NTIA Report TR-03-403 

Measurements of Channel Transfer 

Functions and Capacity Calculations 

for a 16x16 BLAST Array over a 

Ground Plane 

Peter B. Papazian 

Yeh Lo 

John J. Lemmon 

Michael J. Gans 

U.S. DEPARTMENT OF COMMERCE 

Donald L. Evans, Secretary 

Nancy J. Victory, Assistant Secretary 

for Communications and Information 

June 2003 

CONTENTS 

Page 

FIGURES........................................................................................................................... iv 

TABLES ..............................................................................................................................v 

ABSTRACT.........................................................................................................................1 

1. INTRODUCTION ......................................................................................................1 

2. TRANSMITTER AND RECEIVER OPERATION...................................................3 

3. ANTENNAS AND GROUND PLANE .....................................................................8 

4. DATA PROCESSING..............................................................................................10 

5. CHARACTERISTICS OF THE PN SEQUENCE ...................................................11 

6. SYSTEM CALIBRATION.......................................................................................11 

7. DATA COLLECTION FORMATS AND PROCEDURES.....................................12 

7.1 16x16 BLAST Test.......................................................................................12 

7.2 1x16 BLAST Test.........................................................................................13 

 7.3 Keyhole Test .................................................................................................13 

 7.4 CW Tests.......................................................................................................14 

7.5 Antenna Coupling Tests................................................................................14 

7.6 Antenna Element Calibration........................................................................14 

7.7 Data Collection Summary.............................................................................16 

8. TRANSFER FUNCTION AND H MATRIX CALCULATIONS...........................17 

9. RESULTS .................................................................................................................18 

 9.1 Transfer Function Identification ...................................................................18 

 9.2 Theoretical Capacity Calculations................................................................19 

9.3 Power Lobing Patterns..................................................................................21 

9.4 Comparison of Measured and Predicted Results..........................................27 

10. CONCLUSIONS.......................................................................................................29 

11. REFERENCES .........................................................................................................30 

APPENDIX A: ANTENNA COUPLING DATA SUMMARY TABLES ......................31 

APPENDIX B: ANTENNA ELEMENT CALIBRATION SUMMARY TABLES........38 

iii 
APPENDIX C: DATA COLLECTION SUMMARY ......................................................40 

APPENDIX D: TRANSMITTER CALIBRATION DATA.............................................42 

APPENDIX E: SOFTWARE DESCRIPTION.................................................................43 

E.1 CalTx ..............................................................................................................43 

E.2 CalRx..............................................................................................................43 

E.3 CalSys.............................................................................................................43 

E.4 Praw Hij ..........................................................................................................44

E.5 Praw 1x16.......................................................................................................44 

FIGURES 

Page 

Figure 1. 16-channel wideband sounder transmitter .........................................................4 

Figure 2. 16-channel FPGA P/N code generator at transmitter ........................................5 

Figure 3. 4 RF channels of 16-channel transmitter array..................................................5 

Figure 4. Block diagram of 4-channel receiver.................................................................6 

Figure 5. Preselector filters and low noise amplifiers of 4-channel receiver....................6 

Figure 6. Block diagram of data acquisition system .........................................................7 

Figure 7. Antenna arrays on ground plane, the closer array is the receiving antenna. 

The antenna elements are shown in Figure 8.....................................................8 

Figure 8. Dipole antenna elements in vertical array..........................................................9 

Figure 9. Maximal length sequence shift register connection for period of 29

-1 (511) 

chips.................................................................................................................11 

Figure 10. E-plane co-polarized and cross-polarized antenna patterns for element L01..15 

Figure 11. H-plane co-polarized and cross-polarized antenna patterns for element L01..16 

Figure 12. Transmit and receive array geometry ..............................................................17 

Figure 13. Signals received by 16 antenna elements after correlation..............................19 

Figure 14. Capacity calculated for the 16x16 BLAST array with and without ground 

plane. Capacity is for horizontal polarization and ρ=10..................................20 

iv
Figure 15. Capacity calculated for the 16x16 BLAST array with and without ground 

plane. Capacity is for vertical polarization and ρ=10......................................21 

Figure 16. Power lobing patterns versus receiver number for horizontal antenna 

polarization ......................................................................................................23 

Figure 17. Power lobing patterns versus receiver number for vertical antenna 

 polarization ......................................................................................................24 

Figure 18. Horizontal polarization power lobing patterns for receivers 1-16 from: 

(a) transmitter 1, (b), transmitter 2, (c) transmitter 3, (d) transmitter 16.........25 

Figure 19. Vertical polarization power lobing patterns for receivers 1-16 from: 

(a) transmitter 1, (b), transmitter 2, (c) transmitter 3, (d) transmitter 9...........25 

Figure 20. Frequency effect on null location versus receive antenna height, red for 

f = 2.29 GHz, blue for f = 2.3 GHz, green for f = 2.31 GHz............................26 

Figure 21. Magnitude (abs) and phase (angle) surface plots of the measured and 

calculated H matrix..........................................................................................27 

Figure 22. The capacity of a 16x16 element array situated over a ground plane versus 

the antenna array separation (d), and the height above the ground plane 

of the top element of the receiving array (hmax).............................................29 

TABLES 

Page 

Table 1. Difference between Measured and Calculated H Matrix for 16x16 

Element Array over NIST Ground Plane.........................................................28 

Table 2. Measured and Theoretically Predicted Channel Capacities for 16x16 

Element Array over NIST Ground Plane for ρ =10.........................................28 

Table A-1. Vertical Antenna Coupling Summary..............................................................31 

Table A-2. Horizontal Antenna Coupling Summary .........................................................34 

Table B-1. E/H Co-polarized and Cross-polarized Antenna Scans for Element L01........38 

Table B-2. Summary of E and H Scan Co-polarized Antenna Element Calibration 

Data. Bore-sight Gain and Phase at 2300 MHz for Each Element and 

Range Calibration Files....................................................................................38 

v 
Table C-1. Broadband Channel Sounder BLAST Data Files and Data Descriptions........40 

Table C-2. Spectrum Analyzer (CW) Narrowband BLAST Data Files and 

 Descriptions.....................................................................................................40 

Table C-3. Vector Network Analyzer Antenna Element Coupling Data Files and 

Descriptions.....................................................................................................41 

Table C-4. Anechoic Chamber Antenna Element Calibration Data Files and 

 Descriptions.....................................................................................................41 

Table D-1. Transmitter Power Levels Measured at Coupler and Used for TxCal Data ....42 

vi
MEASUREMENTS OF CHANNEL TRANSFER FUNCTIONS AND CAPACITY 

CALCULATIONS FOR A 16X16 BLAST ARRAY OVER A GROUND PLANE 

Peter B. Papazian, Yeh Lo, John J. Lemmon,* and Michael J. Gans**

Wideband channel transfer function measurements were made for a 16-

element transmit and 16-element receive, multiple input, multiple 

output (MIMO) antenna array. The measurements were conducted 

using the National Institute of Standards and Technology (NIST) open 

area test site (OATS), allowing analytic calculations of the channel 

transfer functions. The H matrix for the BLAST array was then 

determined from measured data and the link capacity was calculated 

using information theory. The theoretical link capacity was then 

calculated and found to be 22.16 Bits/Hz/s for horizontally polarized 

antennas and 22.19 Bits/Hz/s for vertically polarized antennas. It was 

then found that the measured results agreed with the theoretical 

calculations with 5% error using horizontally polarized antennas and 

with <0.3% error for the vertically polarized case. The objective of this 

work was to verify that wideband measurements could be used to 

accurately measure H and predict the capacity of a MIMO channel. 

Key words: BLAST; capacity; H matrix; impulse response; information theory; 

MIMO; radiowave propagation; transfer function 

1. INTRODUCTION 

It has been shown that the capacity of communications channels can be increased 

significantly by dividing the transmit power between multiple antenna elements and 

receiving with multiple antenna elements, when operating in a scattering environment 

[1,2]. This technique is called the ìBell Laboratories Layered Space-Timeî (BLAST) 

communication technique in this report. 

The narrowband channel capacity for a communications link with nT transmitting 

antennas and nR receiving antennas is: 





















 



 = + Ü log2 det I HH

T n

C ρ Bits/Hz/s, (1) 

where H is the normalized, narrowband complex transmission coefficient matrix from

each transmitting antenna to each receiving antenna and ρ is an average signal-to-noise 

 

*

 The authors are with the Institute for Telecommunication Sciences, National Telecommunications and

Information Administration, U.S. Department of Commerce, Boulder, Colorado, 80305. ** The author is retired from Lucent Technologies, Holmdale, New Jersey. 
ratio at the receiving antennas. The H matrix is normalized to signify an average power 

transmission over all combinations of transmitter antenna and receiver antenna of unity; 

i.e., 

T R

All j k

jk ∑ = n n ,

2

H . (2)

HÜ

 is the Hermitian conjugate (transpose of the complex conjugate) of H. The 

normalization of Equation (2) is a result of the definition of ρ as the average signal-tonoise ratio at the receiving antennas when the total transmitter power is radiated from a 

single transmitting antenna. ρ is averaged over all combinations of transmitting and 

receiving antennas. 

By measuring the transmission coefficient matrix, H, in a given environment, one can 

compute the channel capacity, C, of Equation (1). This can be computed for any assumed 

signal-to-noise level, ρ, of the communication link, which we term the system signal-tonoise level. The measurement signal-to-noise ratio, γ, is that which is achieved by the 

measurement equipment used to measure the transmission coefficient matrix, H. Clearly, 

one wishes to maintain a large γ in order to obtain accurate measurements of H. Once H

is accurately measured, one can predict the link capacity for any system ρ , as mentioned 

above. 

It is of interest to know how accurately H can be measured. This has never been done 

using a wideband measurement system in a known propagation environment. The 

National Institute of Standards and Technology (NIST) has an open area test site (OATS) 

in which one can accurately model an array transmission link. The site consists of a 60 m

by 30 m metallic ground plane with mast sites separated by 30 m. Mounting plates at 

these sites are used to support the transmitting and receiving antenna arrays and allow 

access to underground tunnels to route cables below the ground plane. In this way, the 

cabling used for the two arrays is hidden from the propagation environment by the back 

planes of the antenna arrays and the ground plane. Simple half-wave dipoles are 

supported on the reflecting back planes to provide predictable patterns, with minimal 

mutual coupling due to the wavelength spacing of the array elements. A theoretical 

prediction of the channel capacity of such a communication link is given in [3,4] and in 

Section 8 and Section 9 of this report. 

The remainder of this report is organized as follows: Section 2 describes the wideband 

transmitter and receiver and data acquisition system used for this experiment. Section 3 

describes antenna arrays. Section 4 outlines the data processing procedure. Section 5 

describes the psuedo noise coding used to identify transmitter elements. Section 6 

discusses the system calibration methods. Section 7 describes the data collection 

procedures and the test data collected. Section 8 explains how the transmission link was 

modeled. Section 9 reports the results. Section 10 gives conclusions and Section 11 is the 

reference list. 

2 
2. TRANSMITTER AND RECEIVER OPERATION 

Wideband measurements of the channel impulse response were made using a pseudo 

noise channel sounder. Figure 1 is a block diagram of the sounderís transmitter. 

Wideband signals are generated using a psuedo-noise (PN) sequence generator clocked 

by a 10-MHz rubidium frequency standard. The sequence generator (see Figure 2) is a 

self-controlled field programmable gate array (FPGA) and uses a maximal length shift 

register code of length 511 chips clocked at 10 mega-chips per second. Using the FPGA, 

the 16 outputs from the code generator are successively delayed by 32 chips (3.2 microseconds) relative to the previous output. These delayed codes are orthogonal. Thus the 

impulse response of each transmitter is able to avoid interference with all other 

transmitters provided the propagation delay spread is less than 32 chips (3.2 

microseconds or 0.9 km). In this way, the sequences can be transmitted simultaneously 

and continuously using the rubidium clock reference signal, and the transfer matrix can 

be measured at the receiver. 

Figure 3 shows a picture of the up-conversion and RF portions for 4 channels of the 

transmitter. The PN sequences are level shifted by a wideband limiter to create ±1 

outputs that are then low-pass filtered (LPF) for pulse shaping. The 10-MHz clock also 

synchronizes a 2.3-GHz local oscillator which is split 16 ways and used to feed the 16 

upconverter mixers that provide a 20-MHz bandwidth RF signal, to each of the power 

amplifiers. The power amplifiers operate at +22 dBm. The output RF filters eliminate 

unwanted sidebands in the simultaneous radiation from the 16 antenna elements. 

A 4-channel receiver is time-shared between 4 groups of 4 receiving antenna elements to 

achieve the measurement capability of a 16-element receiver. The switching between 

each of the 4 antenna groups is accomplished in 80 nanoseconds using a multiplexer 

(MUX). For this experiment the MUX was operated manually at 10-second intervals. 

Since the antennas and environment were stationary, automatic fast switching was not 

necessary. For each group of 4 antenna elements, a burst of impulse data was collected. 

Figure 4 shows a block diagram of the 4-channel receiver. The signals received by the 

antenna array are first filtered with preselection filters (Figure 5) to eliminate out-of-band 

interference before amplification by low noise amplifiers. A 2.14-GHz local oscillator, 

synchronized to the same rubidium clock, is used to down-convert the signal to the first 

IF of 160 MHz. The signal is then filtered to remove unwanted sidebands and amplified. 

A programmable analog gain control (AGC) amplifier is then inserted to provide 70 dB 

dynamic range with constant output levels for the digitizers. The AGC control loop 

averages output power over one millisecond and the AGC level control data is output to 

the data recording equipment. The IF is then downconverted with a 150-MHz local 

oscillator, again synchronized by the rubidium clock, to a signal centered at 10 MHz. The 

second local oscillator frequency is chosen to maintain an output signal that is periodic at 

the sequence length duration (51.1 μsec). The 4-channel receiver outputs analog data to a 

VME bus 8-bit digitizer, sampling at 40 mega-samples per second (MS/s). Since the 

maximum frequency of the second IF only extends to 20-MHz, the sampling rate meets 

the Nyquist requirement. 

3 
LPF

10 dB

Level

Shifter

37dB

LPF

10dB

LPF

10 dB

Level

Shifter LPF 37dB

10dB

Rubidium

Frequency

Standard

16 Copies

pn code

generator

Signal

Generator

37dB

3dB

3dB

LO

2300 MHz

LO

2300 MHz

pn # 1

pn # 16

TX # 1

TX # 16

Figure 1. 16-channel wideband sounder transmitter. 

4 
Figure 2. 16-channel FPGA P/N code generator at transmitter. 

Low Pass Filter

Level Shifter

Mixer

10 dB Pad

3dB Pad

10 dB Pad

Power Amp

Power

Supply

Figure 3. 4 RF channels of 16-channel transmitter array. 

5 
VME

Digitizer

3dB 3dB

Ch3 Ch4

3dB 3dB

Ch2 Ch1

LPF

3 dB

BPF 37dB 27dB

Trigger

40 MHz Sampling clock

Ref. in

LO

2140 MHz

LO

150 MHz

3 dB 3 dB 16 dB 3 dB

LPF

3 dB

BPF

BPF

37dB

27dB AGC

27dB

LPF

3 dB

BPF 37dB 27dB

LPF

3 dB

BPF 37dB 27dB

LO

2140 MHz

LO

2140 MHz

LO

2140 MHz

LO

150 MHz

LO

150 MHz

2300 MHz RF in

2300 MHz RF in

Power

Divider

Power

Divider

Absolute

Timing

Circuit

Rubidium

Frequency

Standard

3 dB 3 dB 16 dB 3 dB

BPF 27dB AGC

3 dB 3 dB 16 dB 3 dB

BPF 27dB AGC

3 dB 3 dB 16 dB 3 dB

BPF 27dB AGC

Multisource

Generator

LO

150 MHz

Figure 4. Block diagram of 4-channel receiver.

 

Figure 5. Preselector filters and low noise amplifiers of 4-channel receiver. 

6 
The VME digitizer has its own dedicated 2-Gbyte hard drive to which the data is 

streamed at a rate of 2 Mbytes per second. The FPGA timing circuit at the receiver 

controls the data sampling and recording. It is configured to record a burst of 128 

impulses, 51.1 μs long with 3 milliseconds between impulses (2044 8-bit samples per 

receive channel per impulse). The receiver then waits 10 seconds while the antenna 

multiplex switch is set to receive the next set of 4 antennas. Thus a complete set of data 

for the 16 transmit elements by 16 receive elements is about 4.1 Mbytes plus 800 bytes of 

AGC data and other overhead information in file headers. A block diagram of the data 

acquisition and storage equipment is shown in Figure 6. 

4 Channel

40 Ms/s A/D

SCSI

Tape Drive

Hard Drive

CD

Writer

Rcvr

Comm

8 Channel Ports

20 Ms/s A/D

SCSI

Hard Drive

Hard

Drive

Network

Computer

8 Channel

Audio A/D

Mix

Bus

Ok for

another

Burst

Rhubidium

Clock FPGA

Comm

Ports

486

PC

Quad

DSP

VME

Bus

Ether

Net

GPS

Figure 6. Block diagram of data acquisition system.

Raw data can be sent to the network computer for further processing and archived on CD 

ROMs. The raw data is a collection of the digital samples of all the received waveforms. 

These digital samples are then processed in the PC or in the network computer to obtain 

the impulse response representation of each transmission matrix element corresponding 

to a given transmitting antenna element and a given receiving antenna element. 

7 
3. ANTENNAS AND GROUND PLANE 

The antenna elements are half-wave dipoles mounted one-quarter wavelength above a 

reflecting back plane. The back plane allows the dipole feed cabling to have negligible 

interaction with the propagation between the transmitting and receiving arrays. The 

dipole elements are spaced one wavelength apart (0.13m) along a vertical from 17.5 

wavelengths above the ground plane to 32.5 wavelengths at both the transmitter and 

receiver. The aluminum back planes are 4 wavelengths wide, extending from the ground 

plane to a height of 34.5 wavelengths. The distance from the transmitting array to the 

receiving array is 231.71 wavelengths (30.2m), and the arrays are centered on the 60 m

by 30.5 m ground plane. The arrays and ground plane are shown in Figure 7 and Figure 8. 

 

Figure 7. Antenna arrays on ground plane, the closer array is the receiving 

antenna. The antenna elements are shown in Figure 8. 

8 
Figure 8. Dipole antenna elements in vertical array. 

The ground plane is terminated along its edges with triangular serrations to minimize 

edge reflections, so that the propagation is well approximated by dipoles over an infinite 

ground plane. This feature allows for a simple analytic model of the communications 

channel described in Section 8. The receiving antenna cables are fed under the ground 

plane and through a tunnel approximately 8 m long to the receiving and data recording 

equipment. The transmitter equipment was shielded from the experiment by the transmit 

array backing plate. The cables connecting the transmitter to the antenna elements were 

approximately 5 m long. Receiver equipment is located in a climate-controlled room at 

the end of the access tunnel under the receive array and ground plane. Coupling between 

cables was measured to be less than ñ100 dB. The mutual coupling between antenna 

elements was measured using a network analyzer over the 20-MHz band centered at 2.3 

9 
GHz. These results are discussed in section 7.5 and reported in detail in Appendix B. It 

was concluded that the mutual coupling between antenna elements had a negligible effect 

on the H matrix magnitude measurements. The antenna patterns were measured for all 

the antenna elements over 4λ backing plates. The backing plates increased the forward 

gain of the elements. The antenna impedance match was better than 10 dB return loss 

over the band. The cross-polarization discrimination was better than 30 dB in most 

directions. The antenna patterns were matched over all the elements to within .1 dB at 

boresight and 1 dB in most directions. More details on antenna calibration are given in 

sections 7.5 and 7.6. 

4. DATA PROCESSING 

Post acquisition processing of the digitized IF signal provides impulse response data for 

all the receiving antenna elements. This impulse data is then processed to yield the H

matrix required by Equation 1 for the capacity calculation. There are several steps in the 

processing that include down conversion, correlation, transmitter receiver channel 

identification, and calibration which are performed prior to the calculation of the H

matrix. 

 

The first stage of the processing is to down convert the real IF signal to complex 

baseband; this is done in the time domain. These results are then transformed into the 

frequency domain using a discrete Fourier transform (DFT) and then low pass filtered to 

remove unwanted side lobes. A copy of the transmitted PN code is also transformed to 

the frequency domain using a DFT and then the data and the PN code are convolved at 

baseband by multiplying the Fourier coefficients of each transform. The result is a band 

limited system response for each antenna element. This data can then be translated back 

to the time domain using an inverse DFT. Since each transmit antenna broadcasts a 

delayed version of the same psuedo noise sequence, each transmitter can be identified by 

its delayed impulse response. These signals are separated in time, zero padded and 

transformed back to the frequency domain where a 16x16 calibration matrix can be 

convolved with each matrix element corresponding to the 256 channel transfer functions. 

After multiplication by the calibration constants for each transmitter receiver pair, the 

calibrated transmission matrix is normalized to produce the H matrix. The psuedo noise 

sequence transmitted is defined in Section 5 and the calibration matrix is described in 

Section 6. 

10 
5. CHARACTERISTICS OF THE PN SEQUENCE 

The PN sequence is stored in ROM memory on the FPGA chip. The stored sequence is 

equivalent to the output of a shift register with 9 delays and 2 modulo 2 additions 

connected for a maximal length sequence at taps 4 and 9, as shown in Figure 9. 

Figure 9. Maximal length sequence shift register connection for period of 29-1 

(511) chips. 

6. SYSTEM CALIBRATION 

A series of wideband system calibration measurements were made without antennas in 

preparation for BLAST testing. The purpose of these calibrations was to determine 

relative amplitude and phase calibration between receiver channels. Additionally, these 

data can be used to determine the system response of each measurement channel in order 

to deconvolve the effects of the measurement system. The calibrations were completed 

using two system configurations that produced two sets of raw calibration data. 

The first configuration is called TxCal. This configuration utilized all transmitter 

channels fed through the transmitter cables, arrayed as they were to be used during the 

testing, into an N-Type coupler and then connected to the appropriate receiver cabling 

and through the MUX to the receiver and digitizers. The output power for each 

transmitter is constant but can be varied in 10-dB steps using a set of precision 

attenuators. Each transmitter power level was measured at the coupler and stored. The 

power level was then varied over a 70-dB range to check the linearity of the AGC, 

receiver dynamic range and sensitivity. In this way each receiver channel can be 

calibrated for transmitter power levels as referenced to the receiver antenna terminal. The 

data for this calibration is stored in 4 data files consisting of 7 bursts of data. Each burst 

has 128 impulses for 4 channels at one power level. 

The second configuration is called RxCal. Here one transmitter channel is utilized to 

provide identical signals to all 16-receiver channels using the antenna cabling and all the 

hardware except the antennas used for the BLAST tests. Using this data the system

calibration can be described using the following equations.

11 
The system response calibration matrix cij is 

ij TiRj c = , (3) 

where Ti is the transfer function of the i

th transmitter and Rj is the transfer function of the 

j

th receiver. The TxCal configuration provides measured values of cii , i=1,Ö,16. The 

RxCal configuration provides measured values of c1j , j=1,....,16. The remaining elements 

of cij can be determined from the measurements by writing cij as 

i

ii j

i

j

i i

i

i

ij i j i j c

c c

T R

T R

T R

R

R

T

T

c T R T R

1

1

1

1

1

1 = = = = . (4) 

7. DATA COLLECTION FORMATS AND PROCEDURES 

This section describes the data collection procedures for the BLAST tests. Wideband data 

was collected using the 16-channel pseudo-noise transmitter, 4-channel wideband 

receiver, and 4-channel A/D section configured for burst mode acquisition. The burst 

mode combined with a 16-channel multiplexer (MUX) enabled the 16 receive antenna 

signals to be recorded as multiple data bursts in a single or multiple data files. Each burst 

of data consists of 128 impulses per channel with 2044 IF samples per channel per 

impulse sampled at 25-ns intervals (40-MHz rate). The delay between impulses is set to 3 

ms and the delay between bursts to 10s. Channel data were stored using multiple data file 

configurations for different wideband tests and these configurations are described in the 

following sub-sections. 

7.1 16x16 BLAST Test 

This was a fundamental test, as it was accomplished with simultaneous transmissions 

from all transmitters. To record this data on the 4-channel receiver it required the 16-

channel MUX. The MUX was manually switched 4 times between data bursts allowing 

16 receive antenna signals to be recorded in one data file. This file contained 4 bursts of 

data. If all transmitters were operational this resulted in a 16x16 data set. Each receiver 

antenna element senses the 16 signals that were transmitted simultaneously. The integer 

A/D values along with header and AGC data corresponding to the received voltage vj for 

each receive antenna element, j=1,2Ö. 16, are stored in one file. The data structure can 

be summarized using the burst # and channel number as follows: 

Burst 1 Ch1 = v1,

Burst 1 Ch2 = v2,

Burst 1 Ch3 = v3,

Burst 1 Ch4 = v4,

Burst 2 Ch1 = v5,

12 
Burst 2 Ch2 = v6,

• 

• 

Burst 4 Ch4 = v16.

7.2 1x16 BLAST Test 

These tests used one transmitter channel and 16 receive channels (1x16) 16 times to 

collect the 256-element channel matrix data. The objective was to increase the signal-tocorrelation noise level of the measured channel impulse response. This should have 

decreased the correlation noise level caused by transmitting 16 codes simultaneously. 

Since an increase in the signal to correlation noise level was not observed, this indicated 

that the psuedo noise generator was not the limiting factor. It is assumed that noise and 

distortion generated by analog components like filters in transmitter and receiving 

circuitry limited the signal to correlation noise level. 

By manually switching the MUX between data bursts, 16 receive antenna signals were 

recorded in one data file. Because only one transmitter at a time was operational, this 

resulted in a 1x16 BLAST data set. By repeating the procedure 16 times, a 16x16 BLAST 

data set was recorded. When a 1x16 data set was being recorded all unused transmitters 

and transmitter antenna elements were terminated into 50 Ω loads. The recorded integer 

A/D values correspond to the receive antenna element voltages vi,j, where i is the 

transmitter number and j is the index for the receive antenna element number. The data 

structure can be summarized using the file #, burst #, and channel number as follows: 

 

File1 (Tx1) File2 (Tx2) File3 (Tx3)ÖÖÖÖÖ...File 16 (Tx16) 

Burst 1 Ch1 = v1,1 Burst 1 Ch1 = v2,1 Burst 1 Ch1 = v16,1

Burst 1 Ch2 = v1,2 Burst 1 Ch2 = v2,2

Burst 1 Ch3 = v1,3

Burst 1 Ch4 = v1,4

Burst 2 Ch1 = v1,5

Burst 2 Ch2 = v1,6

• 

• 

• 

Burst 4 Ch4 (v1,16) Burst 4 Ch4 = v2,16 Burst 4 Ch4 = v16,16

7.3 Keyhole Test 

The objective of these tests was to determine the measurement signal to noise level, γ. 

These tests were made using the 16-channel transmitter and a power splitter at the 

receiver. v1,1 was split 16 ways and fed into the MUX to all 16-receiver channels. Unused 

receiving antennas were terminated into 50 Ω loads. This data was not analyzed because 

13 
it was clear from the received power levels that the measurement signal to noise level 

was in excess of 30 dB. Data for the keyhole test were stored in one data file containing 4 

bursts of data as in the 16x16 BLAST tests. 

7.4 CW Tests 

CW tests utilized a signal generator tuned to 2300 MHz at the transmitter. The signal 

source was used to feed single transmitting antenna elements. Power at the transmit 

antenna terminals varied from ñ11.8 to ñ10 dBm (see Appendix D). The received signal 

strengths were measured using a spectrum analyzer and corrected for receiver cable loss 

to yield the received signal power at the antenna terminals. These data were collected for 

comparison with the wideband results. 

7.5 Antenna Coupling Tests 

Antenna coupling was measured using a vector network analyzer (VNA). These tests 

were performed on the receiving antenna array in-situ over the ground plane. All receiver 

cables were in place and configured as in the BLAST testing (see Figure 7). The VNA 

was calibrated for 2-port operation with the measurement plane situated at the end of the 

antenna cables. After calibration, a through measurement was recorded using port 1 and 

port 2 cables only. The through VNA calibration is labeled in the data log (Appendix A) 

as Cal. For coupling tests the stimulus cable was hooked to port 1 on the VNA and the 

receiver cable was hooked to port 2. Data is stored in HP CITI format on disks, as 

summarized in Tables A1 and A2. Tables A1 and A2 also give a summary S12 or S21 in 

dB at 2300 MHz. 

From the tables in Appendix A, we see that S12 = S21, and antenna coupling between 

adjacent antenna elements is ≤ -20 dB for horizontal polarization and ≤ -30 dB for 

vertical polarization. Coupling then decreases with increased element separation. The 

phase and amplitude data are archived in case more detailed modeling of the H matrix is 

required in the future. For our purposes the coupling was sufficiently small to allow the 

magnitude of H to be measured without including the coupling terms in the analysis. An 

analytical coupling analysis also indicated that antenna element coupling could be 

ignored.∗

7.6 Antenna Element Calibration 

35 dipole antenna elements were manufactured using designs for a 1.92-GHz dipole 

antenna and then scaled to 2.3 GHz. Tests were performed in an anechoic chamber to 

confirm the performance of the scaled antenna elements. The tests were made using a 

calibrated standard gain horn as transmitter. The antenna under test (AUT) was mounted 

 

∗

 M.J. Gans, Personal Communication, June 2002.

14 
on a 4λ square ground plane and the center of rotation of the test fixture was aligned to 

the ground plane. A prototype antenna numbered L01 was first tested in the anechoic 

chamber by making co-polarized and cross-polarized E and H scans over a 100-MHz 

frequency range. This data was used to confirm that the frequency scaling worked and 

that the cross polarization discrimination met the design specifications of -40 dBC. Copolarized and cross-polarized patterns for L01 at 2300 MHz are shown in Figures 10 and 

11. After it was confirmed that the antenna met specifications, 34 additional elements 

were made with sequential serial numbers. These elements were then tested, but this time 

only at the center frequency of 2300 MHz. These tests were used to determine if the 

machining process was uniform and that the antennas had similar gain and phase 

responses. It was found that all 35 elements had a gain variation of not more than 0.5 dB 

and phase variability of about ± 4° at bore sight at 2300 MHz. This allowed all 

transmitting and receiving antennas to be treated as identical elements in the analysis 

sections. These test data are summarized in Appendix B, Table B-1 and Table B-2. Raw 

antenna scan data are stored in TAR format. Since all elements were almost identical, 

numbers L1-L16 were chosen for the receiver antenna array and numbers L17-L32 were 

used for the transmitting antenna array (see Figures 7 and 8). 

-45

-30

-15

0

-100 0 100

Cross Pol

Co Pol

Elevation(deg)

dBi

E Plane Antenna Gain Element L01

Figure 10. E-plane co-polarized and cross-polarized antenna patterns for element L01. 

15 
-45

-30

-15

0

-100 0 100

Cross Pol

Co Pol

Azimuth(deg)

dBi

H Plane Antenna Gain Element L01

 

Figure 11. H-plane co-polarized and cross-polarized antenna patterns for element L01. 

7.7 Data Collection Summary 

Calibration and transfer function data were collected over a period of several months and 

multiple tests were conducted to verify that data was repeatable. A data collection 

summary for all tests is given in Appendix C. 

16 
8. TRANSFER FUNCTION AND H MATRIX CALCULATIONS 

In the theoretical calculations the antenna elements were treated as identical isotropic 

radiators and the ground plane was incorporated using the theory of images. The 

geometry of the antenna array at the OATS is shown in Figure 12. 

hb

hb+ (nT-1)s

s

d

Ground Plane (when present)

nT - Element

Transmit Array Receive Array

Figure 12. Transmit and receive array geometry. 

Here hb is the height of the bottom antenna element over the ground plane, d is the 

distance between the arrays and s is the separation between elements. For the tests hb was 

17.5 λ, d was 231.5 λ, and s was λ. Since we are interested in only relative amplitude and 

phase between antenna elements, the transfer function Tkm can be simply represented as 

,

2

km

j r

km

r

e T T

km

λ

− π

= (5) 

where 2 2 ( ) km d hk hm r = + − and hk and hm are the transmit and receiver antenna 

element heights respectively. If we let r represent the distance between the k '

km

th image 

source and the m

th receiver, then T , the image source transfer function (for the reflected 

path), is 

'

km

, '

2

'

'

km

km

km r

e T T

j r

λ

− π

= (6) 

17 
with ( ) ' 2 2

km k m r = d + h + h . Then if is used to represent the transfer function for the 

direct and reflected signal from the ground plane, 

Tkm

~

, ~ '

2 2 '





















= +

− −

km

j r

km

j r

km

r

e

r

e T T

km km

λ

π

λ

π

 (7) 

for vertical polarization, and 

, ~ '

2 2 '





















= −

− −

km

j r

km

j r

km

r

e

r

e T T

km km

λ

π

λ

π

 (8) 

for horizontally polarized signals. H is then obtained from H=B with B chosen so that 

the average of |H

~

T

km| over the matrix elements is unity as in Equation 2. The theoretical 

capacity of the link can now be calculated using Equation 1 and compared with the 

capacity predicted using the measured channel transfer function. 

9. RESULTS 

9.1 Transfer Function Identification 

Figure 13 shows the magnitude of the measured impulse response from receiver antenna 

elements 1ñ16. This is an example of a BLAST 16x16 data set at an early stage of 

processing. During this test the transmitter and receiver antennas were aligned 

horizontally. 16 successively delayed orthogonal psuedo-noise codes were 

simultaneously transmitted from all transmitter elements. The orthogonal coding allowed 

the signal from each transmitter element to be identified at each receiver antenna as a 

delayed impulse response. Figure 13 has 16 plots, each with 16 impulses separated by 3.2 

μs. Each successive impulse represents the received signal from transmit antennas 1 

through 16. Plot 1 is in the upper left hand corner and plot numbers increase from left to 

right. Row two begins with plot 5, row 3 with plot 9 and row 4 with plot 13. In plot 1, 

impulse 1 corresponds to the magnitude of the transfer function between transmitter 1 

and receiver 1 or T1,1. Also on plot 1, impulse 2 corresponds to T2,1 , impulse 3 to T3,1,

etc., up to T16,1 . The first impulse on plot 16 (lower right hand corner) corresponds to 

T16,1 , the second impulse to T16,2 , etc. Since multipath was non-resolvable (the time 

difference between the direct and reflected signal is less than a chip period), the 

amplitude of each impulse response forms a lobing pattern (for example, the path length 

difference between the top transmitter and receiver was 8.95λ, 1.17m or 3.9 ns). Because 

different transmitter receiver pairs experience fading nulls caused by interference 

18 
between the direct and reflected paths, we see the vertical power lobing patterns in the 

impulse response data. One can see how the lobing pattern changes for different 

transmitter and receiver combinations by examining the sixteen plots. Note that signals 

below the peaks of the impulse response represent correlation noise. This data set (Figure 

13) contains the 256 transfer functions needed to define the BLAST radio channel and 

calculate its capacity (C (Bits/Hz/s)). These data are separated into the 256 complex 

transfer functions, which are then deconvolved using the calibration data. After 

normalization, H is computed in both the time and frequency domains for comparison 

with the calculated results. 

Figure 13. Signals received by 16 antenna elements after correlation. The signals 

from transmitters 1-16 are seen as delayed impulses. The vertical scale 

is relative power and measured in dB. 

9.2 Theoretical Capacity Calculations 

Theoretical capacity curves versus antenna array separation in wavelengths were 

calculated using the equations in Section 8 for a signal-to-noise ratio (ρ) of 10. Figure 14 

and Figure 15 show these results for horizontal and vertical polarization respectively. At 

small and large separations, capacities with and without the ground plane are similar, 

although the capacities are much larger at small separations. These results can be 

understood as follows. Equations (7) and (8) for T imply that as the separation d becomes 

19 
vanishingly small, the diagonal elements become infinite and the off-diagonal elements 

remain finite. Thus, T is proportional to I (the identity matrix). Using Equation (2) to 

normalize H, and substituting into Equation (1), it is easy to see that in this limit the 

capacity is given by C = n log 2 (1 + ρ). Similarly, as d becomes infinite, all propagation 

paths (both direct and reflected) between all transmitters and all receivers become

identical. Thus, all the elements of H (both diagonal and off-diagonal) approach unity. 

Again substituting into Equation (1), it can be shown that the capacity in this limit is 

given by C = log 2 (1 + nρ). These results imply that for n = 16 and ρ = 10, the 

capacities for both polarizations approach 55.4 bits/Hz/s and 7.3 bits/Hz/s for small and 

infinitely large separations, respectively. At intermediate separations the capacity curves 

interpolate between these two limits. As we move beyond 20λ separation, the capacity 

without the ground plane drops relative to the capacity with a ground plane present. Now 

nulls caused by the reflected signal cause off diagonal elements to become small again. 

This caused the capacity with the ground plane to be greater than without the ground. It 

was in this region that our tests were performed. The capacities at d=231.5 λ (test 

separation) are marked on the curves for comparison with the measured results. We see 

that the curves for vertical and horizontal polarization are similar and that the capacities 

of the channel at the test antenna separation are almost equal. 

Figure 14. Capacity calculated for the 16x16 BLAST array with and without 

ground plane. Capacity is for horizontal polarization and ρ=10. The 

predicted capacity with ground plane at d= 231.5 is 22.16. 

20 
Figure 15. Capacity calculated for the 16x16 BLAST array with and without 

ground plane. Capacity is for vertical polarization and ρ=10. The 

predicted capacity with ground plane at d= 231.5 is 22.19. 

9.3 Power Lobing Patterns 

In addition to the wideband H matrix measurements, a series of narrowband 

measurements were taken for comparison with the wideband results. The CW data was 

not collected using simultaneous transmission as in the wideband case. Instead single 

tones were transmitted and received one antenna pair at a time using a signal generator 

and spectrum analyzer. 

Figure 16 shows the theoretical lobing patterns for horizontal antenna polarization. 

Measured CW data, time domain impulse peak data, and frequency domain data from the 

wideband measurements are also displayed on this figure. These CW data are labeled 

using blue circles. The impulse peak data (Ht) were collected using the wideband system

with simultaneous transmissions on all transmitter elements. The impulse peaks, black 

stars, can be extracted from the received signals at each receiver element as described in 

Section 9.1 and shown in Figure 13. The wideband frequency domain data (Hw) from this 

graph are then obtained from the impulse data by time shifting the impulse peaks, zero 

filling to interpolate and remove the unwanted peaks beyond 3.2 μs, and then Fourier 

transforming the results. The frequency data used for this analysis was one step from the 

center frequency of the impulse spectrum. This frequency was chosen to avoid possible 

feed-through at the carrier frequency. These data are displayed as purple diamonds. These 

data points also represent measured transfer functions between antenna elements before 

21 
normalization. The blue line is the lobing pattern calculated at a fine spacing so we can 

see the curve shapes. 

The general trends in these patterns, such as the alignment of lobes seen as a function of 

elevation (receiver #) versus transmitter, can be seen. We see a good comparison between 

the calculated lobing pattern and the CW and Hw frequency domain data in these general 

trends. A similar plot for the vertically polarized antennas is given in Figure 17 (on 

Figure 17 the CW data is not displayed because it was only collected for 3 transmitters). 

We also see that the vertically polarized measured data follows the general trends 

predicted by the calculated curves. A close comparison of plots 16 and 17 shows that the 

nulls and peaks for the horizontally polarized test are 180 degrees out of phase with the 

vertically polarized test, as expected from Equations 7 and 8. 

However, if we look at the data in more detail we see that the impulse peak fit is less 

accurate near the signal nulls than the CW or Hw data. This can be seen more easily in 

Figure 18 which shows the lobing patterns for only 4 transmitters: 1, 2, 3, and 16 (h = 

32.5 λ, 31.5 λ, 30.5 λ, 17.5 λ). The difference in fit is caused by a combination of 

problems when using the time domain results. Some of the error is due to system nonlinearity caused by local oscillator feed-through and port-to-port mixer coupling. These 

effects are filtered out in the frequency domain data, hence the better fit. Figure 19 shows 

a more detailed view of the data fit for the vertical polarized data. Here we only show 

plots for the 3 transmitters that had CW data. Another noticeable effect is that the data 

does not fit equally well for all transmitters. This fit can be adjusted by tweaking the 

model parameters for antenna element positioning errors. We adjusted the distance 

between antenna arrays and height of the arrays above the ground plane by .01 to 0.1 λ to 

obtain the best fit. This was done visually and a least squares approach may have been 

more accurate, but it was felt the fit was good enough given the number of parameters 

that may have affected the fit such as gain variations between array elements, array tilt, 

array height, array rotation etc. Another effect that changes the data fit that can be 

mitigated in the frequency domain is a shift in the position of nulls as a function of

frequency. 

22 
Figure 16. Power lobing patterns versus receiver number for horizontal antenna 

polarization. Patterns are measured and calculated received power for 

transmitter 1 to receivers 1-16, top left, transmitter element 4 to 

receivers 1-16, top right, transmitter 13, bottom left, and transmitter 

16, bottom right. Transmitter 1 was the upper transmit element at an 

elevation of 32.5 λ above the ground plane. On the graphs, blue circles 

are CW, black stars are impulse peaks, and purple diamonds are 

frequency domain data. 

23 
Figure 17. Power lobing patterns versus receiver number for vertical antenna 

polarization. Patterns are measured and calculated received power for 

transmitter 1 to receivers 1-16, top left, transmitter element 4 to 

receivers 1-16, top right, transmitter 13, bottom left, and transmitter 

16, bottom right. Transmitter 1 was the upper transmit element at an 

elevation of 32.5 λ above the ground plane. On the graphs, black stars 

are impulse peaks and purple diamonds are frequency domain data. 

24 
Figure 18. Horizontal polarization power lobing patterns for receivers 1-16 from: (a) transmitter 

1, (b), transmitter 2, (c) transmitter 3, (d) transmitter 16. Transmitter 1 is on the top

of the array at 32.5 λ above the ground plane. Receiver 0 is also on the top at 32.5 λ

above the ground plane. 

Figure 19. Vertical polarization power lobing patterns for receivers 1-16 from: (a) transmitter 1, 

(b), transmitter 2, (c) transmitter 3, (d) transmitter 9. Transmitter 1 is on the top of

the array at 32.5 λ above the ground plane. Receiver 0 is also on the top at 32.5 λ

above the ground plane. 

25 
We can see these frequency effects for horizontal polarization by using Equation 7. An 

analysis of null shifting at three frequencies is shown in Figure 20. This graph shows the 

dB power fluctuation near receiver antenna element 4 for a signal from transmitter 

element 17. Although a 20-MHz shift in frequency can cause a 14.6-dB fade to decrease 

to only an 8.2-dB fade (which is on the order of the observed deviations from narrowband), the results should be averaged over the bandwidth (depending on how the wide 

band impulse peak fluctuations are observed in the recordings). Therefore the shift in null 

location with frequency seems to come up short as the sole explanation for the impulsepeak deviations from the narrowband results. An examination of the frequency domain 

measurement results indicated that LO feed-through is also a contributing factor for 

errors at null locations. It was concluded that the combination LO feed-through and null 

shifting as a function of frequency are responsible for errors when comparing the 

narrowband calculations to the wideband time domain data. Since there is no easy way to 

remove this effect in the time domain, the H matrix and capacity calculation comparisons 

were done in the frequency domain where these effects could be filtered out. 

Figure 20. Frequency effect on null location versus receive antenna height, red 

for f = 2.29 GHz, blue for f = 2.3 GHz, green for f = 2.31 GHz. 

In this analysis, we use d = 231.5 wavelengths at center frequency and hb = 17.25 center 

frequency wavelengths. 

26 
9.4 Comparison of Measured and Predicted Results 

Using Equations 7 and 8, H was calculated and compared to the measurement results for 

both horizontal and vertical polarization. Figure 21 shows a surface plot of the calculated 

and measured results for both magnitude and phase. It was found that the measured phase 

results did not agree well with the predictions, presumably due to quadrant errors that we 

were unable to resolve. 

Figure 21. Magnitude (abs) and phase (angle) surface plots of the measured and 

calculated H matrix. The vertical scale is in linear units and the phase 

is measured in radians. The horizontal scale is the i,j index of H. 

The error in the magnitude of H was evaluated using the following equations: 

 , meas

ij

calc

εij = Hij − H (9) 

 , 1 = ∑

ij

ij

t r n n

ε ε (10) 

27 
 ( ) ( ) , 1

var 2

= ∑ − ij

ij

t r n n ε ε ε (11) 

σ var( ) ε . ε = (12) 

Using Equation 1 the capacity was calculated for a system ρ=10 for both the horizontally 

polarized and vertically polarized cases using the measured H matrix and the calculated 

H matrix. 

The statistical comparisons between the H matrices are given in Table 1 and Table 2. We

see from Table 1 that the variance of the difference in magnitudes between H measured 

and H calculated was 0.026 and 0.023 for the horizontal and vertical polarization cases 

respectively. In Table 2 we see the error between the capacity calculated using the 

measured H and the theoretical H was 5% for horizontal polarization and 0.27% for 

vertical polarization. Larger errors for the horizontal polarization case may be due to 

mutual antenna coupling which was ignored in the calculations and was stronger for the 

horizontal polarization case. 

Table 1. Difference between Measured and Calculated H Matrix for 16x16 

Element Array over NIST Ground Plane 

ε var(ε ) σε

H Polarization -0.0376 0.0260 0.16 

V Polarization -0.0084 0.0230 0.15 

 

Table 2. Measured and Theoretically Predicted Channel Capacities for 16x16 

Element Array over NIST Ground Plane for ρ =10 

Ccalc(b/Hz/s) Cmeas(b/Hz/s) ∆C 

(b/Hz/s) 

% 

Error 

H 

Polarization 

22.16 21.04 1.12 5

V 

Polarization 

22.19 22.25 0.06 0.27

Since it was known that small changes in transmitter separation and array height could 

change the H matrix, a parameter study was done to evaluate the effects of array 

positioning errors. The results of this parameter study relating receiver antenna array 

height and transmitter to receiver separation versus channel capacity is shown in Figure 

22. We can see that changes in separation (d) on the order of 1λ and in hmax on the order 

of 0.1λ will only cause changes in C on the order of 0.1 Bits/Hz/s. 

28 
Figure 22. The capacity of a 16x16 element array situated over a ground plane 

versus the antenna array separation (d), and the height above the 

ground plane of the top element of the receiving array (hmax). 

10. CONCLUSIONS 

A 16-channel MIMO antenna system for simultaneous measurement of the BLAST 

channel transfer function was developed. It utilized a wideband maximal sequencecoding scheme to identify different radio paths between antenna elements. A 

methodology was implemented for analyzing the accuracy of transfer function estimates 

and predicted channel capacity based on the channel response (H matrix) measurements 

using the NIST OATS and RF analysis of the radiowave propagation environment. The 

variance of the magnitude difference between the measured and calculated H matrix was 

between 0.023 and 0.026. The difference between the channel capacity calculated using 

the measured H and the theoretical H was between 0.27% and 5%. 

The experiment demonstrated that a wideband system accurately measured the H matrix. 

This measurement is necessary for prediction of the channel capacity. The 16-element 

MIMO antenna system was also shown to behave as predicted by the model developed to 

calculate the channel transfer functions in Section 9. 

29 
11. REFERENCES

1. G. J. Foschini, ìLayered space-time architecture for wireless communication in a 

fading environment when using multiple antennas,î Bell Labs Technical Journal, 

Vol. 1, No. 2, pp. 41-59, Autumn 1966. 

2. G. J. Foschini and M. J. Gans, ìOn limits of wireless communications in a fading 

environment when using multiple antennas,î Wireless Personal Communications, 

Kluwer Academic Publishers, Vol. 6, 1998, pp. 311-335. 

3. S. Verdu and S. Shamai, ìSpectral efficiency of CDMA with random spreading,î 

IEEE Transactions on Information Theory, Vol. 45, No. 2, pp. 622-640, Mar. 1999. 

4. P. Wilson, P. Papazian, M. Cotton and Y. Lo, ìAdvanced antenna test bed 

characterization for wideband wireless communications,î NTIA Report 99-369, Aug. 

1999. 

5. D. Chizhik, G. J. Foschini, and R. A Valenzuela, ìCapacities of multi-element 

transmit and receive antennas: Correlations and keyholes,î Electronics Letters, Vol. 

36, No. 13, pp. 1099-1100, Apr. 2000. 

6. D. Chizhik, J. Ling, P. Wolinsky, R. Valenzuela, N. Costa, and K. Huber, ìMultiple 

input multiple output measurements and modeling in Manhattan,î in Proc. IEEE Fall 

2002 Vehicular Technology Conference, Vancouver, B.C., Canada, Sep. 24 -29, 2002.

30 
APPENDIX A: ANTENNA COUPLING DATA SUMMARY TABLES 

Coupling data is summarized using the following convention: Anum1, num2 = S (dB), 

where num1 = antenna element connected to port 1, num2 = antenna element connected 

to port 2. 

Table A-1.Vertical Antenna Coupling Summary 

Measurement File# Disk# S21 @ CF Comments 

Amp(dB) ± Phase° ±

Cable(1,2)

Cal1-thru 00 1 -0.5 -0.7

A1,2 01 -31.5 -58

A1,3 02 -52.5 102.7

A1,4 -51.4 146.3

A1,5 03 -53.4 162

A1,6 04 -57.8 146

A1,7 05 -54 133

A1,8 06 -54 147

A1,9 00 2 -56 153

A1,10 01 -57 169

A1,11 02 -62 -178

A1,12 03 -78 92

A1,13 04 -67 146

A1,14 05 -65 5 76

A1,15 06 -70 7.5

A1,16 00 3 -70 10 -175

A1,2 01 -31.5 0.2 -58 Repeat

A1,3 02 -52 0.5 105 Repeat

A1,4 03 -51 0.5 150 Repeat

A1,5 04 -53 1 164 Repeat

A1,6 05 -58 2 147 Repeat

A1,7 06 -60 5 132 Repeat

Cable(2,3)

Cal2-thru 00 4 0.1 0 -0.1 0

A2,3 01 -32 0.15 -54 6

A2,4 02 -50 1.5 105 15

A2,5 03 -50 2 150 15

A2,6 04 -53 2

A2,7 05 -58 4 180 50

A2,8 06 -57 3 130 20

A2,9 00 5 -56 1.5 140 20

A2,10 01 -57 1.5 0 30 0 indicates phase 

A2,11 02 -58 4 0 301 crosses 0,180° 

A2,12 03 -65 10 0 50 boundary

31 
A

2,1304-6510050

A2,1405-70100100

A2,1506-7515050

A2,16006-662050

Cable(3,4)

Cal3-thru01

A3,402-31.70.1546

A3,503-49.5111010

A3,604-50214510

A3,705-53215515

A3,806-57114015

A3,9007-561.513020

A3,100156314030

A3,1102564025

A3,1203608025

A3,1304-585025

A3,1405-7010025

A3,1506-6650

A3,16008-6660

Cable(4,5)

Cal4-thru010.010.0020.070.01

A4,502-320.3-546

A4,603-49.51.510515

A4,704-49.50.7514510

A4,805-52116020

A4,906-572.515020

A4,10009-56414030

A4,1101-5430

A4,1202-5840

A4,1303-5520

A4,1404-6230

A4,1505-6230

A4,1606-65100

Cable(5,6)

Cal5-thru00100.005-0.759Baddata

Cal6-thru010.025-0.0206

A5,602-320.15-565

A5,703-490.410510

A5,804-50114512

A5,905-5220

A5,1006-5830

A5,1107-53314015

A5,120011-54415025

A5,1301-5120

A5,1402-5820

A5,1503-6040

32 
A

5,1604-6760

Cable(6,7)

Cal7-thru05

A6,706-31.90.1-564

A6,80012-50210510

A6,901-50215016

A6,1002-5220

A6,1103-56415025

A6,1204-58413025

A6,1305-531.514020

A6,1406-561.50

A6,150013-6040

A6,1601-6350

A7,8 02 -32 0.2 -54 5 Use cable 6, 7 A7,9 03 -47 2 110 15 A7,10 04 -48 1.5 140 15 A7,11 05 -50 1.5 150 20 A7,12 06 -54 2 150 20 A7,13 00 14 -55 1 140 15 A7,14 01 -55 1.5 140 25 A7,15 02 -56 3 0 A7,16 03 -60 5 0 A8,9 04 -31.9 0.2 -54 6 A8,10 05 -50 1 110 10 A8,11 06 -50 1 140 12 A8,12 00 15 -51 0.75 160 15 A8,13 01 -57 1.5 150 20 A8,14 02 -56 2.5 140 30 A8,15 03 -56 2.5 140 30 A8,16 04 -58 2.5 0 A9,10 05 -32 0.15 -56 6 A9,11 06 -49 0.5 105 10 A9,12 00 16 -49 0.75 145 15 A9,13 01 -52 1.5 160 20 A9,14 02 -58 3 0 A9,15 03 -58 3 140 30 A9,16 04 -56 3 140 30 Cable(10,11) Cal8-thru 05 A10,11 06 -31.9 0.15 -54 4 A10,12 00 17 -50 1.25 105 15 A10,13 01 -50 1.5 140 20 A10,14 02 -53 2.5 0 A10,15 03 -55 4 0

33 
A10,16 04 -58 4 140 25

A11,12 05 -31.8 0.2 -54 5 Use cable 10, 11 

A11,13 06 -50 2 110 15

A11,14 00 18 -50 2 140 20

A11,15 01 -53 2 0

A11,16 02 -60 4 0

A12,13 03 -32 0.25 -52 5 Use cable 10, 11 

A12,14 04 -48.5 2 110 15

A12,15 05 -50 2 140 15

A12,16 06 -53 2 0

A13,14 00 19 -31.9 0.25 -56 5 Use cable 10, 11 

A13,15 01 -50 1.25 105 10

A13,16 02 -51 1.5 145 15

A14,15 03 -31.9 0.2 -56 5 Use cable 10, 11 

A14,16 04 -52 1.5 95 13

A15,16 05 -31.4 0.2 -56 5 Use cable 10,11 

Table A-2. Horizontal Antenna Coupling Summary 

Measurement File# Disk# S21 @ CF Comments 

Amp(dB) ± Phase° ±

Cable(1,2)

Cal1-thru 00 20 0 0.005 -0.100 0.020

A1,2 01 -22.8 0.15 170 6

A1,3 02 -31.8 0.4 170 8

A1,4 03 -37.0 6 0

A1,5 04 -42.2 0.6 0

A1,6 05 -45.6 0.5 0

A1,7 06 -48.5 1.5 0

A1,8 00 21 -50 2 0

A1,9 01 -54 2 0

A1,10 02 -56 3 0

A1,11 03 -56 4 0

A1,12 04 -58 2 0

A1,13 05 -60 1 0

A1,14 06 -65 7.5 0

A1,15 00 22 -70 20 0

A1,16 01 -65 10 0

Cable(1,2)

Cal2-thru 02 -0.35 0.0 0.74

34 
A

2,303-22.60.21666

A2,404-31.40.41706

A2,505-370.40

A2,606-4210

A2,70023-451.50

A2,801-4820

A2,902-502.50

A2,1003-522.50

A2,1104-5420

A2,1205-5610

A2,1306-5620

A2,140024-60100

A2,1501-70150

A2,1602-70120

Cable(1,2)

Cal3-thru03-0.350.03.90.020

A3,404-22.40.11706

A3,505-31.40.21708

A3,606-370.117010

A3,70025-421.30

A3,801-451.50

A3,902-4820

A3,1003-5020

A3,1104-520.10

A3,1205-5420

A3,1306-5640

A3,140026-60100

A3,1501-7012.50

A3,1602-70170

Cable(1,2)

Cal4-thru03-0.70.66

A4,504-22.60.21686

A4,605-31.40.417010

A4,706-370.50

A4,80027-4110

A4,901-45.510

A4,1002-4810

A4,1103-5010

A4,1204-5220

A4,1305-5450

A4,1406-607.50

A4,150028-607.50

A4,16010

Cable(1,2)

Cal5-thru02-0.050-0.02060

A5,603-22.601646

35 
A

5,704-31.40.216510

A5,805-370.40

A5,906-410.40

A5,100029-450.40

A5,1101-4810

A5,1202-5020

A5,1303-5240

A5,1404-5640

A5,1505-5850

A5,1606-5850

Cable(1,2)

Cal7-thru0030-0.0800.4390

A6,701-22.50.20.1666

A6,802-31.50.31705

A6,903-370.30

A6,1004-420.70

A6,1105-451.50

A6,1206-4820

A6,130031-502.50

A6,1401-522.50

A6,1502-5430

A6,1603-5720

Cable(1,2)

Cal8-thru04-0.010-1.40

A7,805-22.60.11686

A7,906-31.60.41708

A7,100032-370.50

A7,1101-420.50

A7,1202-451.50

A7,1303-4720

A7,1404-5020

A7,1505-521.50

A7,1606-550.750

Cable(1,2)

Cal9-thru0033-0.07-3.20

A8,901-22.50.21706

A8,1002-31.50.517010

A8,1103-3710

A8,1204-4210

A8,1305-451.50

A8,1406-481.50

A8,150034-5010

A8,1601-520.40

Cable(1,2)

Cal10-thru02-0.090-1.70

36 
A

9,1003-22.60.21626

A9,1104-31.40.416510

A9,1205-370.50

A9,1306-41.50.750

A9,140035-450.50

A9,1501-47.900

A9,1602-50.50.750

Cable(1,2)

Cal11-thru03-0.10-1.80

A10,1104-22.60.151666

A10,1205-31.40.51709

A10,1306-370.40

A10,140036-41.80.20

A10,1501-45.50.10

A10,1602-48.50.10

Cable(1,2)

Cal12-thru03-0.10-1.640

A11,1204-22.50.11686

A11,1305-31.40.21707.5

A11,1406-370.40

A11,150037-4210

A11,1601-4610

Cable1,2

Cal13-thru-0.110-2.8

A12,1302-22.60.11646

A12,1403-31.50.21658

A12,1504-37.20.50

A12,1605-42.50.10

Cable(1,2)

Cal13-thru-0.1.700

A13,1406-22.60.21644

A13,150038-31.60.416510

A13,1601-37.60.60

Cable(1,2)

Cal15-thru-0.10-4.90

A14,1502-22.60.151626

A14,160039-320.4165100

Cable(1,2)

Cal16-thru-0.120-1.760

A15,1601-22.90.11646

37 
APPENDIX B: ANTENNA ELEMENT CALIBRATION SUMMARY TABLES 

Table B-1. E/H Co-polarized and Cross-polarized Antenna Scans for Element L01 

File Type Description

ITS01 E/H co/cross scan data Element L01 

ITS01b E/H co/cross scan data Repeat after 2 hours 

ITS01c E/H co polarized Bore-sight Freq. Scan 

Table B-2. Summary of E and H Scan Co-polarized Antenna Element Calibration 

Data. Bore-sight Gain and Phase at 2300 MHz for Each Element and 

Range Calibration Files 

Bore-sight Gain and Phase Antenna Element Calibration Data 

Ant file v phase h phase1 v amp h amp ∆v phase2 ∆h phase2 ∆ v amp2

(deg) (deg) (dB) (dB) (deg) (deg) (dB)

04/04/2001

sacal1**

L01cal1 -52 7.52

L01 -51.9 127.7 7.51 0.1 -0.01

L02 -53.9 -54.5 7.47 -1.9 -0.05

L03 -53.6 -53.9 7.47 -1.6 -0.05

L04 -52.2 -52.9 7.48 -0.2 -0.04

L05 -53.2 -53.4 7.49 -1.2 -0.03

L01cal2 -52.41 7.46 -0.41 -0.06

sacal23

04/05/2001

sacal33 0 16.5

L01cal2 -74.61 7.6

L06 -77.4 102.9 7.63 7.61 -2.79 0.03

L07 -75.2 104.5 7.53 7.53 -0.59 -0.07

L08 -74.1 105.9 7.66 7.63 0.51 0.06

L09 -74.7 105.1 7.6 7.61 -0.09 0

L10 -74.63 105.3 7.58 7.57 -0.02 -0.02

L11 -75.21 104.6 7.55 7.56 -0.6 -0.05

L12 -74.09 105.6 7.5 7.49 0.52 -0.1

L01cal4 -73.89 7.56 0.72 -0.04

L13 -73.97 106 7.54 7.53 0.64 -0.06

L14 -75.4 104.3 7.61 7.61 -0.79 0.01

L15 -74.3 105.6 7.52 7.5 0.31 -0.08

L16 -74.1 105.5 7.56 7.56 0.51 -0.04

L17 -75.1 104.72 7.51 7.5 -0.49 -0.09

L18 -74.9 104.81 7.51 7.54 -0.29 -0.09

L19 -74.7 105.4 7.42 7.41 -0.09 -0.18

L20 -74.4 105.6 7.51 7.52 0.21 -0.09

38 
L01cal5 -67.58 7.26 7.03 -0.34

sacal43 -4.65 16.45

04/06/2001

sacal53

L01cal6 -63.67 7.56

L21 -64.28 115.51 7.54 7.56 -0.61 0

L22 -58.34 121.15 7.11 7.14 5.33 -0.42

L23 -56.86 123.2 7.09 7.09 6.81 -0.47

L24 -59.15 121.2 7.28 7.22 4.52 -0.34

L25 -54.86 125.2 6.94 6.95 8.81 -0.61

L26 -62.5 117.08 7.61 7.63 1.17 0.07

L27 -60.5 118.7 7.27 7.3 3.17 -0.26

L28 -62.97 116.9 7.53 7.56 0.7 0

L29 -64.69 115 7.52 7.58 -1.02 0.02

L30 -63.59 116.2 7.49 7.52 0.08 -0.04

L31 126.1 6.64

L31r -63.37 116.3 7.55 7.59 0.3 0.03

L01cal7 -62 7.55 1.67 -0.01

sacal63

04/09/2001

sacal63

L01cal8 -66.52 7.64

L32 -67.05 112.85 7.59 7.6 -0.53 -0.05

L33 -67.36 112.34 7.59 7.61 -0.84 -0.05

L34 -67.22 112.7 7.55 7.55 -0.7 -0.09

L35 -66.78 112.9 7.56 7.58 -0.26 -0.08

L22r -67.83 112.4 7.54 7.54 -1.31 -0.1

L23r -65.36 114.64 7.56 7.58 1.16 -0.08

L24r -67.52 112.6 7.53 7.54 -1 -0.11

L25r -66.32 113.75 7.51 7.54 0.2 -0.13

L26r -66 113.66 7.56 7.56 0.52 -0.08

L01CAL9 -64.63 7.53 1.89 -0.11

sacal93

1 h phase can be 180° out of phase due to misalignment of calibration horn and antenna test fixture. 2 ∆ phase and ∆ amp data are relative to LO1 cal data from the beginning of the measurement set. 3 range calibration data collected using the range calibrated standard gain horn. 

39 
APPENDIX C: DATA COLLECTION SUMMARY 

Tables C-1 to C-4 summarize the data collected in this experiment. 

Table C-1. Broadband Channel Sounder BLAST Data Files and Data Descriptions 

Data Type Date Data File Description 

Calibration 5/30/02 377-380.xr Diagonal TxCal Data, i=j=1ÖÖÖ16.

Calibration 5/30/02 381-396.xr RxCal Data, i=1, j=1ÖÖÖ16.

16x16 BLAST 6/7 663.br Vertical Polarized Antennas 

16x16 BLAST 6/7 665.br Repeat Vpol Test 

1x16 BLAST 6/8 666.br VPol, Tx=17, Rx=1-16 

16x16 BLAST 6/8 667.br Repeat Vpol Blast after disconnecting Tx 

cabling and moving Tx overnight. 

16x16 BLAST 6/8 668.br Repeat Vpol Blast after removing timing 

cable which was left on ground plane. 

1x16 BLAST 6/13 672,673,674.br HPol, Tx=17 Rx = all, 

repeat after computer malfunction. 

1x16 BLAST 6/13 675-689.br HPol, Tx=18,19ÖÖ.32 Rx=all 

16x16 BLAST 6/14 690,691.br Repeat Hpol BLAST twice. 

Keyhole Test 6/14 692.br HPol, splitter feeds Rx A1 to all channels 

1x16 BLAST 6/15 693-708.br VPol Tx=17,18Ö..32 

16x16 BLAST 6/15 710.br VPol, transmitter cables reversed data does not 

repeat, discard. 

Keyhole Test 6/15 711.br VPol, splitter feeds Rx A1 to all channels. 

16x16 BLAST 6/16 713.br VPol repeat after cables reset. 

16x16 BLAST 6/16 714.br VPol repeat 

16x16BLAST 6/18 715.br VPol, repeat after the weekend because 6/16 

data didnít match original VPol tests of made 

on 6/8. 

16x16 BLAST 6/18 716.br VPol repeat. 

16x16 BLAST 6/21 718,719.br Hpol, repeat. 

16x16 BLAST 6/21 724.br Hpol, Set Lo=153 MHz, IF=7MHz 

Table C-2. Spectrum Analyzer (CW) Narrowband BLAST Data Files and Descriptions 

Data Type Date Data File Description 

CW 6/6/02 cw_vpol.txt VPol, Tx(17), Rx(1-16), PTX=-11.8 dBm

CW 6/11/02 cw_hor.dat HPol, Tx(17,18,25) Rx(1-16), PTX= -11.8dBm

CW 6/21/02 cw_16x16_hor.dat Hpol, Tx(1-16),Rx(1-16), PTX= -10.0 dBm

40 
Table C-3. Vector Network Analyzer Antenna Element Coupling Data Files and 

Descriptions 

Data Type Date Data File Description 

Ant. Coupling 6/4,5,6 Disks 1-19 VPol, S Parameters, In=A1-A15,Out=A2-A16 

Ant. Coupling 6/12/02 Disks 20-39 Hpol, S Parameters, In=A1-A15,Out=A2-A16 

Component 3/12/02 Data01-10 Low Pass Filter, Power Divider 

AGC Amp 6/29/02 Data01-55 AGC Amp Calibration Data 

Table C-4. Anechoic Chamber Antenna Element Calibration Data Files and Descriptions 

Data Type Date Data Files Description 

E/H Scans 3/1 ITS01,b,c Antenna #1, E/H co/cross polarization data 

E/H Scans 4/6 M-LOC Disk1 TAR Data, E/H, Antennas 1-19 

E/H Scans 4/6 M-LOC Disk2 TAR Data, E/H, Antennas 20-35 

Mfiles 4/6 Misc. mfiles for reading and plotting TAR data 

41 
APPENDIX D: TRANSMITTER CALIBRATION DATA 

Table D-1. Transmitter Power Levels Measured at Coupler and Used for TxCal Data 

Transmitter Power (dBm) 

1 -40.44

2 -39.86 

3 -40.42 

4 -39.65 

5 -40.63 

6 -40.65 

7 -40.87 

8 -41.29 

9 -40.14 

10 -40.42 

11 -42.19 

12 -41.2 

13 -40.53 

14 -40.35 

15 -41.11 

16 -41.01 

42 
APPENDIX E: SOFTWARE DESCRIPTION 

This section gives an overview of the software developed for the ordering and analysis of 

the BLAST data. 

E.1 CalTx 

CalTx is used to read the raw calibration data from 16 transmitter channels and assemble 

the diagonal elements of the 256-element system response matrix. Calibration data is 

recorded at 7 power levels for the 16 transmitter channels. These calibration signals are 

fed into the 16 MUX channels using the same transmit and receive antenna cables used 

during the BLAST field tests at the NIST OATS. Raw calibration data is stored in four 

separate data files. Each data file has four channels of data and 7 bursts of data 

corresponding to the 7 input power levels per channel. Each burst of data has 128 

impulses spaced at 3 ms intervals. A total of four data files are needed to store the 16 

channels of raw calibration data. Input to CalTx is the first of four sequential raw data file 

numbers. The program automatically reads the AGC gain phase table and applies these 

scaling factors to the raw data. Output is Ctxi,j(w,n), i=j=1,2,3Ö16, n=1,2Ö7, the 

transmitter system response calibration file at 7 power levels.

E.2 CalRx 

CalRx reads raw calibration data using all receiver channels and a single transmitter to 

calculate the first row of the 256-element system response matrix. The transmitter is 

connected to the receiver using transmit antenna cable 17 and receive antenna cable 1 

connected with an N type barrel. Input power level corresponds to n=2 of the CalTx data. 

Raw data is stored in 16 separate files, 1 burst per file, 128 impulses per burst at 3 ms

intervals. The program also reads the AGC gain phase tables and applies these scaling 

factors to the raw data. Output is CRxi,j(w),i=1,j=1,2,3Ö16, the receiver system response 

matrix. 

E.3 CalSys 

 

CalSys reads the transmitter and receiver system response output files from CalRx and 

CalTx. CalSys then calculates the 256-element system response matrix for the transmitter 

receiver system. It also calculates P_cal(16,7), power calibration factors for all 16 

transmitters so that raw data can be scaled to units of dBm or dBm/Hz if required. Input 

requirements are: the appropriate HTx.mat and HRx.mat output files from CalRx and 

CalTx, and the TxPower.txt data file containing the transmitter power levels for the 16 

transmitters measured at the end of each transmit antenna cable. The program outputs 

CSysij(w), the 256-element system response matrix. 

43 
E.4 Praw Hij

Praw Hij processes raw BLAST data files and calculates the 256-element H matrix for the 

BLAST radio channel. The raw data files are arrayed as described in section 7.1. All raw 

data are scaled by the AGC gain phase and then the 128 IF signals per receiver channel 

are averaged before down conversion and correlation processing which calculates the 

channel response H(w) for each of the 16 receiving antennas. H(w) is then translated to 

the time domain to separate h(t)ij into its 256 elements after time shifting each of the 16 

transmitter signals received at each antenna element to zero phase and zero padding. h(t)ij 

is then translated back to the frequency domain where the system response is 

deconvolved using CSysij(2). Assumptions here are linear phase and constant relative 

amplitude. By only using frequency 2 (first frequency above 0 at baseband) this avoids 

deconvolution near the nulls of the system response function and also effects due to local 

oscillator feed-through at the carrier frequency. 

E.5 Praw 1x16 

Praw 1x16 processes the raw data for 16 receive antennas when only one transmitter was 

operational. After arraying the data from the 16 receivers, one transmitter at a time, it 

follows the same processing algorithm as PrawHij to calculate the H matrix of the 16x16 

BLAST channel.

44