  We consider the Massive Multiple-Input Multiple-Output (MIMO) downlink with
maximum-ratio and zero-forcing processing and time-division duplex (TDD)
operation. To decode, the terminals must know their instantaneous effective
channel gain. Conventionally, it is assumed that by virtue of channel
hardening, this instantaneous gain is close to its average and hence that
terminals can rely on knowledge of that average (also known as statistical
channel information). However, in some propagation environments, such as
keyhole channels, channel hardening does not hold.
  We propose a blind algorithm to estimate the effective channel gain at each
user, that does not require any downlink pilots. We derive a capacity lower
bound of each user for our proposed scheme, applicable to any propagation
channel. Compared to the case of no downlink pilots (relying on channel
hardening), and compared to training-based estimation using downlink pilots,
our blind algorithm performs significantly better. The difference is especially
pronounced in environments that do not offer channel hardening.
