Landsat Imaginery is not about software, is about aritmetics so the second answer is any of them will be usefull. The first is harder because "sediment concentration/quality" depends in what are you looking for, there are a lot of indexes and bands convination to know the chemestry of the surface (or more precicely the optical properties).

A good start is taking into acount the known geology of the area. Could you be more explicit in what kind of sediments are you dealing with?

Good look,

Ernesto Iglesias

There are a number of methods of calculating suspended sediment concentration (if this is indeed what you want. Most require that the data are atmospherically corrected (you can do this using free code called SeaDAS). You then really need to go out and measure the sediment reflectance vs concentration from filtered water samples to properly fit to models for your specific sediment type. These models can then be applied to your data. Read Turbid wakes associated with offshore wind turbines observed with Landsat 8 (RSE 2014, Vol 145) or http://www.mdpi.com/2072-4292/8/7/556 and there are plenty of others.

Several methods have been used. Water colour values have been used to identify areas of suspended sediment to give estimated levels of sediment concentration. Also, the spectral mixture analysis have been used, etc. The terrain of your study area and the season/time when the  Landsat images were taken will assist to determining the appropriate method to used. For the software, your expertise/familiarity will be helpful. However, ERDAS might be more appropriate.

 Thanks for your kind answer. I am trying to assess sediment concentration along-shore. And dealing with mainly non-cohesive sediment. I need to know if there is any particular index to have an idea on qualitative sediment concentration as I have no data for sea @Ernesto Iglesias Rodríguez 

Thank you Mark Broomhall for your kind reply :)

Thank you Makinde-Omodanisi E. O.  Do you have any kinda reference from where I can get a overall idea!!