One can use the biological pathway that is the least expensive: nitrification, which consists of transforming, by enzymatic oxidation, ammonium into nitrites, then nitrates, under the influence of specific bacteria.Nitrogen from wastewater is mainly ammoniacal (NH4 +). The biological treatment to eliminate it is longer than for a simple carbon treatment and the activated sludge is alternately aerated then deprived of oxygen. At first, nitrifying bacteria oxidize ammonia to nitrates (NO3-) and, in the absence of oxygen, denitrifying bacteria reduce nitrates to non-polluting nitrogen gas (N2). Thus, more than 90% of the nitrogen can be removed from the wastewater.
To treat phosphates, the bacteria must first be deprived of oxygen. Some of them (notably Acinetobacter) release their intracellular phosphates in water in the form of phosphoric granules. When reoxygenating the medium, these bacteria reabsorb and store the phosphate present in the water in excess of their metabolic needs: they are said to be dephosphating. The surplus they store will be used to survive momentarily in an environment deprived of oxygen.
The most cost effective methodology when it comes to BNR is biological means. you might want to read this paper in the link provided below for more insight. Article Nitrogen and Phosphorus Removal from Wastewater Treatment Pl...
Your best bet is biological method of removal. However, "low cost" is a relative term. Activated sludge (BNR) is one of the cheapest to set up however, due to aeration demand, at full scale it may be expensive to run due to energy demand. If your concern is reduced energy cost, a system incorporated with optimized diffused aeration mode may be better.
You check this article: Energy-Efficiency Showdown: A Comparison Of Aeration Technologies By Mark Gehring and John Lindam
I agree with Mohammad Aljaradin, with the exception of using (MATURATION PONDS) a type of (STABILIZATION PONDS) , which is a very low cost and requiring no energy to be consumed for aeration. Please refer to the link:-
The nitrogen & phosphorus from waste water can be removed following the biological route, a cost effective process; this has been explained by Prof. Bachir Achour.
A recent study shows the application of mixed microalgae and bacteria culture in the removal of nitrogen & phosphorus from waste water. You may read the same (I found - Mohammad Aljaradin has already provided the article).