Using a 30dB gain preamplifier is ludicrous, it can only create more problems than it might fix. Things like a digital cliff have been mentioned, which is when the receiver is simply starved for signal and the signal level has dropped below what the receiver can make use of. But you also have to consider signal to noise ratio which is completely different. You can have a signal thats so strong its about to overload the receiver but if the signal to noise ratio is say 4dB, you have no picture because there is not enough signal to deal with, its all amplified noise. This is why you want to put a preamp at the antenna and not at the TV.
I'll just pick a number here, so lets say you have 8dB signal to noise for a particular ATSC TV station right off the antenna and that's good enough to give a reliable picture. But you have 5dB of cable loss to the TV leaving you with a 3dB signal to noise ratio and the TV won't lock. Stick a preamplifier at the TV and you still have a 3dB signal to noise ratio, actually a tiny bit less depending on preamp noise figure, but the signal and noise are now amplified by whatever the gain of the preamp is. TV still won't lock.
Now place the preamp at the antenna and you will have the original 8dB signal to noise ratio minus a tiny bit due to preamp noise figure and the signal and noise are amplified enough to overcome cable loss and probably some splitter loss and the signal to noise ratio at the TV is near 8dB and the TV locks fine. Bravo!
However, there are several other specs that are very important when choosing an antenna preamp. The 1dB compression point, IP3 which is a calculated number and noise figure. If you buy a cheap preamp that has a lousy 1dB compression point of 0dBm or even 5dBm it can be easily overloaded by all the TV and FM signals plus police, fire, paging, ham radio operators, etc. All these signals picked up by the TV antenna can add up to a huge number and easily overload a preamp where it will create Inter Modulation Distortion or many sum and difference "ghost signals" of all the stuff clogging the spectrum with more junk. This raises the noise floor considerably covering up weak TV signals your trying to receive and there is no dynamic range left in the preamp because its saturated or near saturated.
The more gain a cheap preamp has the less signal levels it requires to trash it out and create IMD. Then you have noise figure and modern preamps should have noise figure numbers under .5dB, that's under a half dB for the VHF/UHF TV bands and enough gain to make up for cable and splitter loss plus maybe a few dB more. That coupled with a 1dB compression point of 20dBm or up to the 27dBm range should give you problem free performance in most cities.
But most TV preamps are 15 to 30dB gain, 3-4dB noise figure and a 1dB compression point of 10 or 12dBm at best, which is junk. Most TV preamps don't tell you any of these specs because you would cringe and not buy them. Many preamps are built into active splitters designed only to amplify cable TV signals, which are delivered at a higher level and with a finite number of carriers (maybe 100) in a very controlled RF environment where they can work fine. Put that same active CATV splitter on a TV antenna with some very weak signals mixed with thousands of other signals of extreme level and they spew out crap and your TV won't lock. CATV is not off air TV and those are two very different RF environments with different needs. That's why I originally recommended a known good performing off air TV preamp and then feed a passive splitter.
It's not 4X7!! You only need enough ot get you above the digital cliff. The 7dB is the total loss in the splitter, the 4 is built into the 7dB. Companies use a 30dB amplifier to make up for line losses plus splitting.
IF your noise floor is low and you use a low noise pre-amp, a 30dB pre-amp can bring the usable signal up for very weak stations, but the caveat for amplifying is that amplifiers amplify the noise floor plus they add whatever noise is in the amplifier itself and usually end up narrowing the difference between usable signal and the noise in the signal.
ONLY use a 30dB pre-amp in deep fringe situations, if you have a moderately strong station nearby, slapping a 30 dB pre-amp can overload you tuner and really mess things up.
One last comment. Digital TV reception is part science (the numbers) and part art (trial and error). You never really know if something is going to work until you try it. TVFool may say your signal is too weak to receive but you may be able to slap a 30dB pre-amp on your antenna and the station may work. Got an idea - give it a try and see if it works for you.