So, how do you get over 110 dB dynamic range from your software receiver when the ADC only has 77 dB SNR? Simple. Create virtual bits with SDR receiver processing gain.

Begin by remembering the difference between signals and noise. In your SDR, noise arises mainly from quantization errors and random fluctuation of voltages and currents from temperature noise. Such noises are mostly random. Their spectral density is flat. The distribution of noise power is uniform across the sampling range.

Noise power is proportional to bandwidth. Less bandwidth, less noise. Signals on the other hand are not random; they are periodic, correlated samples. As long as the bandwidth is wide enough for demodulation, signal strength stays constant. This is true for both analog and digital radios.

Since noise is spread out while signals are concentrated, you can reduce bandwidth to improve signal to noise ratio. As you narrow the filter on your radio, you reduce noise while maintaining the signal, hence better SNR. This is called processing gain, a magical process that effectively increases the bit depth provided by your analog-to-digital converter.

The diagram above depicts how processing gain increases the performance of the ADC in the ICOM 7300. The LTC2208-14 ADC in this radio has an effective number of bits ENOB = 12.5. By itself, it can only produce dynamic range of 77 dB. However, as the sampling bandwidth is reduced from 120 million samples per second down to a 12 kHz low if, the DSP introduces another 39 dB of dynamic range. This SDR receiver processing gain is equivalent to bolting another 6.5 bits onto the ADC.

## SDR Receiver Processing Gain – How It Works

The most popular approach to creating this extra dynamic range is by oversampling and decimation. Oversampling means that you sample much faster than is necessary to achieve your desired bandwidth. Decimation means throwing away data (mainly noise) that you don’t need.

Decimation is achieved by low pass alias filtering and downsampling. Without low pass filtering, the broadband noise you are trying to get rid of will simply fold back (alias) into your reduced bandwidth. Nothing would be gained. Downsampling by M simply means that you only keep every Mth sample and discard the rest. Each doubling of decimation creates another 3 dB of dynamic range and adds another half-bit to the ENOB of your ADC.

Oversampling provides additional benefits. Alias filtering becomes easier because the distance between a desired signal and its alias is increased. At the same time, the higher sampling rate means that the desired band becomes a smaller fraction of sampling bandwidth; the potential for aliasing is reduced. Finally, sampling resolution is increased.

By the way, you also create SDR receiver processing gain by increasing the size of an FFT. This reduces the size of FFT bins and hence the amount of noise they contain.

With a high enough oversampling ratio, you can create almost any dynamic range you desire with decimation or Fourier Transforms. Designers need to keep track of these ratios to make sure levels of signals in the receiver and displayed on the spectrum scope are consistent.