An engine system includes a turbine engine including a compressor section, a combustor section having a burner, a turbine section, and a nozzle in an open-loop configuration. The engine system also includes a bottom-cycle apparatus and an exhaust heat exchanger downstream of the turbine section of the turbine engine configured to reject heat from the turbine engine to the bottoming-cycle apparatus and create a cooled turbine exhaust in the turbine engine. The engine system further includes an exhaust compressor arranged downstream of the exhaust heat exchanger and upstream of the nozzle of the turbine engine configured to compress the cooled turbine exhaust stream and increase a pressure of the cooled turbine exhaust stream prior to exiting the nozzle of the turbine engine.