GNU Radio, Frequency Hopping Spread Spectrum for High Hopping Intervals

Question

I am planning to implement a frequency hopping spread spectrum transmitter and receiver in GNU Radio. In my project, the bandwidth of the message signal is around 200 kHz and the maximum frequency hopping interval is around 80 MHz. On the other hand, the USRP that I use can only support 40 MSample/sec which can not cover all the frequency bands of interest. Therefore, the use of a numerically controlled oscillator (NCO) is not applicable. Instead (as far as I consider), I should manipulate the carrier frequency of the local oscillator in the RF stage for such high carrier-frequency jumps.

My questions are:

1. Is it possible to change the carrier frequency of the local oscillator instantaneously?
2. How can I provide the synchronization of the receiver? (I am assuming that the transmitter sends a sync-word over a predetermined frequency. When the receiver detects the sync-word, the receiver changes the local oscillator frequency according to the hopping rule)

Answer 1

No you cannot change the carrier frequency of your local oscillator instantaneously. The RF local oscillator will be in a Phase-Lock Loop (PLL) circuit to a low frequency reference (to provide frequency stability and tunability) and the switching time can be approximated from the loop bandwidth of that PLL when operating within the linear range of the PLL (relatively small frequency changes). As a first approximation, you can use the relationship of 10% to 90% rise time to bandwidth for a first order system:

$$t_r = \frac{0.35}{B}$$

Where $t_r$ is the 10% to 90% rise (or fall) time, and $B$ is the bandwidth in Hz.

This is derived from $1-e^{-t/\tau}$ which you could also use for any degree of accuracy for the settled value. The PLL itself will inevitably be a higher order system than this first-order approximation, and having the actual PLL transfer function model would lead to higher accuracy, but this can give you an initial idea of the time required.

Receiver synchronization is done using a cross-correlation of the received sequence with the locally generated pattern as the delay between the two is varied. For spread-spectrum the data is typically modulated by a known pseudo-random pattern, so that pattern can be used directly for synchronization and demodulation (a sync word is typically used however for framing a complete data packet).