It has long been known that techniques of spatial multiplexing can be used to improve the spectral efficiency of wireless networks. (Spectral efficiency describes the transmitted data rate per unit of frequency, typically in bits per second per Hz.) In typical examples of spatial multiplexing, an array of multiple transmit antennas sends a superposition of messages to an array of multiple receive antennas. The channel state information (CSI), i.e., the channel coefficients between the respective transmit-receive antenna pairs, is assumed known. Provided that there is low correlation among the respective channel coefficients, the CSI can be used by the transmitter, or the receiver, or both, to define a quasi-independent channel for each of the transmitted messages. As a consequence, the individual messages are recoverable at the receiving antenna array.
More recently, experts have proposed extensions of the spatial multiplexing technique, in which a multiplicity of mobile or stationary user terminals (referred to herein as “terminals”) are served simultaneously in the same time-frequency slots by an even larger number of base station antennas or the like, which we refer to herein as “service antennas”, or simply as “antennas”. Particularly when the number of service antennas is much greater than the number of terminals, such networks may be referred to as “Large-Scale Antenna Systems (LSAS)”.
Theoretical studies predict that the performance of LSAS networks scales favorably with increasing numbers of service antennas. In particular, there are gains not only in the spectral efficiency, but also in the energy efficiency. (The energy efficiency describes the ratio of total data throughput to total transmitted power, and is measured, e.g., in bits per Joule.)
One such study is T. L. Marzetta, “Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas,” IEEE Trans. on Wireless Communications 9 (November 2010) 3590-3600, hereinafter referred to as “Marzetta 2010” and the teachings of which are incorporated herein by reference in their entirety.
In some approaches, the base stations may obtain CSI through a procedure that relies on time-division duplex (TDD) reciprocity. That is, terminals send pilot sequences on the reverse link (aka the uplink), from which the base stations can estimate the CSI. The base stations can then use the CSI for beam forming. This approach works well when each terminal can be assigned one of a set of mutually orthogonal pilot sequences.
Generally, it is considered advantageous for the mobiles to synchronously transmit all pilot sequences on a given frequency, and possibly even on all frequencies, making use of the mutual orthogonality of the pilot sequences.
The number of available orthogonal pilot sequences, however, is relatively small, and can be no more than the ratio of the coherence time to the delay spread. Terminals within a single cell can use orthogonal pilot sequences, but terminals from the neighboring cells will typically be required to reuse at least some of the same pilot sequences. This reuse of pilot sequences in different cells creates the problem of pilot contamination. Pilot contamination causes a base station to beam-form its message-bearing signals not only to the terminals located in the same cell, but also to terminals located in the neighboring cells. This is so-called directed interference. Directed interference does not vanish as the number of base station antennas grows. In fact, directed inter-cell interference—along with the desired signals—grows in proportion to the number of base station antennas.
As shown in Marzetta 2010, for example, as the number of base station antennas grows in an LSAS network, inter-cell interference arising from pilot contamination will eventually emerge as the dominant source of interference.
U.S. Patent Application Publication No. 20130156021 (“the '021 publication”), the teachings of which are incorporated herein by reference in their entirety, describes an approach that can suppress the inter-cell interference resulting from pilot contamination in uplink signals and thus achieve even greater SINRs. The approach described in the '021 publication involves a zero-forcing slow-fading postcoding (ZF-SFP) technique for generating slow-fading postcoding matrices, that gives very good results when the number of base station antennas is very large, like 10,000 or more. For smaller numbers of antennas, like 100, however, the ZF-SFP technique of the '021 publication does not provide sufficiently good results.