# Bit error rate calculations for a photodiode receiver driven from a laser

I'm having problems understanding how the following specification for a photo-diode (with built-in amplifier) rationalizes the bit error rate: - Circled in red are two important figures. One is NEP (noise equivalent power) and the other is minimum receivable sensitivity. The way I figure it works is like this but please correct me if I'm wrong: -

NEP is typically 310nW and note 3 says this is for a single-ended measurement and therefore I assume that for the diff outputs of the device, the power is doubled to 620nW. From this I conclude that the noise voltage out is sqrt(50 x power) = 5.6mVrms.

Next is the minimum receivable sensitivity of -25.5dBm. Laser jargon talks about a 10dB extinction ratio which means that the logic levels transferred via light are 10dB apart so I naturally assume that -25.5dBm is for logic 0 (dimmer) and -15.5dBm is for logic 1 (brighter). These, in mW terms are simply 0.0028mW and 0.028mW.

Now, if I look at photo sensitivity, this tells me how to convert these to voltages. The figure quoted is single-ended and therefore light powers convert to 4.2mV and 42mV respectively. These double up because the output is differential to a peak to peak output of 76mVp-p.

So now, I have rms noise (5.6mV) and p-p signal amplitude (76mV)

Here is where I may also be going wrong. I can convert the noise to a p-p value by assuming it is Gaussian and, for instance if I used 6.6sigma (99.9% "coverage"), the rms voltage becomes 37mVp-p. This is approximately 50% of the signal p-p amplitude and as far as I can tell will be high enough in amplitude to produce bit errors.

Any smaller than 50%p-p and it isn't quite enough to do bit-damage. I used 6.6sigma and this means the noise signal is below 37mVp-p for 99.9% of the time. For those occasions it is greater than 37mVp-p, 50% of those times the amplitude of the symbol may be enhanced and 50% of those occasions the symbol will be destroyed. I therefore conclude that the BER rate is 1 in every 2000 bits.

However the spec (in the picture) says BER = 10^-10 and this is totally at odds with my calculation.

My calculations suggest a bit error rate of 1 in every 2000 and the spec suggests 1 in every billion.

Where am I going wrong?