## 3 Multi-Modal Distribution of RSSI
### Experiment  
A simple experiment is conducted to investigate how exactly the quantity of carriers is influencing the signal strength. The experiment involves two USRP B200 mini devices [32]. It is a small-scale SDR platform, used in combination with the GNU Radio software [33] installed on a host computer. GNU Radio provides an example implementation of the OFDM transceiver, which is used to generate the OFDM signals for this experiment. The two USRPs are used as the transmitter and receiver, respectively. To eliminate the possibility of fading, the receiver is connected via a coaxial cable to the transmitter with a 30-dB attenuator in between. Figure 3 illustrates the OFDM packet structure in GNU Radio, where each row denotes an OFDM symbol in time and each column denotes a subcarrier. There are 64 subcarriers in total, among which  
Figure 1: An example RSSI trace of a discontinuously-transmitted signal (**left**) and the corresponding PDF (**right**). Figure 2: An example RSSI trace of the signal modulated with a variable amount of subcarriers (**left**) and the corresponding PDF (**right**). 52 are occupied, while the rest are idle. The first two OFDM symbols are used for preamble transmission (indicated by yellow grids in Figure 3); the third symbol is used to transmit the header of the packet; while the remaining symbols contain the payload data. Except for the preamble, all of the OFDM symbols contain four pilot carriers, as indicated by the red grids. The packets are successfully decoded by the receiver, which guarantees that the signal is properly transmitted. The simple OFDM transmitter does not have medium access control; hence, packets are transmitted continuously. Furthermore, the packet size is static, and there are no bits padded at the end of a packet. This means that the number of occupied carriers in the last OFDM symbol of a packet is dependent on the payload size. By applying the payload size of 123, 127 and 131 bytes, there are 12, 28 and 44 subcarriers occupied in the last OFDM symbol, respectively. The samples are transmitted at the rate of 200 kHz. The same rate is used to capture samples by the receiver side. An RSSI is calculated with Equation (1) for \(N\) = 160. The RSSI traces are shown in the first row of Figure 4. These plots illustrate that the RSSI fluctuates periodically over time, and the period corresponds to the duration of a single packet (including the header and preamble, a packet contains 14 OFDM symbols, each symbol has 80 samples, including 16 samples for cyclic prefix, hence a packet lasts for 80 \(\times\) 14/200 kHz = 5.6 ms). It is observed that the signal strength of the last OFDM symbol in a packet is weaker than the rest of the packets. Additionally, the magnitude of variations becomes smaller when more subcarriers are occupied. The same conclusion can be drawn from the histogram in the second row of Figure 4. The histograms of \"12 occupied carriers\" and \"28 occupied carriers\" exhibit bimodal distributions, where the peak on the left side and that right side represent the signal strength of the last OFDM symbol and the remainder of the packet, respectively. The peak on the left side gradually moves towards the main peak with the increment of the number of occupied carriers and eventually merges with the main peak, as shown in the normalized histogram for the case of \"44 occupied carriers\". In conclusion, this simple experiment proves that for multi-carrier modulated signals, the more carriers are occupied, the stronger the signal strength gets. However, unlike the situation in non-continuous transmission, the peaks are situated relatively close to each other (only a few dB difference in between). This is because the impact on signal strength of the amount of subcarriers is significantly smaller than the impact of burst transmission. A multi-modal RSSI distribution may be formed when more flexible subcarrier allocation schemes are applied, such as the usage of resource block in LTE, which will be explained in the following sections.