MmWave channel estimation via atomic norm minimization for multi-user hybrid precoding

Abstract

To perform multi-user multiple-input and multipleoutput transmission in millimeter-wave (mmWave) cellular systems, the high-dimensional channels need to be estimated for designing the multi-user precoder. Conventional grid-based Compressed Sensing (CS) methods for mmWave channel estimation suffer from the basis mismatch problem, which prevents accurate channel reconstruction and degrades the precoding performance. This paper formulates mmWave channel estimation as an Atomic Norm Minimization (ANM) problem. In contrast to grid-based CS methods which use discrete dictionaries, ANM uses a continuous dictionary for representing the mmWave channel. We consider a continuous dictionary based on sub-sampling in the antenna domain via a small number of radio frequency chains. We show that mmWave channel estimation using ANM can be formulated as a Semidefinite Programming (SDP) problem, and the channel can be accurately estimated via off-the-shelf SDP solvers in polynomial time. Simulation results indicate that ANM can achieve much better estimation accuracy compared to grid-based CS, and significantly improves the spectral efficiency provided by multi-user precoding.

Performance Loss of Hybrid Beamforming with Imperfect Phase Shifters in Millimeter Wave Systems

“…As we mentioned before, the upper bound of achievable sum rate with imperfect phase shifters can be derived according to (15), which is an approximation, exactly lower bound, of the practical achievable sum rate shown in (14). In Figure 1, we can see that there is only a very small gap between (15) and (14). Therefore in the following figures, we use (15) as the simulation result of achievable sum rate with imperfect phase shifters.…”

“…In massive MIMO systems, formula (15) can be very approximate to (14) as shown in Fig. 1 in the section V thus formula (15) can describe the effect of phase-shifting error and gain error upon the achievable sum rate well. Then we calculate the theoretical value of the expectation of x k I in theorem 1.…”

“…The above HBF algorithms are based on the assumption that perfect CSI is available at both the transmitter and the receiver. With no CSI knowledge, channel estimation should be carried out through the ways of dividing the whole space into beam grids and then applying compressive sensing algorithms [10], [11] or the off-grid ways applying spatial spectrum method [12], [13], gradient descent method [14] and so on [15].…”

Beamspace Channel Estimation for Massive MIMO mmWave Systems: Algorithm and VLSI Design

“…Fortunately, wave propagation at mmWave frequencies is predominantly directional and real-world channels typically comprise only a small number of strong propagation paths, such as a line-of-sight (LoS) component and a few first-order reflections [16]. These properties enable the design of sparsityexploiting CSI estimation algorithms that effectively suppress channel estimation errors [17]- [20]. Compressive sensing (CS)based methods have been proposed for mmWave channel estimation in [21], [22], including methods that rely upon orthogonal matching pursuit (OMP) [22]- [24].…”

“…The denoising and sparse signal recovery literature [17]- [20], [41] describes a number of algorithms that are suitable for channel-vector denoising in the beamspace domain. The least absolute shrinkage and selection operator (LASSO) [42]- [44] is among the most popular methods, which, in our application, corresponds to the following optimization problem:…”