# Questionable Eb/N0 results for different modulations - measurements for 8-PSK do not match the theory

I would like to warn you that this post will be long, so thank you in advance to everyone who reads it and is able to help.

I am running a certain simulation. I created a measurement environment (transmitter and receiver project) where I send 1000 packets from the transmitter that the receiver should, well, receive. I run the simulation using three modulations: BPSK, QPSK and 8-PSK. Now the measuring thing - the transmitter stands still, and the receiver is systematically moved away from the transmitter by 2, 3.5, 5, 7, 10, 13, and 15 meters (I had to choose such distances because I run the simulations at home, I did not have any better environment [below I will post a picture of my environment]). Simulations are run in what is called "free space".

I always set the same parameters on the transmitter and receiver (only the antennas power are d) - in this case:

• the carrier is set to: 2.4375 GHz
• bandwidth (IQ sampling rate): 1MHz

On the transmitter and receiver side. Only the Tx gain is set to 10 and Rx gain to 23. The symbol rate on transmiter depends on bandwidth and is calculated as 125k symbols/sec if set to 1MHz.

I ran simulations for three different bands 1Mhz, 500kHz and 250kHz. As can be inferred, the 8-PSK modulation performs best with throughput, and this is also confirmed by the results of the measurements (example results for 1MHz band):

As we can see, 8-PSK performs slightly better than the other modulations, and BPSK is the most inefficient in this case.

The problem begins when comparing $$E_b/N_0$$ values for these modulations. In this case, shouldn't the $$E_b/N_0$$ for 8-PSK be lower? Meanwhile, it continues to perform the best:

And it's not the case of band, because for 250kHz and 500kHz 8-PSK has still highest $$E_b/N_0$$ ratio. From what I have found out, at constant bandwidth (and power) my receiver divides the transmit power on three times as many bits as BPSK and $$E_b/N_0$$ should be reduced. In my case it doesn't. 8-PSK has still the best $$E_b/N_0$$ and I wonder what is the reason for that and where's the problem.

Below is a picture of my measurement environment (simplified), a part of my house (of course, when simulating measurements in the free space, all doors were open and the transmitter and receiver could "see" each other)

The measurements were in a straight line (red line) at the distances given above. Site 1 Antenna is the transmitter.

• I do agree that if you're constraining power and bandwidth to be fixed across the different modulations that your Eb/N0 for 8PSK should be the lowest. Can you explain how you're measuring Eb/N0? And have you considered looking at Carrier-to-Noise Ratio (CNR) and deducing Eb/N0 from that (e.g. if you can take the I/Q data at the receiver and run say a fft/ welch / bartlett spectral estimator on it to estimate CNR)? Jan 18 at 6:56