Of course, an alternative to a grain mix is to feed your birds on pigeon pellets. These are milled from crushed grains, greenstuffs and meat by-products and usually have vitamin and mineral additives to make a balanced feed. Given a choice however, pigeons tend to prefer more natural grains over this type of food.
Pigeons like all birds, do not have teeth. Their food is swallowed whole and is stored initially in a sac at the base of the throat called the crop. The food is then passed through the digestive tract to the gizzard where it is broken down into more basic nutritional elements. For this to happen, your birds will need to have access to a supply of grit. Put simply, pigeons need to eat stones in order to thrive. The best grit is hard granite or quartz which is broken down to about 1/8 to 1/4 of an inch in diameter, though pigeons are happy to eat grit of varying size. A different kind of grit which tends to break down more quickly in the gizzard, is shell grit. This can be given in addition to the harder grit and has the added benefit of providing a good supply of calcium to the birds. Pigeons that have free access to the outside world will find their own grit. Those which remain confined to the loft, will need it supplied. Pigeons also like salt and will readily attack salt blocks such as those made for horses and sheep.
There are other bits and pieces that some fanciers like to feed their birds. A little cod liver oil mixed into the feed is a good tonic for birds that are a little jaded and for those coming out of a moult. Linseed meal can be mixed in small quantities to the feed to give added gloss and lustre to the birds' plumage, particularly before shows. And in those countries where it is legally available... ahem... hempseed (marijuana) can be given as a special treat. Pigeons seem to love them, even though they hold no particularly useful nutritional value.
Now we come to the single most important nutritional item required by a pigeon. Water! Pigeons love the stuff too... none of your prissy, chicken-like drinking habits for a pigeon... no siree! Pigeons will just stick their whole head into the water right up to the eyes and suck the stuff down like there is no tomorrow. And pigeons that are breeding will need lots of fresh, clean, cool water in order to make a good supply of rich milk for their babies. Fresh water should always be readily available for your birds. Besides, pigeons love to bath in it too, even on the coldest days.