Since each user’s demodulation reference signals are superimposed and interfere with each other in the case where multiple users simultaneously transmit signals at the same frequency

it is difficult to accurately estimate the channel impulse response for each user. In this paper

a special signal matrix is designed for the transmission format 4 of the 5 G system Physical Uplink Control Channel（PUCCH） by using the characteristics of demodulation reference signals of different users. Then we combine this signal matrix with traditional single-user channel estimation algorithms to propose three channel estimation algorithms including Least Squares（LS）-based spline interpolation

LS-based Discrete Cosine Transform（DCT） interpolation algorithm

and Liner Minimum Mean Squared Error（LMMSE）-based DCT interpolation algorithm. Finally

the scenes of two users and four users are simulated. The simulation results show that three proposed channel estimation algorithms are applicable to the format 4 of 5 G system PUCCH

which has great reference value for engineering applications.