Equal Gain MIMO Beamforming in the RF
Domain for OFDM-WLAN Systems
´Alvaro Gonzalo1, Ignacio Santamar´ ıa1, Javier V´ ıa1, Fouad Gholam1, and Ralf
1University of Cantabria, 39005 Santander, Spain
2Dresden University of Technology, 01062 Dresden, Germany
Abstract. Equal gain beamforming (EGB) schemes are typically ap-
plied in the baseband domain and hence require complex RF transceivers.
In order to simplify the circuitry and energy consumption of the MIMO
transceiver, in this paper we consider an EGB scheme that operates in
the RF domain by means of analog phase shifters. Under OFDM trans-
missions, the design of the optimal phases is a complicated nonconvex
problem with no closed-form solution. Building upon a previously pro-
posed solution for flat-fading MIMO channels, this paper describes an
alternating minimization algorithm to find an approximate (suboptimal)
solution for the OFDM case. Monte-Carlo simulations are performed in
order to demonstrate the effectiveness of this new analog beamforming
scheme under coded and uncoded WLAN 802.11a transmissions.
Key words: Analog Combining, Multiple-Input Multiple-Output (MIMO),
Equal-Gain MIMO Beamforming, Orthogonal Frequency Division Mul-
tiplexing (OFDM), Wireless Local Area Networks (WLAN).
Conventional multiple-input multiple-output (MIMO) systems require all an-
tenna paths to be independently acquired and jointly processed at baseband.
The hardware cost, complexity and power consumption are therefore increased
accordingly. These drawbacks might explain, at least partially, why MIMO tech-
nologies have not found yet widespread use in low-cost wireless terminals. One
way to increase the energy-efficiency of MIMO terminals and reduce their costs is
to simplify the associated hardware and radio-frequency (RF) circuitry as much
as possible, while still retaining some of the benefits provided by the MIMO
channel (e.g., spatial diversity) by means of specifically designed signal process-
ing algorithms. With this goal in mind, a RF-MIMO architecture that performs
spatial processing directly in the analog domain is currently being developed
within the EU-funded project MIMAX [1, 2].
The combining scheme considered in [1, 2], which is depicted for conve-
nience in Fig. 1, permits to change the amplitudes and phases of the trans-
mitted/received RF signals by means of vector modulators (VM). Therefore, for
flat-fading MIMO channels and assuming perfect channel state information at
2A. Gonzalo et. al.
both sides of the link, it can implement the optimal maximum ratio beamforming
(MRB) solution. For this reason, in this paper we will refer to this architecture
as RF-MRB (i.e., radio-frequency maximum ratio beamforming). A drawback of
Antenna 1 Antenna 1
Fig. 1. Maximum ratio beamforming in the radio-frequency domain (RF-MRB).
the RF-MRB topology is that the average power can vary widely across anten-
nas, which is undesirable for the amplifiers since it can decrease their efficiency
. In order to mitigate this problem, in this paper we investigate an alternative
radio-frequency equal gain beamforming (RF-EGB) scheme, which substitutes
the vector modulators along each branch by analog phase shifters. Specifically,
we focus on the optimization problem that results from this beamforming archi-
For flat-fading single-input multiple-output (SIMO) or multiple-input single-
output (MISO) channels, the equal gain beamformers that maximize the signal-
to-noise (SNR) ratio are given by the phases of the SIMO or MISO channel,
respectively . For flat-fading MIMO channels, however, the optimization prob-
lem is nonconvex and no closed-form solution is known. Recently, Zheng et. al.
have proposed in  an alternating minimization algorithm for the flat-fading
MIMO case that uses the SIMO and MISO closed-form solutions iteratively by
fixing one side of the link and solving for the other. Under OFDM transmis-
sions the optimization problem becomes more challenging, since now we have to
optimize a global measure of performance (typically the SNR) using a common
set of Tx-Rx phases for all subcarriers. Building upon  and our own previous
work in [6, 7, 8], the main contribution of this paper is to provide a suboptimal
solution for this optimization problem and study its performance by means of
This paper is organized as follows. In Section 2 we present the analog MIMO
beamforming architecture based on phase shifters. In Section 3 we summarize the
EGB algorithm for flat-fading MIMO channels proposed in . Section 4 contains
the main contribution of this paper, which is the approximate maximum SNR
solution for the RF-EGB architecture under OFDM transmissions. In Section
5 we compare the performance in 802.11a WLAN systems of the proposed RF-
EGB beamforming architecture with the RF-MRB, the full-baseband MIMO
Equal Gain RF-MIMO Beamforming 11
Fig. 6. Convergence of the algorithm for different values of ρ. 4x4 antenna configura-
Fig. 7. BER curves for different number of iterations. 4x4 RF-EGB system, QPSK
uncoded symbols and channel with ρ = 0.7.
vector modulators as previously proposed (RF-MRB scheme). Under OFDM-
WLAN transmissions, the proposed scheme results in a complicated optimization
problem since the Tx-Rx analog equal gain beamformers simultaneously affects
all subcarriers. We have proposed simple (but suboptimal) solutions for the
MISO and SIMO cases, and based on these, a cyclic minimization algorithm to
get the maximum SNR solution for the MIMO case. The proposed algorithm has
been shown to provide good results with a low computational complexity, since it
converges in very few iterations. Coded and uncoded data 802.11a transmissions
have been simulated, and in both cases, RF-EGB has shown to behave only
slightly inferior to the RF-MRB scheme.
12 A. Gonzalo et. al.
The research leading to these results has received funding from the European
Community’s Seventh Framework Programme (FP7/2007-2013) under grant
agreement n 213952, MIMAX. The work of the fourth author has been sup-
ported by MAEC-AECID (Agencia Espa˜ nola de Cooperaci´ on Internacional para
1. Eickhoff, R., et. al.,: MIMAX: Exploiting the maximum performance and mini-
mum system costs of wireless MIMO systems, in 17th ICT Mobile and Wireless
Summit, Stockholm, Sweden, (2008).
2. Eickhoff, R., Kraemer, R., Santamaria, I., Gonzalez, L.,: Integrated low power
RF-MIMO transceiver for enhanced 802.11a short-range communication,” IEEE
Vehicular Technology Magazine, pp. 34-41, (2009).
3. Ellinger F.,: Radio Frequency Integrated Circuits and Technologies, Springer-
Verlag, Berlin 2007.
4. Love, D. J., Heath, R. W.,: Equal gain transmission in multiple-input multiple-
output wireless systems, IEEE Trans. Commun., vol. 51, pp. 1102-1110, (2003).
5. Zheng, X., Xie, Y., Li, J., Stoica, P.,: MIMO transmit beamforming under uniform
elemental power constraint, IEEE Trans. Signal Process., vol. 55, pp. 5395-5406,
6. Via, J., Elvira, V., Santamaria, I., Eickhoff, R.,: Analog antenna combining for
maximum capacity under OFDM transmission, in IEEE International Conference
on Communications, Dresden, Germany, (2009).
7. Via, J., Elvira, V., Santamaria, I., Eickhoff, R.,: Minimum BER beamforming
in the RF domain for OFDM transmissions and linear receivers, in IEEE Inter-
national Conference on Acoustics Speech and Signal Processing, Taipei, Taiwan,
8. Via, J., Santamaria, I., Elvira, V., Eickhoff, R.,: A general criterion for joint Tx-
Rx beamforming in the RF domain under OFDM transmissions, to appear in
IEEE Transactions on Signal Processing, (2010).
9. IEEE Std. 802.11a, Supplement to Part 11: Wireless LAN Medium Access Control
(MAC) and Physical Layer (PHY) specifications: High-speed Physical Layer in
the 5 GHZ Band. IEEE., (1999).
10. Van Nee, R., Prasad, R.,: OFDM for wireless multimedia communications, Artech
11. Andersen, J. B.,: Array gain and capacity for known random channels with mul-
tiple element arrays at both ends, IEEE Journal on Selected Areas in Communi-
cations, vol. 11, pp. 2172-2178, (2000).
12. Rahman, M., Witrisal K., Das, S., Fitzek F., Olsen O., Prasad, R.,: Optimum
pre-DFT combining with cyclic delay diversity for OFDM based WLAN systems,
in IEEE 59th Vehicular Technology Conference, vol. 4, pp. 1844-1848, (2004).
13. Li, S., Huang, D., Letaief K., Zhou, Z.,: Pre-DFT processing for MIMO-OFDM
systems with space-time-frequency coding, IEEE Trans. on Wireless Comm., vol.
6, no. 11, pp. 4176-4182, (2007).