Any good suggestion exercise to improve the fight sense at home workout?

The best thing you can do, and this goes for whatever art you study, is to create a mental / visual opponent.

It can be your instructor, Brock Lesner, one of the Gracie brothers, or even yourself.

A coach will often say, "Picture someone throwing a jab at you" and you sort of create an image of what that's like, but if you are really invested in the moment and picture a competition, the fight outside a club, or even just a good sparring session against your visual opponent you'll vastly improve.

Remember as you improve your visual opponent must improve.

In addition to the above ask yourself, "How would I beat me?"

This will tell you what areas you need to improve on. Maybe picture your imaginary opponent exploiting those weak areas.

You have a heavy bag, but do you treat it as such, or do you picture it as a live opponent. The heavy bag can make you lazy and slow you down. It's easy to plant yourself and throw the heavy bombs.

Picture the opponent and theme the rounds.

Round 1. Move in and out of range with the jab.

Round 2. As above, but let the rear cross go.

Round 3. Slip, or parry a shot before your attack.

Round 4. Add the lead or rear hook. Angle off on completion.

Round 5. Add elbows or kicks and so on.

There is much you can do, it just needs visualisation. It's a powerful tool.