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284 MIMO System Technology for Wireless Communications

with and without I/Q mismatch cancellation for MIMO2×

2, SIMO1×

2, and

SISO systems. These ﬁgures show that there is a 5dB improvement due to

I/Q mismatch cancellation in a 2 ×

2 system, and about 2.5dB in the SISO

and SIMO1×

2 cases. This highlights the importance and efﬁcacy of I/Q

mismatch cancellation in MIMO-OFDM systems. It can also be observed

from Figure 10.3(b) and Figure 10.4 that receive diversity (N v

) cancels

I/Q mismatch, albeit being a suboptimal solution [9].

10.4.2.1 A Simulation Model for I/Q Mismatch

The models for frequency-dependent I/Q mismatch reported in the literature

are simplistic and consider a linearly varying gain and phase on each of the

subcarriers [5]. I/Q mismatch can be modeled much more realistically (sim-

ilar to what is observed on the testbed) by controlling the gain, phase, and

delay mismatches. The measure of I/Q mismatch used is the average image

suppression (or a plot of the per subcarrier image suppression). On the 2 ×

2 MIMO testbed the average I/Q mismatch is approximately –20dB. This

can be modeled in the simulator by choosing an I/Q gain mismatch of 0.91

dB, delay mismatch of 5% of Ts, and a phase mismatch of 2.8°. This is

illustrated in Figure 10.5.

FIGURE 10.3

4QAM at 40dB SNR in the presence of I/Q mismatch in (a) SISO, (b) SIMO1×

2, (c) MIMO 2x2,

(d) MIMO4 ×

0.5

−0.5

−1 −0.5 0

(a)

(b)

0.5 1

−1 −0.5 0 0.5 1

0.5

−0.5

−1

0.5

−0.5

−1−1

0.5

−0.5

−1

SISO

SIMO1×2

MIMO2×2 MIMO4×4

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Multi-Antenna Testbeds for Wireless Communications

285

10.4.3 Phase Noise

An important analog impairment in any wireless transceiver is phase noise.

It degrades the performance of the transceiver in the up- and down-conversion

process of the RF chain. The Local Oscillator (LO) signals are not perfectly

sinusoidal, but rather show random ﬂuctuations of the phase/frequency

around the desired LO frequency, which results in skirts in the power spectral

density of the LO signal. The wider the power spectrum skirt, the poorer

FIGURE 10.4

CDF of slicer SNR with and without I/Q mismatch cancellation on the testbed.

FIGURE 10.5

Image suppression (a) on the testbed and (b) in the simulator.

0.9

0.8

0.7

0.6

0.5

Probability(slicer SNR ≤ abscissa)

0.4

0.3

0.2

0.1

5 10 15 20

Slicer SNR

25 30

SISO, no IQ mismatch

cancellation

MIMO, with IQ mismatch

cancellation

MIMO, no IQ mismatch

cancellation

SIMO, with IQ

mismatch

cancellation

SIMO, no IQ

mismatch

cancellation

SISO, with IQ mismatch

cancellation

Power in

−10

−20

−30

−40

Power in dB

−10

−20

−30

−40

−100 −50

(a) (b)

Subcarriers

100 −100 −50

Subcarriers

100

−20.17 dB −20.40 dB

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286 MIMO System Technology for Wireless Communications

the quality of the LO. A simple model for phase noise in a multi-carrier

system is illustrated in Figure 10.6.

This model [10] represents the three components of the power spectrum

skirt: (a) the ideal and desired pulse, (b) close-in phase noise and (c) sideband

phase noise. The close-in phase noise has a relatively high power and is

band-limited by the loop bandwidth of the Phase Locked Loop (PLL) gen-

erating the LO signal. The PLL magniﬁes the close-in phase noise, which

mainly determines the noise performance of the receiver. It can be mitigated

with a proper design of the PLL circuit, as described later. The amount of

the sideband phase noise is mainly given by the phase noise characteristic

of the Voltage Controlled Oscillator (VCO) used in the PLL circuit. In a multi-

carrier system (as shown in Figure 10.6), the close-in phase noise is common

to all the carriers after an up- or down-conversion and can be cancelled in

software. The sideband phase noise overlaps and causes Inter-Carrier Inter-

ference (ICI). The interference due to the superposition of the skirts from all

the other subcarriers is random in nature.

The effects of the phase noise can be reduced by a proper hardware design

or can be cancelled in the demodulator. Both approaches are discussed in

the following sections.

10.4.3.1 Design of Low Phase Noise Local Oscillators

Figure 10.7 shows a block diagram of the PLL circuit that was used to

generate the low phase noise LOs in the 5.25 GHz MIMO-OFDM testbed.

The basic PLL consists of a phase frequency detector (PFD), a charge pump

(CP), a loop lowpass ﬁlter (LPF) and a voltage-controlled oscillator (VCO)

[9,11]. In the feedback loop is a divide-by-N block to generate the high

frequency LOs from the crystal (Temperature Compensated Crystal Oscilla-

tor, TCXO). At the input there is also an input reference divider R. Each block

contributes to the total phase noise at the output [12]. Analysis of the PLL

FIGURE 10.6

Phase noise in multi-carrier transceivers.

Subcarriers

Frequency

(a) Ideal

impulse

(b) Close-

in PN

Frequency

Power

Frequency

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Multi-Antenna Testbeds for Wireless Communications

287

shows that the close-in phase noise can be reduced by minimizing the con-

tributions from the reference and feedback dividers as well as the phase

noise of the TCXO. In addition, choosing the feedback divider N small and

the reference divider R large reduces the close-in phase noise further. For

frequency offsets outside the loop bandwidth, the phase noise is dominated

by the VCO. Figure 10.8 shows the frequency spectrum of the TCXO and

the VCO used to generate the 1.75GHz LO at the transmitter in the 5.25GHz

MIMO OFDM testbed. It can be seen that within the loop bandwidth, the

PLL magniﬁes the phase noise (close-in part). Outside of the loop bandwidth

(sideband part), the phase noise of the PLL converges with the VCO, as

predicted by theory.

For reference, the phase noise measured at 100kHz frequency offset of the

LO frequencies was in the range of –120 dBc/Hz to –105 dBc/Hz for the

5.25 GHz MIMO-OFDM testbed.

FIGURE 10.7

Basic PLL block diagram

FIGURE 10.8

Phase noise power spectral density.

PF D

TCXO CP LPF

VCO

−

Transmitter LO1(1.75 GHz)

VCO

TCXO

Transmitter LO1(1.75 GHz)

Phase noise(dBc/Hz)

−20

−40

−60

−80

−100

−120

−140

−160

Frequency oﬀset(Hz)

Close-in PN

Sideband PN

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288 MIMO System Technology for Wireless Communications

10.4.3.2 Phase Noise Cancellation in the Demodulator

by Signal Processing

The effects of phase noise in SISO-OFDM systems has been extensively

analyzed and reported in the literature [13–15]. The results can be extended

to MIMO-OFDM systems. The per-subcarrier received signal after the FFT

can be represented as

(10.1)

where X

(ke

), Y

(ke

and H

(ke

) represent the transmit data vector, receive data

vector, and the channel matrix, respectively. N

is the number of subcarriers

and k

is the index of the subcarrier under consideration. MIMO decoding

involves reversing the effect of the channel and estimating each of the trans-

mitted data streams by left multiplying Y

(

)

in Equation 10.1 with the weight

matrix W

(ke

), which is an estimate of the pseudo-inverse of the channel

matrix H

(ke

). The result is

(10.2)

The ﬁrst term represents the estimated data vector. The second and third

terms represent the interference due to phase noise. The second term repre-

sents the “common phase error” (CPE) and is called this because its effect

is an identical phase rotation on all the subcarriers and all the transmit data

streams. This term can be estimated and corrected for every MIMO-OFDM

symbol. The CPE term is also scaled by the transmit signal on each subcarrier.

Therefore, in a MIMO system, as the number of transmit branches increases,

the CPE term decreases. The third term is the sum of the projection of the

phase noise skirts on all the other subcarriers and is commonly called the

inter carrier interference (ICI) due to phase noise. This is random in nature

and needs to be minimized by proper choice of the VCO.

The impact of canceling the CPE part of phase noise was evaluated on the

5.25 GHz 2 ×

2 MIMO-OFDM testbed. The results are shown in Figure 10.9.

It can be observed that canceling CPE has a much bigger impact on SISO

systems (approximately 4–4.5dB SNR gain) than on the 2 ×

2 MIMO system

(1.5–2 dB SNR gain). This is because the testbed is a power constrained

Yk Hk Xk

lHkXk

() ()() () ()()





() ( ) ( )

()

lHkXke

lk k

kkk

= |



()

() ()()

() ()

()Xk WkYk Xk

lXk

¾¾



lHkXk

()

() ( ) ( )

kkk

lk k

eVk



2U ()

()



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Multi-Antenna Testbeds for Wireless Communications

289

system (the total transmit power is divided equally among the two trans-

mitters), and the CPE term is scaled by the data transmitted on each sub-

carrier of an OFDM system. Therefore CPE cancellation yields a smaller

improvement in the MIMO system. On the testbed, phase noise caused a

performance ceiling at 27dB SNR during the benchtop calibration process,

and it was removed after adding the CPE cancellation algorithm to the

demodulator.

10.4.3.3 A Discrete-Time Simulation Model for Phase Noise

Although analytical results show that the phase noise process has a Power

Spectral Density (PSD) that falls off at 1/f

[16], in reality (on hardware) the

phase noise PSD ﬂattens out for large frequency offsets [17]. In [18] Salz

mentions (although in the context of laser phase noise) that the spectral

density of this phase noise has a 1/f

to 1/f

characteristic up to around 1 MHz

offset and is ﬂat for higher frequencies. Also, at very low frequency offsets,

it has a 1/f

characteristic [17]. In discrete time simulations, it is difﬁcult to

model phase noise to exactly match with what is measured on the testbed.

Approximate models with a 1/f

characteristic are used. Generally, the phase

noise process is modeled with an FIR ﬁlter that is generated with a user-

deﬁned mask as in [15,21]. The user-deﬁned mask is a rough approximation

of the PSD measured using a spectrum analyzer or a phase noise meter.

Although this method can model the phase noise behavior to be close to

what is observed on the hardware, the FIR ﬁlter can be fairly large, and

simulations are slow. An alternative method proposed by Kasdin [19,20] in

FIGURE 10.9

CDF of slicer SNR for indoor wireless measurements with SISO, SIMO1×

2, and MIMO2×

2 with

and without CPE cancellation.

Impact of phase noise cancellation on the testbed(EE54–114)

Probability

(

slicer SNR ≤ abscissa)

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 5 10 15

Slicer SNR

20 25 30 35 40

MIMO, no CPE

cancellation

MIMO, with CPE

cancellation

SISO, with CPE

cancellation

SISO, no CPE

cancellation

SIMO, with CPE

cancellation

SIMO, no CPE

cancellation

4190_book.fm Page 289 Tuesday, February 21, 2006 9:14 AM

290 MIMO System Technology for Wireless Communications

the early 1990s models phase noise using an ARMA process with an IIR

ﬁlter. This is an elegant method that can model any kind of power law noise

(ex. 1/f

, 1/f

, etc.). Although not widely discussed and used in the wireless

communication literature in the context of phase noise, it is a popular method

in industry (an example: MATLAB Simulink). This method was used to

model phase noise in the simulator that was used to analyze and compare

the performance of the 5.25 GHz MIMO-OFDM testbed.

10.4.4 Benchtop Calibration of the 5.25 GHz 2 ××

××

2 MIMO Testbed

This section brieﬂy discusses the results of the entire benchtop calibration

process of the 5.25 GHz 2 ×

2 MIMO broadband testbed. The discussion that

follows considers uncoded SISO links, i.e., the wireless channel was replaced

with RF cables and variable attenuators between individual (paired) radio

units, resembling SISO AWGN channels.

The combined effect of CPE phase noise removal and I/Q mismatch can-

cellation is illustrated in Figure 10.10 for the case with 64-QAM modulation

and approximately 20 dB SNR.

Figure 10.11 plots the symbol error rate curves for various signal constel-

lations and compares the testbed with theory and simulation when the

testbed is in perfect-timing mode. This means that the clock signal, which

also drives the LOs, is common to both the transmitter and the receiver units.

The results lie within 1–2 dB of the theoretical curves. The simulator, with

all the analog impairments modeled to match the testbed’s, is within 1 dB

of the testbed’s performance. The slight difference between the simulations

and the testbed is mainly due to the non-white nature of the noise on the

testbed, caused by non-linearities in the RF sections. These were not modeled

in the simulator.

An important metric to measure testbed performance is the implementa-

tion loss, which compares the average SNR at the input of the decision device

FIGURE 10.10

A 64 QAM constellation measured on the testbed at an input SNR of 20dB (a) without I/Q

mismatch cancellation and phase noise (CPE) cancellation, (b) with I/Q mismatch cancellation

but no phase noise (CPE) cancellation, (c) with I/Q mismatch cancellation and phase noise

(CPE) cancellation.

(a)

−1

−2

(b)

−1

−2

(c)

−1

−2

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Multi-Antenna Testbeds for Wireless Communications

291

of the receiver (“slicer SNR”) vs. the SNR at the input of the receiver. The

difference in dB between the input SNR and the slicer SNR is the implemen-

tation loss. Figure 10.12 plots the implementation loss of the testbed in perfect

and non-perfect timing modes and compares the results with the simulator.

Also plotted is the implementation loss when the carrier frequency synchro-

nization algorithm is turned on and the testbed is in perfect timing mode.

This quantiﬁes the impact of the frequency offset estimation errors and

allows for incorporating it into the system’s performance data sheet. In

perfect timing mode, when the I/Q mismatch canceller and phase noise

canceller are turned on, the implementation loss is within 2 dB in the entire

SNR range up to 30 dB. However, the loss is higher in the non-perfect timing

mode due to estimation errors in the synchronization algorithms. In this

case, it increases to about 3 dB at an input SNR of 25 dB. It can also be

observed that the carrier frequency offset estimation errors start having an

impact on the implementation loss at about 25 dB, increasing to about 3 dB

at 30 dB. In all these cases, it can be observed that with all the analog

impairments modeled, the simulator matches the testbed very closely. Other

key parameters of the RF and analog frontend (AFE) were measured as well

and are listed in Table 10.2.

FIGURE 10.11

SER calibration curves for the 5.25 GHz testbed over AWGN channel and in perfect timing

mode.

SER for 4QAM, 16QAM and 64QAM

eoretical AWGN curves

Simulation curves

Testbed

−1

16QAM

SER

−2

−3

−4

−5

0 5 10 15

Input SNR (dB)

20 25 30

64QAM

4QAM

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292 MIMO System Technology for Wireless Communications

FIGURE 10.12

Implementation loss vs. input SNR curves for the 5.25 GHz 2 ×

2 MIMO testbed in perfect

timing and non-perfect timing modes.

TABLE 10.2

System Parameters of the 5.25 GHz 2 × 2 MIMO Testbed

Radio architecture Heterodyne

System setup 2 × 2 (extendible to 4 × 4 antennas)

Carrier frequency 5.25 GHz

Signal bandwidth 25 MHz

Effective bandwidth 21.5 MHz

TCXO temperature stability <1 ppm (–10°C to +60°C)

Transmitter power –13 dBm to +18 dBm

Transmitter D/A converter 16 Bits/100 MHz

Receiver noise ﬁgure 7.93 dB

Receiver sensitivity –99 dBm

Receiver dynamic range 70 dB

Receiver IIP3 –25.4 dBm

Receiver A/D converter 14 Bits/25 MHz or 50 MHz

Image suppression Approx –20 dB

Local oscillator phase noise

@100 KHz offset

–120 dBc/Hz to –105 dBc/Hz

Comparing perfect and non-perfect timing modes

16 18 20 22 24

SNR

26 28 30 32

Simulation—non-perfect timing

Simulation—perfect timing, tracking ON

Simulation—perfect timing, no tracking

Testbed—non-perfect timing

Testbed—perfect timing, tracking ON

Testbed—perfect timing, no tracking

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Multi-Antenna Testbeds for Wireless Communications 293

10.4.5 Radio Receiver Distortion

An example from the development of the narrowband, DSP-based MIMO

testbed might be illustrative of both the impact of radio distortion and for

the need of emulation and simulation. The narrowband wireless modem was

built and tested in 2002 using the powerful concept of a super-orthogonal

trellis code [39,40]. Simulations of the whole baseband system were com-

pleted and performance looked quite promising (see lower curves on Figure

10.13a). During the calibration stage the system was subject to a real radio

and no fading (benchtop and cabled) and the system had some implemen-

tation loss but otherwise performed well. The next stage of calibration intro-

duced rapid time varying fading with a channel emulator and surprisingly

a signiﬁcant error ﬂoor was produced (see upper curves on Figure 10.13a).

The cause of this degradation was not at ﬁrst apparent.

The source of the degradation was a non-linearity in the radio receiver for

the testbed. The radio was implemented using a single chip radio frequency

transceiver that was designed for GSM applications (Analog Devices

AD607). This radio system caused some signiﬁcant distortions to the received

linear modulated signal because of a signiﬁcant non-linearity in the IF ampli-

ﬁer. This distortion destroyed the Nyquist characteristics of the pulses in the

linear modulation and resulted in signiﬁcant inter-symbol interference (ISI)

(see the scatter diagram in Figure 10.13b). These distortions in a time ﬂat

fading environment did not cause signiﬁcant degradation as the benchtop

calibration tests demonstrated, but for reasons that were not clear at ﬁrst,

these distortions caused signiﬁcant degradations in time varying fading.

After signiﬁcant effort [43] that iterated back and forth between the sim-

ulation environment and the channel emulator, the cause of the error ﬂoor

was identiﬁed. An error ﬂoor is caused by a situation where the distortion

in the radio causes an error in the absence of thermal noise. It is pretty clear

from the scatter plot that in the static channel an error would not be caused

by this ISI. In a rapidly varying channel the situation is signiﬁcantly different.

Two issues impact time varying fading: ISI being relatively larger due to

deep fades and ISI causing biases in pilot symbol-based channel estimation

during a deep fade.

ISI has a bigger impact during a deep fade. In rapid fading the number of

symbols that are impacted by a deep fade is often a very small number.

Consequently, the channel gain for the symbol being detected during a deep

fading can be small, but the ISI, due to the other interfering symbols, can be

large since the channel gain for these symbols is also large. Consequently,

the scatter plot does not directly scale but has a form as seen on the right

side of Figure 10.14. Simulation showed that the error ﬂoor was partially

due to this interaction with fading and ISI.

ISI causes biases in the channel estimation, and this bias is another source

of errors in the absence of noise. This idea can best be explained by examining

the vector diagram on the left side of Figure 10.14. A deep fade occurs when

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