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A scheme is proposed, called polar coded spatial modulation (PCSM), to provide both detection/decoding of the transmitted symbol and the transmit antenna index in multiple‐input–multiple‐output (MIMO) antenna systems. Based on the free polar set and the frozen polar set in polar codes, the proposed PCSM scheme maps the transmitted information data in the free polar set and the transmit antenna index bits in the frozen polar set whose positions are known at the receiver. This has the advantage that the bits that identify the transmit antenna are not transmitted to the receiver and do not need to be detected as is the case in conventional spatial modulation (SM). Thus, PCSM presents a spectrally efficient and a power‐efficient system. For the simulations, MIMO channels with transmission over independent and identically distributed flat fading characteristics are exploited. Firstly, capacity results for coded SM …