Simple cycle and open cycle are the same thing. When gas turbine is run in stand alone mode i.e, its exhuast energy is not utilized it is called open / simple cycle.
Hence when the exhaust energy of the turbine is utilised in a heat exchanger for example it is normally called an advanced gas turbine or a joule/brayton cycle turbine.. The action of the heat exchanger heats the compressor exhaust on inlet to the turbine thereby decreasing fuel needed to raise the gas temperature in the combustion chamber and inceasing work done/efficiency.
