Using capacitors for radio communication
Do you realize a general purpose 100uF can have an ESR of 2 Ohms ? while a LOW ESR 100uF will be &lt; 10us or 0.1 Ohm.  

It is always important to know ( by testing ) the sensitivity to supply ripple for any RF radio when you consider the sensitivity threshold is in uV range.

Even if the Rx current is only 10mA and the LDO output impedance is only 0.1 Ohm at some high ripple frequency, you need to understand that load regulation is frequency sensitivy as loop gain in the LDO drops with rising f.  The parallel cap ESR must be very low for this RC attenuation or better to use LC decoupling to get a 2nd order effect.

What I would do is inject noise with a sine wave FM sweep and find the threshold for loss in Rx sensitivity at the minimum RF level. This can be done by using a voltage FM sweep gen with a resistor divider and measure the energy with a spectrum anlyzer AC coupled into 50  Ohms.  Then you can measure the RX load current spectrum during Tx data using a 1 Ohm ground shunt resistor and AC couple into the 50 Ohm Spectrum Analyzer.

Once you know the ESR of the present system , Ripple current and the Rx noise sensitivity, the choice of low ESR Caps with optional low ESR series L, you can design the transfer function of your power LPF to get no change in x uV Rx sensitivity threshold and thus no dropout and no loss in range or rise in BER.

This is a routine operation for any RF designer, unless they know from experience and design the right filter and get it right 1st . RF Beads will help from induced RF noise as well as paying attention to all other sources of interference or BER degradation from crosstalk.

Once you know this ripple sensitivity threshold vs f. then you can design your LDO LPF filter to ensure load ripple and verify it.  

Get the right tools and understand 1/Zo load regulation error with ESR and SRF of filter parts vs  f helps save time in debugging Radio issues so you can look at other causes like group delay error , antenna mismatch, PLL performance, xtal error etc.