Hello,
I'm simulating a network of multiple wireless nodes that can transmit to one another using finite battery resources. I'm getting some really strange results in my testing of some power calculations. It's not a complicated problem - the problem exists in finding the bounds on my transmit power before even doing anything with it.
There is a technical term for the minimum received power that a node must receive for it to be able to decipher a message, known as the minimum input receiver sensitivity (MIRS). Also, because each node as a finite amount of battery power, there is a maximum transmit power that can be achieved to ensure that the power dissipated for a transmission does not exceed the amount of battery power that a node has. With these two pieces of information, I form these constraints on my transmit power:
Pt >= max(0, P_MIRS) -> Lower Bound
Pt Upper Bound
Now the first constraint is formed by observing that the minimum transmit power must be the maximum of 0 watts and the transmit power required to reach the MIRS at the receiver. I calculate P_MIRS as:
MIRSdBm = -92; pathLossExponent = 1.8; Txpower = MIRSdBm - Gt - Gr + 20*log10(4*pi* (freq * 1E6) / (3E8)) +
10*pathLossExponent*log10(distance); P_MIRS = 10^((Txpower-30)/10);
Now, with Gt = Gr = 0 dBi, freq = 2400 (I'm modeling frequency 2.4 GHz or 2400 MHz) and distance = 2m, my Txpower = -46.5dBm and P_MIRS =
2.2205e-008 Watts. This is my Lower Bound.
For the second constraint, P_max is calculated by considering the remaining battery power and power dissipation. The power dissipation of a transmission is calculated using q*R: q is the energy consumption/ bit of the wireless technology used and R is the transmission rate in bits/sec. R = w*log2 (1 + (P_max*G) / (w * N + Interference) is the physical representation of the transmission rate called the Shannon Capacity. Multiplying the two quantities gives energy consumption/sec which gives units of power. Now, the quantity q is a term that can be found in the literature for a technology, but since it is considered for the transmission as a whole (including a transmitter and receiver), to find the power dissipation at the transmitter only, I assume a 50-50% split for power dissipation between transmitter and receiver. So I form the constraint below to find P_max by stating that the battery power must be greater than or equal to the maximum power dissipation for a transmission that has used P_max of transmit power in Watts:
P_battery >= (q/2)*R >= (q/2)*w*log2 (1 + (P_max*G) / (w * N + Interference);
Rearranging this formula gives: P_max= [2^(P_battery/(w*q/2)) - 1]*[(w * N + Interference)]/G
Now, I have P_battery = 1 Watt, w = 1 MHz = 1E6 bandwidth, q = 0.5E-6 joules/bit (for the Zigbee technology), N is the noise @ center frequency 2400 MHz around bandwidth w, Interference is the interference @ center frequency 2400 MHz around bandwidth w, and G is the channel gain @ center frequency 2400 MHz calculated as
Gdb = Gr + Gt - 20*log10(4*pi*(freq * 1E6) *d0/c) -
10*pathLossExponent*log10(distance/d0); G = 10^(G/10);
Again, Gr = Gt = 0 dBi, freq = 2400, d0 = 1m, c = 3.0E8, pathLossExponent = 1.8 and distance = 2m. So I get values for Gdb =
-45.46 dB and G = 2.8415e-005.
Now this gives me a P_max of 1.9479e-009 Watts. For this calculation my N = kT = (1.23E-23)*(300 Kelvin) and Interference = 0. This P_max =
1.9479e-009 Watts is my Upper Bound.
So after all of this without even any interference, my upper bound < lower bound. Also, as you can see, with 1 whole Watt of battery power and no interference, I can't even transmit a distance of 2m away. There's definitely something wrong.
I hope someone can show me what I've done wrong.
Thanks a bunch! Omar