# Relationship between data rate, bandwidth, sensitivity etc

WiSense CC1101 radio based sensor nodes operate at 38400 bps in the 865 – 867 Mhz band (which is license free in India).

Channel bandwidth is the region of the RF spectrum occupied by a channel. The channel bandwidth required by WiSense CC1101 radio based nodes is around 113 KHz. Channel bandwidth depends on the data rate and the modulation used (2-GFSK in our case).  You can configure a WiSense CC1101 based radio network to operate at any one of 9 different channels in the 865-867 MHz band (from 865.199829 MHz to 866.799437 MHz). You can see that the  channel separation (we have chosen to use) is around 200 KHz.

The receiver bandwidth is a major factor in determining the noise floor of a channel.

Noise floor (in dBm) = –174 + 10 log10 (receiver-bandwidth)

At 113 kHz, the noise floor will be -174 + 10 log10(113000) -> -123.5 dBm.  A radio can demodulate a received signal only if the received signal’s strength (RSSI) is above the noise floor of the channel.

Receiver sensitivity of an RF receiver is the lowest power signal which it can successfully receive. It is specified in dBm. Here’s the definition from Wikipedia – “The dBm is an abbreviation for the power ratio in decibels (dB) of the measured power referenced to one milliwatt (mW)”.

Power in dBm = 10 * (log10((Power in milli-watts) / (1 milli-watt)))

If received signal power is 1 milli-watt, the corresponding power level in dBms is (10 * (log10 (1 / 1))) -> 0 dBm. If received signal power is say 1 micro-watt, the corresponding power level in dBms is (10 * (log10 ((10^-3) / 1))) -> – 30 dBm.

A sensitivity of -112 dBm means that the CC1101 can successfully receive a signal whose power is as low as 6.309 * 10^-12 milli-watts !!!!.

Receiver sensitivity is specified at some data rate (in kilo-bits per /sec) and packet error rate (1 % in our case). 1% packet error rate implies that the receiver cannot loose more than 1 packet for every 100 packets sent by the transmitter.

Note the relationships listed below.

1. Network throughput depends on the raw data rate (among other things).
2. Channel bandwidth depends on the raw data rate.
3. Receiver sensitivity depends on the channel bandwidth.
4. Channel bandwidth determines the noise floor and thereby the receiver sensitivity.

According to the CC1101 spec, the CC1101’s sensitivity at 38.4 Kbps (at 868 MHz) is -104 dBm.

Data Rate                       Receiver Sensitivity (at 25 deg C, 3 V supply)

• 1.2 kBaud                               -112 dBm
• 38.4 kBaud                            -104 dBm
• 250 kBaud                               -95 dBm
• 500 kBaud                              -90 dBm

The table above shows the drop in receiver sensitivity with increasing baud rate.

For a given radio output power, the radio range can be increased by increasing the receiver sensitivity of the receiver. This can be done by reducing the data rate but that increases the time for which the radio is on (thus increasing the energy consumption per message). It also increases the probability of packet corruption and collision. It all depends on the application.