In terms of Shannon formula

multiple-input multiple-output (MIMO) theory tries to derive the formula of wireless channel capacity (WCC)

which is proportional to the number of transmitting and receiving antennas in MIMO system.As multi-antenna is used in MIMO system to transmit signals with the same carrier frequency in the same time

one physical channel in MIMO system will contain multi-virtual independent Rayleigh fading channel.So

the definition in MIMO theory for the independent Rayleigh fading channel is most possibly to be invalid.This will lead space division multiplex (SDM) to be difficult to be realized

and the derived WCC formula in mathematics to be difficult to be established.Moreover

the directional transmission beams with uncertain directions are employed in the MIMO system.The interference among those transmitting signals can not be avoided

which would form a number of blind spots of radio coverage and an unreasonable wireless communication system.In this paper

the above views are firstly proved by mathematical analysis and the simulation of the transmitting radio beam produced by multi-antenna.Then

an SHPCA system is proposed

in which phase-controlled antenna array is used to produce a narrow directional radio beam with very high power efficiency to form SDM.Finally

the WCC formula for SHPCA system is presented in the paper

and its capacity is proportional to the numbers of antennas and SDM.It has higher efficiency for that WCC formula than Shannon formula.