In this series:

In Part 2 of this blog series on massive MIMO, we addressed some key lessons learned from asymptotic information theoretic analysis on the asymptotic throughput using matching filter for detection and/or eigen-beamforming precoder for transmission. The expected asymptotic performance of other detection/precoding techniques (such as MMSE/zero-forcing) are also discussed in

[1]. Common assumptions in the literature basically consider two main factors, time division duplexing (TDD) mode and hardware capability, when examining the required processing performance within the coherence time interval.

Assuming and recommending TDD as a duplexing mode is also proposed as a key enabler for a new heterogeneous network architecture with the potential to provide ubiquitous coverage and unprecedented spectral area efficiencies [2]. This is the new vision presented by Alcatel-Lucent beyond the conventional LTE Evolution roadmap. In the massive MIMO context, the TDD assumption is mainly enforced to invoke channel reciprocity in order to simplify channel state information (CSI) estimation at the base station.  Acquisition of the CSI fundamentally limits the capacity of any precoder. A system with M antennas that serves K user terminals (UTs) requires CSI between every base station antenna and UT (herein we consider one antenna per UT). Critically, all M*K channel links must be measured within a time span much shorter than the channel coherence time in order to be useful for the subsequent precoding stage. The coherence time of a wireless channel depends on how quickly the terminal speed and environment changes. According to 3GPP Release 9, this is typically on the order of a few milliseconds, but can drop below 500 μs.

In addition to CSI acquisition, the base station shall perform precoding within the remaining time. Whether the precoder is based on eigen-beamforming or zero-forcing techniques [3], the amount of required processing burden (including data/sample transfer to/from distributed processing cores) will advise on the feasibility of serving K users by a given N antennas within a coherence time period. In other words, one might expect eigen-beamforming to outperform zero-forcing in terms of achieved capacity when considering real hardware capabilities. Such an analysis has been addressed in [4], wherein the achieved capacities with regard to coherence time of both precoding techniques are superposed in a single graph. Different hardware capabilities were considered for 64 antennas and 15 UTs. It can be seen that eigen-beamforming outperforms zero-forcing at coherence time up to 38 ms in low-end processing hardware. For a fixed number of antennas and coherence time of 30 ms, it is shown that zero-forcing performance degrades as the number of UTs increases. With 15 UTs, zero-forcing barely achieves 65% of the eigen-beamforming precoder. This is due to the increase in the overhead due to the large amount of data transfer and processing.

To conclude this short post, one can state that the implication of such findings dictates:

(i) The importance of considering the capability of the processing hardware in regards to coherence time for a given maximum number of antennas and served UTs.
(ii) Another dimension is related to an open research activity on adaptive precoder design to maximize the achieved capacity .


[1] J. Hoydis, S. ten Brink, and M. Debbah, Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?, IEEE J. Sel. Areas Commun, vol. 31, no. 2, pp. 160-171, Feb. 2013.

[2] J. Hoydis, K. Hosseini, S. ten Brink, and M. Debbah, Making Smart Use of Excess Antennas: Massive MIMO, Small Cells, and TDD, Bell Labs Technical Journal, vol. 18, no. 2, pp. 5-21, Sep. 2013.

[3] M. Ahmed Ouameur, “Massive MIMO – Part 2: A few lessons learned from asymptotic information theoretic analysis,”

[4] C. Shepard, N. Anand, and L. Zhong, “Practical Performance of MU-MIMO Precoding in Many-Antenna Base Stations,”