Earlier quoted context omitted.
Virtually every professional radio is software defined to some extent these days, so every company that designs radios wants signal processing and information theory skills, more so if they are doing proprietary protocols rather than implementing a standard. It's pretty well the same skill set, whether you are designing or analysing systems. There is a surprising amount of reverse engineering in building radio system…
Where can I read more about this? It's always nice to see RF and Signal Processing stuff on HN.
If you're seriously interested, download Octave (Matlab replacement) and write a program from scratch to simulate a BPSK system and generate a "waterfall" (bit error vs. noise) curve. Don't stop until you can get your curve to perfectly match the one in a text book [1]. By doing this, you will learn about modulation, demodulation and and "Additive White Gaussian Noise" (AWGN) channel models. If you can get the waterfall curve to match exactly, you will also be covering concepts such as "energy per bit". A BPSK should be quite doable for an amateur.
Once you have the BPSK simulation, try extending your simulation in different directions and matching the textbook curves. The following challeges are roughly in order of increasing difficulty
1) Add a block code, such as Hamming or BCH.
2) Replace the simple AWGN channel model with a Rayleigh or Ricean model
3) Add a convolutional code (with Viterbi decoder)
4) Implement Orthogonal Frequency Division Multiplexing (OFDM)
5) Implement an LMS receiver
6) Implement a Low-Density Parity Check code (use the one from the WiFi standard)
7) Implement a complete 802.11a simulation
8) Implement a complete DVB-T simulation
9) Implement a MIMO system, assuming perfect channel knowledge
10) Implement a MIMO system with channel estimation
Get to number 10, and you will know more about radio signal processing than most engineers.
[1] eg. "Lin and Costello" Error Control Coding or "Proakis" DSP