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RESEARCH Open Access

Adaptive antenna selection and Tx/Rxbeamforming for large-scale MIMO systems in60 GHz channelsKe Dong1, Narayan Prasad2, Xiaodong Wang3* and Shihua Zhu1

Abstract

We consider a large-scale MIMO system operating in the 60 GHz band employing beamforming for high-speeddata transmission. We assume that the number of RF chains is smaller than the number of antennas, whichmotivates the use of antenna selection to exploit the beamforming gain afforded by the large-scale antenna array.However, the system constraint that at the receiver, only a linear combination of the receive antenna outputs isavailable, which together with the large dimension of the MIMO system makes it challenging to devise an efficientantenna selection algorithm. By exploiting the strong line-of-sight property of the 60 GHz channels, we propose aniterative antenna selection algorithm based on discrete stochastic approximation that can quickly lock onto a near-optimal antenna subset. Moreover, given a selected antenna subset, we propose an adaptive transmit and receivebeamforming algorithm based on the stochastic gradient method that makes use of a low-rate feedback channelto inform the transmitter about the selected beams. Simulation results show that both the proposed antennaselection and the adaptive beamforming techniques exhibit fast convergence and near-optimal performance.

Keywords: 60 GHz communication, MIMO, Antenna selection, Stochastic approximation, Gerschgorin circle, Beam-forming, Stochastic gradient

1 IntroductionThe 60 GHz millimeter wave communication hasreceived significant recent attention, and it is consideredas a promising technology for short-range broadbandwireless transmission with data rate up to multi-gigabits/s [1-4]. Wireless communications around 60 GHzpossess several advantages including huge clean unli-censed bandwidth (up to 7 GHz), compact size of trans-ceiver due to the short wavelength, and less interferencebrought by high atmospheric absorption. Standardiza-tion activities have been ongoing for 60 GHz WirelessPersonal Area Networks (WPAN) [5] (i.e., IEEE 802.15)and Wireless Local Area Networks (WLAN) [6] (i.e.,IEEE 802.11). The key physical layer characteristics ofthis system include a large-scale MIMO system (e.g., 32 32) and the use of both transmit and receive beam-forming techniques.

To reduce the hardware complexity, typically, thenumber of radio-frequency (RF) chains employed (con-sisting of amplifiers, AD/DA converters, mixers, etc.) issmaller than the number of antenna elements, and theantenna selection technique is used to fully exploit thebeamforming gain afforded by the large-scale MIMOantennas. Although various schemes for antenna selec-tion exist in the literature [7-10], they all assume thatthe MIMO channel matrix is known or can be esti-mated. In the 60 GHz WPAN system under considera-tion, however, the receiver has no access to such achannel matrix, because the received signals are com-bined in the analog domain prior to digital basebanddue to the analog beamformer or phase shifter [11]. Butrather, it can only access the scalar output of the receivebeamformer. Hence, it becomes a challenging problemto devise an antenna selection method based on such ascalar only rather than the channel matrix. By exploitingthe strong line-of-sight property of the 60 GHz channel,we propose a low-complexity iterative antenna selectiontechnique based on the Gerschgorin circle and the

* Correspondence: [email protected] Engineering Department, Columbia University, New York, NY,10027, USAFull list of author information is available at the end of the article

Dong et al. EURASIP Journal on Wireless Communications and Networking 2011, 2011:59http://jwcn.eurasipjournals.com/content/2011/1/59

2011 Dong et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons AttributionLicense (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium,provided the original work is properly cited.

mailto:[email protected]://creativecommons.org/licenses/by/2.0

stochastic approximation algorithm. Given the selectedantenna subset, we also propose a stochastic gradient-based adaptive transmit and receive beamforming algo-rithm that makes use of a low-rate feedback channel toinform the transmitter about the selected beam.The remainder of this paper is organized as follows.

The system under consideration and the problems ofantenna selection and beamformer adaptation aredescribed in Section 2. The proposed antenna selectionalgorithm is developed in Section 3. The proposedtransmit and receive adaptive beamforming algorithm ispresented in Section 4. Simulation results are providedin Section 5. Finally Section 6 concludes the paper.

2 System description and problem formulationConsider a typical indoor communication scenario and aMIMO system with Nt transmit and Nr receive antennasboth of omni-directional pattern operating in the 60GHz band. The radio wave propagation at 60 GHz sug-gests the existence of a strong line-of-sight (LOS) com-ponent as well as the multi-cluster multi-pathcomponents because of the high path loss and inabilityof diffusion [3,4]. Such a near-optical propagation char-acteristic also suggests a 3-D ray-tracing technique in

channel modeling (see Figure 1), which is detailed in[12]. In our analysis, the transceiver can be any device,defined in IEEE 802.15.3c [5] or 802.11ad [6], located inarbitrary positions within the room. For each location,possible rays in LOS path and up to the second-orderreflections from walls, ceiling, and floor are traced forthe links between the transmit and receive antennas. Inparticular, the impulse response for one link is given by

h(t, tx, tx, rx, rx) =

i

A(i)C(i)(t T(i), tx (i)tx , tx (i)tx , rx (i)rx , rx (i)rx ) (1)

where A(i), T(i), (i)tx , (i)tx ,

(i)rx ,

(i)rx , are called the inter-

cluster parameters that are the amplitude, delay, depar-ture, and arrival angles (in azimuth and elevation) of raycluster i, respectively, and

C(i)(t, tx, tx, rx, rx) =

k

(i,k)(t (i,k))(tx (i,k)tx )

(tx (i,k)tx )(rx (i,k)rx )(rx (i,k)rx )(2)

denotes the cluster constitution by rays therein, wherea(i,k), (i,k), (i,k)tx ,

(i,k)tx ,

(i,k)rx ,

(i,k)rx are the intra-cluster

parameters for kth ray in cluster i. Some inter-clusterparameters are usually location related, e.g., the severepath loss in cluster amplitude; some are random

01

23

4 0

1

2

30

1

2

3

YX

Z

LOSReflections

RxTx

Figure 1 A typical indoor communication scenario and channel modeling using ray tracing.

Dong et al. EURASIP Journal on Wireless Communications and Networking 2011, 2011:59http://jwcn.eurasipjournals.com/content/2011/1/59

Page 2 of 14

variables, e.g., reflection loss, which is typically modeledas a truncated log-normal random variable with meanand variance associated with the reflection order [12], iflinear polarization is assumed for each antenna. Besides,most intra-cluster parameters are randomly generated.On the other hand, for the short wavelength, it is rea-sonable to assume that the size of antenna array ismuch smaller than the size of the communication area,which leads to a similar geographic information for alllinks. It naturally accounts for the strong and near-deterministic LOS component and the independent rea-lizations from reflection paths in modeling the overallchannel response.In OFDM-based systems, the narrowband subchannels

are assumed to be flat fading. Thus, the equivalentchannel matrix between the transmitter and receiver isgiven by

H = [hij], with hij =Nrays=1

()ij (t 0)|t=0 (3)

for i = 1, 2, ..., Nr and j = 1, 2, ..., Nt, where the entryhij denotes the channel response between transmitter jand receiver i by aggregating all Nrays traced raysbetween them at the delay of the LOS component, 0;

and ()ij is the amplitude of th ray in the corresponding

link. Analytically, we can further separate the channelmatrix in (3) into HLOS and HNLOS accounting for theLOS and non-LOS components, respectively

H =

1

K + 1HNLOS +

K

K + 1HLOS (4)

where the Rician K-factor indicates the relativestrength of the LOS component.We assume that the numbers of transmit and receive

antennas, i.e., Nt and Nr , are large. However, the num-bers of available RF chains at the transmitter and recei-ver, nt and nr, are such that nt Nt and/or nr Nr.Hence, we need to choose a subset of nt nr transmitand receive antennas out of the original Nt Nr MIMOsystem and employ these selected antennas for datatransmission (see Figure 2). Denote as the set ofindices corresponding to the chosen nt transmit anten-nas and nr receive antennas, and denote H as the sub-matrix of the original MIMO channel matrix Hcorresponding to the chosen antennas.For data transmission over the chosen MIMO system

H, a transmit beamformer w = [w1, w2, . . . , wnt ]T, with

||w|| = 1, is employed. The received signal is then givenby

r =

Hws + n (5)

where s is the transmitted data symbol; = EsntN0 is thesystem signal-to-noise ratio (SNR) at each receiveantenna; Es and N0 are the symbol energy and noisepower density, respectively; n CN (0, I) is additivewhite Gaussian noise vector. At the receiver, a receivebeamformer u = [u1, u2, ..., unr ]

T, with ||u|| = 1, isapplied to the received signal r, to obtain

y(, w, u) = uHr =

uHHws + uHn. (6)

For a given antenna subset and known channelmatrix H, the optimal transmit beamformer w andreceive beamformer u, in the sense of maximumreceived SNR

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