format. In the frequency domain, several subcarriers
at both ends of the 6 PRBs are not used to avoid interference with the
adjacent PUCCH/PUSCH. In the time domain, the cyclic prefix (CP) and
guard time (GT) are used to avoid interference with the previous and
next subframes. As it turns out, the GT determines the maximum cell
radius.
How is the GT related to cell radius? Assume there are 3 UEs in the cell, located near the center of the cell, in the middle of the cell, and at the cell edge, respectively. Assume that all of these 3 UEs are not yet UL synchronized and are about to perform a random access. The RACH configuration information is transmitted in the DL. All UEs listen to it and send RACH preambles in the same subframe. For UE3 at the cell edge, its RA preamble arrives at the eNB later than UE1's preamble. The maximum delay between UE3 and UE1 is the round trip delay (RTD) between the eNB and the cell edge, which is determined by the guard time in the expected preamble receive window at the eNB. We can calculate the cell radius based on the GT. The Preamble format is defined in LTE (3GPP TS 36.211, section 5.7). Where Ts is the basic time unit in LTE, Ts = 1/(15000*2048) s = 3.25521 X 10^(5) ms. First, we get the guard time from the number of subframes occupied by the PRACH, the time to transmit cyclic shift, and the time to transmit preamble sequence. In figure 3, it is obvious that the preamble format 0 and preamble format 1 have different guard times, which means they support different maximum cell sizes. We can derive the cell radius from the guard time. 

We
have calculated the cell radius for preamble format 0 and preamble
format 1 in the spreadsheet below, where the equation (1) in Figure 3 is
used to calculate guard time and the equation (2) in Figure 4 is used
to calculate cell radius. Please calculate the cell radius for Format 2
and 3.
