2 MIMO Throughput Analytical Model for RF Front End

Journal of Communications and Information Networks, Vol.5, No.2, Jun. 2020 Research paper

A 2×2 MIMO Throughput Analytical Modelfor RF Front End OptimizationPenghui Shen, Yihong Qi, Xianbin Wang, Wei Zhang, Wei Yu

Abstract—With a given communication protocol,performance optimization of a multiple-input multiple-output (MIMO) wireless system mainly lies on the designof the radio frequency (RF) front end. Currently, theoptimization is mainly achieved based on experiences,such as promoting the multiple antenna gains and re-ducing their correlations. This experience-based methodworks to a certain extent, but is inefficient since the finalperformance impact by each sub-system is not quantified.The challenge lies on how to find the most limiting factorthat restricts the overall communication throughput.This paper presents an analytical model for throughputcalculations of 2 × 2 MIMO wireless system, which isbuilt on a first step of maximum rate calculated under thechosen protocol and channel, followed by a second stepof throughput baseline measurement, and continued withthe third step of throughput calculations of the overallsystem according to the actual settings of subsystems. Themodel can provide a detailed diagnostic report of each RFfactor, which will directly point out the imperfections andmake the troubleshooting and debugging much more ef-fective. Besides, throughput is analyzed in a mathematicalapproach that allows the performance more predictableduring the design phase.

Manuscript received Apr. 21, 2020; revised May 29, 2020; acceptedMay 31, 2020. This work was supported in part by Chinese Min-istry of Education—China Mobile Research Foundation under Grant MCM20150101 and in part by National Natural Science Foundation of China un-der Grant 61671203. The associate editor coordinating the review of this pa-per and approving it for publication was L. Bai.

P. H. Shen, Y. H. Qi. College of Electric and Information, Hunan Uni-versity, Changsha 410082, China (e-mail: [email protected];[email protected]).

P. H. Shen, Y. H. Qi, W. Yu. General Test Systems Inc., Shenzhen 518000,China (e-mail: [email protected]; [email protected];[email protected]).

Y. H. Qi. Peng Cheng Laboratory, Shenzhen 518000, China (e-mail: [email protected]).

X. B. Wang. Department of Electrical and Computer Engineering, WesternUniversity, London, ON N6A 5B9, Canada (e-mail: [email protected]).

W. Zhang. School of Electrical Engineering and Telecommunications,University of New South Wales, Sydney NSW 2052, Australia (e-mail:[email protected]).

Keywords—throughput analytical model, MIMO, RFperformance optimizations

I. INTRODUCTION

The expeditious evolution of wireless technologies through1G to 5G has dramatically increased the compelxity of

communications systems and networks[1,2]. Performance ofan advanced wireless system in 5G era is affected by manyfactors, ranging from physical layer transmission parameters,wireless channel conditions to the supporting communicationsprotocols[3,4]. Determining the accurate performance of acomplex wireless system could be very difficult due to the cas-caded effects of so many parameters as well as the real-timeinteraction among the different layers of the protocol stack.Finding out the factors limiting the overall performance of awireless system could be even more challenging. However,achieving this would be highly beneficial to improve the over-all performance of wireless systems and reduce the productdevelopment time.

This particular situation can be explained by Liebig’s bar-rel. One can easily observe the capacity of a barrel with stavesof unequal length limited by the shortest stave. This impliesthat the most effective way to improve the overall performanceof a system is to address the most limiting factor (i.e., theshortest stave of the barrel). This motivates us to considerthe following question. For a multiple-input multiple-output(MIMO) wireless system, how to find the most limiting fac-tor that restricts the overall communication throughput? Dueto its inherent complexity, performance of a MIMO systemcould be affected by many factors, components and proce-dures, including but not limited to radio frequency (RF) front-end, noise/interference/signal distortion, modulation and cod-ing in time, frequency and space domains, etc.[5,6]. Amongthese parameters, extracting the dominating factors on theachievable data rate and modeling their impact could lead toa very valuable diagnosis of a complex communication sys-tem. Such efforts could directly guide designers to improvethe system performance, which is typically evaluated by sys-tem throughput[7,8].

However, decomposition and analysis of a wirelesssystem’s throughput has specific difficulties. Studies in

Authorized licensed use limited to: HUNAN UNIVERSITY. Downloaded on March 04,2021 at 08:40:01 UTC from IEEE Xplore. Restrictions apply.

A 2×2 MIMO Throughput Analytical Model for RF Front End Optimization 195

Refs. [9,10] have considered several cases for throughputanalysis with ideal RF transceivers, where the impact of cod-ing and modulation on throughput has been discussed. Whilethe related studies have contributed to the performance anal-ysis of communication systems, the actual throughput thata wireless system can achieve is determined not only bytransmission schemes, but also by the RF chain and channelfor achieving signal propagation from transmitter to receiver.Studies in Refs. [11,12] have discussed the effects on overallperformance from antenna correlation to isolation in severalrepresentative scenarios, which are useful for separating an-tenna designing factors. However, the challenge lies on thefact that there is currently no accurate theory to determinewireless system throughput while considering the impacts ofRF metrics. Currently, the only reliable way for finding out awireless system’s throughput rate in the Cellular Telecommu-nications and Internet Association (CTIA) and the 3rd Gener-ation Partnership Project (3GPP) standards is via testing[13,14].

This brings the following challenge to the 5G design en-gineers. When wireless devices fail to pass the network cer-tification measurements, how to do troubleshooting and de-composition? Generally, subsystems such as MIMO anten-nas, multiple receivers, desensitization (also called desense)of a system are designed by different departments. The over-all performance after system integration may differ substan-tially from the simply adding up the performance of each com-ponent due to the omission of cascaded effects[15-17]. Mea-sured throughput does not indicate the most limiting factor,i.e., where the shortest stave is located. To make the situa-tion even worse, the influence of component improvementson overall performance during the design phase couldn’t beassessed without an accurate throughput analytical model. Asa result, debugging and troubleshooting for 5G MIMO sys-tem becomes an extremely time-consuming, uneffective, andexperience-based process.

To solve the issue, an analytical model for 2× 2 MIMOthroughput is proposed in the paper, which is built on a firststep of maximum rate calculated under the chosen protocoland channel, followed by a second step of throughput baselinemeasurement, and continuing with the third step of through-put calculations of the overall system according to the actualsettings of subsystems. The receiver chip throughput perfor-mance is first simulated in the model reflecting the limit ca-pability that the entire system can achieve. Then is the per-formance degradation brought by applied antennas referred totwo omnidirectional and uncorrelated MIMO antennas. Fi-nally, the desense-caused degradation is calculated in num-bers. It is the first time that the mentioned three values areachievable in the research and development (R&D) stage ofa wireless system. Such a diagnostic report makes it possiblefor engineers to estimate the performance degradation broughtto each subsystem during the simulation phase, further signif-

Thro

ughput

(Mbit

/s)

Power (dBm)

RmUE 1

UE 2

Rx

Px1 Px2

Figure 1 Experiential relationship between a MIMO system’s throughputand the downlink power with a selected protocol

icantly reducing the development period.The rest of the paper is organized as follows. Section II

provides the throughput modeling framework, followed by thethroughput model theoretical derivation in section III. In sec-tion IV, the accuracy of the model is validated based on prac-tical experiments, and in section V, a typical application ofthe proposed model is introduced. Finally, the conclusions arepresented.

II. THROUGHPUT MODELING

An actual data rate is lower than the channel capacity givenby Shannon equation because of two reasons. One is pro-tocol, including coding algorithm, modulation process, etc.,which always allocates some resources for carrying the sup-plementary information[18,19]. The maximum throughput, de-noting the upper limit that a chosen protocol can support, ismarked as the protocol rate in the paper. The protocol ratehas been studied for years, and its calculations have been pre-sented in Ref. [10] and Refs. [20,21]. On the other hand,throughput also depends on physical chain performance, in-cluding RF metrics and propagation quality. Protocol rate isalways greater than or equal to the throughput of a wirelesssystem.

According to the standards[13,14], throughput is definedas the time-averaged number of correctly received transportblocks over a reference mathematical channel. The actual rateis defined in a testing and statistical perspective, and thereis no accurate theory to determine a wireless system’s ac-tual rate. Experiments show that the relationship between aMIMO system’s throughput and the downlink power can bedepicted as the solid red line in Fig. 1[13,14,17]. The proto-col rate Rm could be achieved while the downlink power iskept at a relative high level (related to the received noise).For different terminals under a same protocol, the through-put function may differ, as shown by the blue dotted line inFig. 1. The power corresponding to a constant throughputvalue of Rx (0 < Rx < Rm) is selected as the throughput per-formance indicator. As shown in Fig. 1, Px1 and Px2 reflectthe performances with the two RF metrics applied respec-


196 Journal of Communications and Information Networks

Protocol parameters

Bandwidth

modulationModulation

Code rate

Stream number

.

.

.

RF chain parameters

Attenuation

modulationDesense

Correlation

Radiated patterns

.

.

.

Protocol rate

Baseline measurement Throughput

expression Channel

Feature factor extraction

Feature factor extraction

Function κ

Factor ψ

Figure 2 The throughput model is built on three steps: protocol rate achievement, baseline function measurement, and the RF performance related factorcalculation

tively. It is clear that the 1st user equipment (UE) has a betterperformance since a lower power level is required for reach-ing the same throughput value of Rx. Based on experimentalmeasurement results, the paper proposes an analytical modelfor 2×2 MIMO throughput calculation, which is establishedon the perspective that with a selected protocol, throughputdegradation is only determined by the RF performance of anactual wireless system, as shown in Fig. 1. The model is ex-pressed as

Tpm = Rm ∗κ(Snr), Snr = Pd−N0 +Ψ , (1)

where Tpm represents the actual throughput; Rm is the proto-col rate of a 2×2 MIMO system under a chosen protocol (inMbit/s); κ denotes the throughput function, which is deter-mined by the protocol settings and channel; Snr is the receivedsignal noise ratio (SNR) in format of dB; Pd is the downlinkpower in dBm; N0 is the received noise at MIMO receivers; Ψ

is a factor associated with the RF performance (in dB).The analytical model is built on two facts. First, with a cho-

sen combination of protocol and channel, the value Rm can becalculated by referring to the methods in Refs. [20,21], andthe κ function could be achieved via one measurement of athroughput curve. Second, once the RF related factor Ψ is ob-tained, the throughput value in (1) will be acquired. As shownin Fig. 2, the model is based on a first process of looking upthe protocol rate via combining the protocol related informa-tion, and followed by a second process of baseline functionmeasurement of κ , considering both the selected protocol andchannel, and continued with a third process of Ψ calculationvia combining the RF chain factors about desense, antennapatterns, channel, etc. Both Rm and κ function are invari-able under a chosen protocol and channel, so any change inRF front end can be computed for its corresponding impactof throughput. Therefore, the rest of this paper will mainlyfocus on the analysis of how RF performance impacts finalthroughput performance.

III. MODELING OF RF PERFORMANCEIMPACT ON THROUGHPUT

For a mobile system with S antennas equipped at the basestation side and U antennas configured at the UE side, the datatransmission can be expressed as

y(t) =H(t) ·x(t)+n(t), (2)

where x(t) contains the S transmitted signals at base stationtransceivers; y(t) contains the U received signals at UE re-ceiver inputs; n(t) is the noise vector; H(t) is the channelcorrelation matrix of U rows and S columns.

The (u,s) component (u = 1,2, · · · ,U ; s = 1,2, · · · ,S) ofH(t), marked as h(u,s)(t), indicating the signal change fromthe sth transmitting port to the uth receiver, is defined as[22,23]

h(u,s)(t) =N

∑n=1

h(n,u,s)(t), (3)

where h(n,u,s)(t) is the nth propagation ray; N is the number ofrays defined in the channel model. Channel model is definedas the mathematical descriptions of a physical multi-path envi-ronments where wireless UE works, including the microwavepropagating directions, reflections caused by buildings, delay,Doppler, the angle arrival, etc. The 3GPP proposes the spatialchannel model extension (SCME) for specifying the MIMOmobile phone throughput evaluations.

For generality, a typical 3D channel model proposed inRef. [23] is adopted here for throughput modeling, whereh(n,u,s)(t) is rewritten as

h(n,u,s)(t) =M

∑m=1

(e(−j2πλ−1Dtx

s (Ω txm )) ∗ e(−jpνt)∗

e(−j2πλ−1Drxu (Ω rx

n )) ∗

[Frx(V )

u (Ω rxn )

Frx(H)u (Ω rx

n )

]T

·



[χ

V,Vn,m χ

V,Hn,m

χH,Vn,m χ

H,Hn,m

]·

[F tx(V )

s (Ω txm )

F tx(H)s (Ω tx

m )

]), (4)

where Frx(p)u is the uth UE antenna gain in p polarization;

F tx(p)u is the sth base station antenna gain;

[χ

V,Vn,m χ

V,Hn,m

χH,Vn,m χ

H,Hn,m

]are

the channel complex gains; Ω txm and Ω rx

n are the angle of ar-rival and department respectively; Dtx

s (Ωtxm ) and Drx

u (Ω rxn ) are

the phases offsets; pν indicates the Doppler impact. Sincethe channel is a known mathematical model and the antennapattern can be measured, H(t) in (2), (3) and (4) can be cal-culated. While the signal y(t) is achieved, MIMO receiverswill recover the transmitted x(t) and then do demodulations.Errors occurred in the demodulation process will lower theoverall throughput rate.

Compared to a single receiver configured wireless system,a practical MIMO system performance is related to additionalrespects. The first factor is the channel correlation matrixachieved through integrating base station antenna patterns,real channel model, and UE antenna patterns, as discussedbefore. Then are the noise levels at the two receivers. Inthe paper, it is assumed that the difference between the ac-tual noise power density at the 1st receiver (marked as n1(t))and N0 is ∆N1 dB, and the difference between the actual noisepower density at the 2nd receiver (marked as n2(t)) and N0 is∆N2 dB.

A. Impact of Practical Channel Correlation MatrixThe component hi j(t) in H(t) represents the total complex

gain from the jth transmitting port to the ith receiver, as shownin Fig. 3. Define the total received power at each receiveras the sum of power levels of two different streams. So thereceived SNR levels at both receivers (marked as Snrrx1 andSnrrx2 can be expressed as

Snrrx1 = Pr−N0 +10∗ lg(E[|h1,1(t)|2]+E[|h1,2(t)|2]),Snrrx2 = Pr−N0 +10∗ lg(E[|h2,1(t)|2]+E[|h2,2(t)|2])),

(5)

where E[ ] denotes the mathematical expectation. And definethe MIMO average SNR value as the average value of the twoSNR, as

Snrav = 10∗ lg((10(Snrrx1/10)+10(Snrrx2/10))/2

)=

Pr−N0 +Gm, (6)

where

Gm = 10∗ lg((E[|h1,1(t)|2]+E[|h1,2(t)|2] +

E[|h2,1(t)|2]+E[|h2,2(t)|2])/2). (7)

Although Snrav is the defined received average SNR valueat the MIMO receivers, it should not be substituted into (1)

Receiver 1

Receiver 2

Transmitting 1

Transmitting 2

x1(t)

x2(t)

y1(t)

y2(t)

h1,1(t)

h1,2(t)

h2,1(t)

h2,2(t)

Pr

Figure 3 An illustration of the channel correlation matrix in a 2×2 MIMOsystem

for throughput calculations. Since after receiving the multiplestream signals, the system requires to do estimation and inver-sion of the channel correlation matrix, which will additionallyamplify the existed noise.

The vector transmission in a 2×2 MIMO system is rewrit-ten as

y(t) =

[h1,1(t) h1,2(t)

h2,1(t) h2,2(t)

]·x(t)+n(t) =[

1/ fm 0

0 fm

]·

[fm ∗h1,1(t) fm ∗h1,2(t)

1/ fm ∗h2,1(t) 1/ fm ∗h2,2(t)

]·x(t)+n(t) =

Fm ·H f m(t) ·x(t)+n(t), (8)

where

fm = 4

√E[|h2,1(t)|2]+E[|h2,2(t)|2]E[|h1,1(t)|2]+E[|h1,2(t)|2]

,

Fm =

[1/ fm 0

0 fm

],

H f m(t) =

[fm ∗h1,1(t) fm ∗h1,2(t)

1/ fm ∗h2,1(t) 1/ fm ∗h2,2(t)

].

(9)

(8) and (9) give another perspective for describing the 2×2MIMO system, as shown in Fig. 4, where the vector x(t)is processed by H f m(t), Fm and then delivered into the re-ceivers. The received Snrav values (defined in (6)) at themarked “B ports” and the receiver inputs are the same, sincethe defined factor Gm is independent on matrix Fm. How-ever, inversing the matrix Fm and recovering the vector x(t)(demodulating process) will amplify the existed noise. Theo-retically, the larger the norm of the matrix Fm is, the biggerthe matrix condition number is, and the larger the degradingimpact on the final SNR is. Especially, in case of a norm be-ing one (the minimum limit), Fm will have no influence onthe SNR value. By contrast, a norm of positive infinity willresult in that the SNR drops drastically and the receiver can-not demodulate. In the proposed model, the SNR value withthe impact of factor Fm in consideration is built as

Snrav,Fm ≈ Snrav− lg(norm(Fm,2)), (10)



Receiver 2

Transmitting 1

Transmitting 2

Pr

Hfm matrix

Receiver 1

Fm matrix

B ports

x1(t)

x2(t)

y1(t)

y2(t)

Figure 4 Another equivalent representation of Fig. 3

where norm(,2) is the second order norm of a matrix. Whilethe value of norm(Fm,2) reaches its upper and lower limits,the two sides of (10) are strictly equivalent.

Besides the impact caused by Fm, the correlation coeffi-cient of H f m(t) should also be considered for its degradationon the received SNR. Referring to (8) in Ref. [23], the corre-lation coefficient between hk,l(t) and h f ,g(t) is defined as

ρkl, f g =E[hk,l(t)h∗f ,g(t)]√

E[|hk,l(t)|2]∗E[|h f ,g(t)|2], (11)

where hk,l(t) and h f ,g(t) are the (k, l) and ( f ,g) componentsin H(t). Since fm in H f m(t) is time-invariant, the correlationcoefficient ρkl, f g in H f m(t) is equivalent to the correspondingvalue in H(t).

In the paper, we define the transmitting correlation coeffi-cient ρ tx and the receiving correlation coefficient ρrx as

ρtx1 =

E[h1,1(t)h∗1,2(t)]√E[|h1,1(t)|2]∗E[|h1,2(t)|2]

,

ρtx2 =

E[h2,1(t)h∗2,2(t)]√E[|h2,1(t)|2]∗E[|h2,2(t)|2]

,

ρrx1 =

E[h1,1(t)h∗2,1(t)]√E[|h1,1(t)|2]∗E[|h2,1(t)|2]

,

ρrx2 =

E[h1,2(t)h∗2,2(t)]√E[|h1,2(t)|2]∗E[|h2,2(t)|2]

,

ρtx =

√|ρ tx

1 | ∗ |ρ tx2 |,

ρrx =

√|ρrx

1 | ∗ |ρrx2 |,

(12)

where ()∗ means conjugate transpose.The correlation coefficient is a finite value that belongs to

[0,1]. The smaller the coefficient is, the smaller the causeddegradation on throughput performance is. Similar to howthe norm of matrix Fm affects the SNR value, a coefficientof zero will have no influence, and a coefficient of one willresult in that the receiver cannot demodulate. In the analyticalmodel, the SNR with the impacts of factors Fm, ρ tx, and ρrx

in consideration is built as

Snrav,Fm,ρ ≈ Snrav,Fm + lg[(1−ρ

tx)K2(1−ρrx)K3

](13)

where K2 and K3 are constant.

Finally, in case of ∆N1 = ∆N2 = 0, the MIMO throughputmodel can be expressed as

Tpm ≈ Rm ∗κ(Snrav,Fm,ρ). (14)

B. Impact of Receiver NoiseFor more general cases of ∆N1 6= 0 and ∆N2 6= 0, assume

that the noise power density at the 1st receiver is larger thanN0 by ∆N1 dB, which means the received SNR of the 1st re-ceiver is degraded by ∆N1 dB. This situation can also be con-sidered as the received signal power level reduced by ∆N1 dBwith noise level unchanged. The received signal at the 1st re-ceiver is h1,1(t)∗ x1(t)+h1,2(t)∗ x2(t). Thus, the 1st receivedpower is reduced by ∆N1 dB, which can be considered asthe factors h1,1(t) and h1,2(t) degraded by

√10(∆N1/10) times

in real. Similarly, the factors h2,1(t) and h2,2(t) are reducedby√

10(∆N2/10) times in real. Therefore, in the condition of∆N1 6= 0 and ∆N2 6= 0, we can rewrite the factors Gm and fm

as Gpm and f p

m, separately

Gpm = 10∗ lg

(E[|h1,1(t)|2]+E[|h1,2(t)|2]

2∗10(∆N1/10) +

E[|h2,1(t)|2]+E[|h2,2(t)|2]2∗10(∆N2/10)

), (15)

and

f pm = 4

√(E[|h2,1(t)|2]+E[|h2,2(t)|2]E[|h1,1(t)|2]+E[|h1,2(t)|2]

)10(∆N1/10)

10(∆N2/10) . (16)

According to the definitions, ρrx and ρ tx are independent of∆N1 and ∆N2. Finally, in consideration of cases that ∆N1 6= 0,∆N2 6= 0, and H(t) is calculated with antenna patterns andchannel model, from (1) (6) (10) (12) (13) (14) (15) and (16),the ultimate throughput model can be expressed as

Tpm ≈ Rm ∗κ(Pr−N0 +Ψ), (17)

where Pr is the downlink power from the base station,

F pm =

[1/ f p

m 0

0 f pm

],

Ψ = Gpm−10lg(norm(F p

m ,2)) +

10lg((1−ρ tx)K2(1−ρrx)K3).

C. Baseline MeasurementAs discussed earlier, the function κ is obtained via a

process of measurement. A simplified diagram of real-timethroughput simulating and testing system is shown in Fig. 5,where the protocol parameters are configured in the base sta-tion emulator (BSE) and the UE, the channel information isgenerated by the channel emulator, including all informationabout the dynamic channel correlation matrix of H(t). Such



Base station

emulator

Channel

emulator UE

Bandwidth

Modulation

Code rate

Stream number

.

.

.

Attenuation

Desense

Propagation

Antennas

.

.

.

Decoding

Demodulation

H(t) estimation

Desense

.

.

.

Figure 5 A simplified diagram of real-time throughput simulation and test-ing system

Figure 6 The practical MIMO throughput testing system for the validationsin the paper

a system can completely simulate the real use scenarios ofthe wireless UE. Based on the testing system, the κ is mea-sured via two steps. First, configure the protocol parametersin BSE and UE, and select channel information in channel em-ulator. Then, set H(t) to be a dynamic low-correlated matrix,and conduct throughput testing via adjusting the transmittedpower Pr step by step and obtaining the throughput value instatistics. Achieving the throughput curve at a low-correlatedmatrix could reduce as much as possible the testing uncer-tainties caused by channel estimations. It is noted that thenoise level at the receiver can be obtained via techniques inRef. [24]. So the baseline of κ can be clearly depicted.

IV. VALIDATIONS

A. ModelingFor the model’s accuracy validations, a practical through-

put model is built in this part based on a testing system shownin Fig. 6, where the BSE and channel emulator are integratedin one instrument E7515A, and a cellular mobile terminal isutilized as the device under test (DUT). The terminal is lo-cated in a shielding box and connected to the instrument. Es-pecially, the SCME urban micro (Umi) channel model is se-lected for validations, which is one of the only two standardmodels specified by 3GPP and CTIA for 4G long-term evo-lution (LTE) MIMO over the air (OTA) tests, and will be ex-

Table 1 Measurement parameters

Parameter Value

Instruments PC, Keysight E7515A

DUT Samsung Tab2

Test protocol LTE frequency division duplexing (FDD)

Test mode 2×2 MIMO (2 streams)

Test channel SCME Umi

K2, K3 0.25, 0.5

Protocol rate 35.424 Mbit/s

−85 −80 −75 −70 −65 60

Downlink power (dBm/10 MHz)

0

5

10

15

20

25

30

35

40

Thro

ughput

(Mbit

/s)

BaselineMeasured lineCalculated line

Figure 7 The measured baseline is illustrated in this figure as the red lineon the left

panded for further 5G MIMO throughput evaluations. Severalmajor parameters are listed in Tab. 1.

Under the configurations, the baseline is measured as illus-trated by the red real line in Fig. 7, where the x-axis repre-sents the downlink power, and the y-axis denotes the through-put value. The decomposition parameters for the baseline aregiven in detail in Tab. 2. It is noted that during the baselinemeasurement, two omnidirectional, un-correlated, and polar-ized diversity antennas are used for generating a low corre-lated channel matrix. And the corresponding factor Ψ in thebaseline testing (marked as Ψbs in the Tab. 2) is provided.

B. ValidationsFor verifying the accuracy of this model, the case with prac-

tical antennas and desense is adopted into the model for com-parison between the calculated throughput-power curve andthe measured line. The comparison is conducted by followingthree steps.

1. According to the practical antenna patterns, compute thechannel correlation matrix H(t).

2. Achieve the transmitting and receiving correlations ρ tx

and ρrx defined in (12) with the computed matrix H(t).3. With substituting the acquired H(t) and the noise levels

at two receivers into (15) and (16), calculate the values factorsGp

m and f pm.



Table 2 Measurement parameters for baseline

Parameter Value

DUT antenna patterns

The 1st antenna is configured tobe isotropic and single

V-polarized, and the 2ndantenna is configured to be

isotropic and only H-polarized

The value of Gpm

−0.14 dB (with the channelpower normalized)

The value of 10lg(norm(F pm,2)) 0.35 dB

The correlation ρ tx 0.112 7

The correlation ρrx 0.099 7

The noise level at the 1st receiver −96.6 dBm/10 MHz

The noise level at the 2nd receiver −95.2 dBm/10 MHz

The value of Ψbs −0.99 dB

4. Substitute obtained parameters ρ tx, ρrx, Gpm, f p

m into (17)for factor Ψ calculating.

5. Shift the baseline along the x-axis by an offset of Ψ−Ψbs

to get the throughput function with the actual antenna patternsapplied. As shown in Fig. 7, the blue curve shifted from thebaseline is the calculated result.

6. Measure the real throughput curve by using the testingsystem in Fig. 6. Then compare the difference between themeasured line and the computed result.

The estimated line is highly consistent with the measuredresult in Fig. 7. Actually, hundreds of experiments based ondifferent kinds of RF combinations are conducted in the pa-per. All the factors Gp

m, F pm , ρ tx, ρrx, ∆N1, ∆N2 are calculated

according to the actual RF combinations, as listed in Fig. 8,where the x-axis is the index of RF combination, and the y-axis represents the value of each factor. The differences areanalyzed. Especially, for each comparison among calculationand measurement, the power offsets on x-axis that respectivelycorrespond to the three fixed throughput points of 70%Rm,50%Rm, 30%Rm, are calculated, and marked as ∆P0.7, ∆P0.5,∆P0.3, which are finally illustrated in Fig. 9.

C. AnalysisThe experimental results could hold several conclusions.1. All the differences are within ±1.25 dB, and 95% of

which are within ±0.7 dB. The throughput analytical modelhas a good correspondence with the actual testing system.Two main uncertainty contributors may impact the compar-isons. The first one is the MIMO throughput testing uncer-tainties, which is discussed in Ref. [14]. In this paper, theprovided system has a test repeatability of ±0.3 dB. The sec-ond one is the calculation errors on the factors Gp

m, Ipm, ρ tx,

ρrx, which are all computed in a statistical approach. And thethroughput value is high-sensitive to the factors ρ tx, ρrx whilethe two parameters are close to the upper limitation.

2. According to (1), once the analytical model is built, the

0 100 200 300 400

Index of RF combination

−15

−10

−5

0

Gm

p (

dB

)

0 100 200 300 400


0

5

10

Norm

(dB

)

0 100 200 300 400


−98

−96

−94

−92

Nois

e le

vel

(dB

m)

Noise on Rec. 1

Noise on Rec. 2

0 100 200 300 400


0

0.5

1.0

Corr

elat

ion Corr. of Rx

Corr. of Tx

(a) (b)

(c) (d)

Figure 8 The decomposition parameters shown in this figure are to illustratethat in the experimental verifications, the changes of each parameter are inconsiderations: (a) average gain; (b) norm of the matrix; (c) noise levels; (d)correlations

0 50 100 150 200 250 300 350Index of RF combination

−2

−1

0

1

2

Dif

fere

nce

(dB

)

errors@70%Rm

errors@50%Rm

errors@30%Rm

0 50 100 150 200 250 300 350Index of RF combination

0

0.1

0.2

0.3

Sta

ndar

d d

evia

tion

X: 185

Y: −1.24

(a)

(b)

Figure 9 The errors between calculations and measurements and the relatedstandard deviations are listed: (a) differences between calculations and mea-surements; (b) standard deviation of the differences

throughput curve as a function of power under different RFperformances is invariant in shape and has shifted versions inx-axis. Thus theoretically, ∆P0.7, ∆P0.5, ∆P0.3 are equivalentin one comparison. In the paper, the standard deviations of thethree errors are provided, as shown in Fig. 9. All the standarddeviations are smaller than 0.3 and 95% of them are within0.15, which is consistent with the theoretical derivations.

V. APPLICATION SCENARIO

Based on the proposed analytical model, the throughput im-pact caused by each parameter is presented, which is helpfulto guide designers to avoid possible risks during wireless sys-tem design. Furthermore, combined with the test results inprevious sections, a throughput diagnosis report is provided as



Table 3 Measurement results for receiver throughput

Parameter Value

Related noise level at the 1st receiver −101.9 dBm/10 MHz

Related noise level at the 2nd receiver −101.4 dBm/10 MHz

Downlink power correspondingto 70% of the maximum rate

−82.89 dBm/10 MHz(−110.69 dBm/15 KHz)

an example, illustrating how to troubleshoot in a much moreeffective way.

A. Throughput Impact Related to ReceiversThe first concern is the receiver performance. In order to

isolate antenna and desense related impact, the receiver is an-alyzed in the assumptions that two omnidirectional, single-polarized, polarization-diversified antennas are configured,and the external noise could not be coupled and delivered intothe receiver inputs. In this case, the acquired throughput per-formance represents the limit achievable for a system with thisreceiver configured.

Following the model built in section V, the receiverthroughput can be calculated while the noise at receiver in-puts is obtained (with desense isolated). Actually, the con-ducted sensitivity of a receiver can be measured with RF cableconnected to receiver directly, and the noise level of each re-ceiver could be further achieved by the procedures describedin Ref. [24]. Moreover, in a conductive testing, external noisecannot be coupled into the receiver via antennas, that is, thedesense portion is isolated. Substituting the noise and theideal patterns into the analytical model yields the chip’s ownthroughput performance. For the convenience of comparison,the downlink power corresponding to 70% of the maximumrate is selected as the figure of metric of throughput perfor-mance. Then, the receiver performance is listed in Tab. 3,which points out that the value of −110.69 dBm/15 KHz isthe upper performance limited by the receivers.

In fact, if the receiver performance could not meet the net-working requirement, it means that even if the antenna is ide-ally un-correlated and there is no self-interference, the per-formance is still required to be improved. In practice, self-interference and antenna correlation will always degrade thethroughput performance. Thus generally, the chip perfor-mance should be much better than the requirement of net-working.

B. Throughput Impact Related to AntennasA conventional antenna design will go through an itera-

tive process of “designing-manufacturing-throughput impacttesting-improving”, which is extremely time-consuming butcannot be neglected, since the relationship between through-put and the conventional antenna specifications (such as enve-lope correlation coefficient and voltage standing wave ratio)is unknown. That is a common problem of antenna design

−20 −15 −10 −5 0Relative gain (dB)

0

5

10

15

20

Per

f. d

egra

dat

ions

(dB

)

0 5 10 15 20Norm (dB)

0

5

10

15

20

Per

f. d

egra

dat

ions

(dB

)

0 0.5 1.0Transmitting correlation

0

5

10

Per

f. d

egra

dat

ions

(dB

)

0 0.5 1.0Receiving correlation

0

5

10

Per

f. d

egra

dat

ions

(dB

)

(a) (b)

(c) (d)

Figure 10 The throughput performance degradations caused by the fourantenna-related factors: (a) relationship between throughput sensitivity andthe relative gain; (b) the norm; (c) the transmitting correlation; (d) the receiv-ing correlation

0 5 10 15 20Noise increasing at both receivers (dB)

0

5

10

15

20P

erf.

deg

radat

ions

(dB

)

0 5 10 15 20Noise increasing at the 1st receiver (dB)

0

2

4

6

8

10

Per

f. d

egra

dat

ions

(dB

)

(a) (b)

Figure 11 The throughput performance degradation caused by the desense:(a) relationship between throughput sensitivity and the noise levels at bothreceivers; (b) relationship between throughput sensitivity and the noise levelat the 1st receiver

in MIMO systems. Based on the analytical model, the paperdefines four indicators for evaluating antennas: relative gain(defined in (15) and related to the value in baseline), norm(defined in (9)), transmitting correlation (defined in (12)), andreceiving correlation (defined in (12)). And their contributionsto the throughput are provided. Following the previous modelexample, throughput performance degradations caused by thefour factors are given, as shown in Fig. 10.

From the figure, increasing the relative gain or reducingthe norm can linearly improve the throughput performance.In case of a high correlation level, the throughput rate willdrop sharply with the correlation increased, especially withthe receiving correlation raising. It is the first time that engi-neers can directly estimate the degradation of throughput per-formance with the MIMO antennas applied during the R&Dstage, which will significantly reduce the number of iterationsof antenna design.

C. Throughput Impact Related to DesenseThe interference inside DUT would be coupled via anten-

nas and then delivered into receivers, which is how the desense



Table 4 Throughput diagnosis report of the 240th validation result

Sub-systemDecomposition parameter and its impact

Throughput performanceFactors Value Degradation

ReceiverNoise on the 1st receiver −101.90 dBm/10 MHz −

−110.69 dBm/15 KHzNoise on the 2nd receiver −101.40 dBm/10 MHz −

Antennas

Relative gain −7.71 dB 7.71 dB

−96.11 dBm/15 KHzNorm 1.35 dB 1.35 dB

Transmitting correlation 0.68 1.24 dB

Receiving correlation 0.86 4.27 dB

emerges. Increasing noise level at each receiver is equiva-lent to reducing the corresponding antenna gain, as stated be-fore. With the loaded antenna patterns fixed, we can achievethe throughput performance degradation along to the changingnoise. As shown in Fig. 11, the left figure illustrates the degra-dation caused by a synchronous noise increasing at both re-ceivers, and the right figure illustrates the degradation causedby a single noise increasing at the 1st receiver.

D. Throughput Diagnosis ReportTake the 240th validating result in section V as an example

to analyze its diagnosis report. The diagnosis measurement isconducted in following steps.

1. Obtain the noise levels at both the receivers and thenmeasure the throughput result, in a conductive approach, asshown in Tab. 4, where −110.69 dBm/15 KHz is the upperlimitation with the receivers configured.

2. Measure the DUT antenna patterns, and calculate the pa-rameters: Gp

m, F pm , ρ tx, ρrx. And finally, compute the degrada-

tion caused by the antenna factors. Actually, with the practicalantennas equipped, a degradation of 14.57 dB is reached.

3. Achieve the noise level at both the receivers whilethe DUT is in the integrated configuration, and compute thedegradation caused by the desense factors. Finally, with thedesense in consideration, the total degradation is 17.9 dB, andthe entire throughput performance is −92.79 dBm/15 KHz.

VI. CONCLUSION

Throughput reflects a communication system’s true userexperience, which is defined in a perspective of measurementin the 3GPP standardizations. In the paper, it is the first timethat throughput is analyzed via a mathematical model withthe RF hardware performance included. The model consid-ers both transmission specifications about bandwidth, codingrate, modulation, cyclic prefix, and the radio frequency param-eters on antenna correlation, desense, propagation, etc. thatoutput the practical throughput reflecting the achievable datarate of a MIMO system in its realistic application stage. Theoutputted detailed diagnostic report of a communication sys-tem can directly guide designers to avoid disadvantages dur-

ing wireless system design and optimization for the RF frontend improvements. Especially for 5G and Internet of things,where MIMO is the basic technique for holding a high rate andstable network, the mathematic analytical method will makeMIMO performance much more predictable during the designphase.

REFERENCES

[1] SUN S, RAPPAPORT T, SHAFI M, et al. Propagation models andperformance evaluation for 5G millimeter-wave bands[J]. IEEE Trans.Veh. Technol., 2018, 67(9): 8422-8439.

[2] MESLEH R, HAAS H, SINANOVIC S, et al. Spatial modulation [J].IEEE Trans. Veh. Technol., 2008, 57(4): 2228-2241.

[3] ZHANG H, JIANG C, BEAULIEU N, et al. Resource allocation forcognitive small cell networks: A cooperative bargaining game theoreticapproach[J]. IEEE Trans. Wireless Commun., 2015, 14(6): 3481-3493.

[4] DING Z G, FAN P Z, POOR V. Impact of user pairing on5G nonorthogonal multiple-access downlink transmissions[J]. IEEETrans. Wireless Commun., 2016, 65(8): 6010-6023.

[5] YU T Q, WANG X B, SHAMI A. UAV-enabled spatial data sam-pling in large-scale IoT systems using denoising autoencoder veuralnetwork[J]. IEEE Internet Things J., 2019, 6(2): 1856-1865.

[6] LIU X, LIU Y N, WANG X B, et al. Highly efficient 3-D resourceallocation techniques in 5G for NOMA-enabled massive MIMO andrelaying systems[J]. IEEE J. Sel. Areas Commun., 2014, 35(12): 2785-2797.

[7] QI Y H, YANG G, LIU L, et al. 5G over-the-air measurement chal-lenges: overview[J]. IEEE Trans. Electromagn. Compat., 2017, 59(6):1661-1670.

[8] 3GPP. Verification of radiated multi-antenna reception performance ofUser Equipment (UE)[S]. Tech. Report TR 37.977, Revision 15.0.0,2018: 9.

[9] CHEN J S, STERN T E. Throughput analysis, optimal buffer allo-cation, and traffic imbalance study of a generic nonblocking packetswitch[J]. IEEE J. Sel. Areas Commun., 1991, 9(3): 439-449.

[10] PRASAD R. CDMA for wireless personal communications[M].Boston: Artech House Publishers, 1996.

[11] PUPALA R N, GREENSTEIN L J, DAUT D G. Effects of channeldispersion and path correlations on system-wide throughput in MIMO-based cellular systems[J]. IEEE Trans. Wireless Commun., 2009,8(11): 5477-5482.

[12] RHEE C, KIM Y J, PARK T, et al. Pattern-reconfigurable MIMO an-tenna for high isolation and low correlation[J]. IEEE Antennas Wire-less Propag. Lett., 2014, 13: 1373-1376.

[13] 3GPP. User equipment (UE) over the air (OTA) performance; confor-mance testing[S]. Tech. Specif. TS 37.544 v14.5.0, 2018.



[14] CTIA, Washington, DC, USA. Test plan for 2 × 2 downlink MIMOand transmit diversity over-the-air performanc[S]. Revision 1.1, Aug.2016.

[15] SHEN P H, QI Y H, YU W, et al. OTA measurement for IoT wire-less device performance evaluation: Challenges and solutions[J]. IEEEInternet Things J., 2019, 6(1): 1223-1237.

[16] QI Y H, YU W. Unified antenna temperature[J]. IEEE Trans. Electro-magn. Compat., 2016, 58(5).

[17] YU W, QI Y H, LIU K F, et al. Radiated two-stage method for LTEMIMO user[J]. IEEE Trans. Electromagn. Compat., 2014, 56(6):1691-1696.

[18] SHI L, ZHANG W, XIA X G. On designs of full diversity space-timeblock codes for two-user MIMO interference channels[J]. IEEE Trans.Wireless Commun., 2012, 11(11): 4184-4191.

[19] MENG Y, ZHANG W, ZHU H J, et al. Securing consumer IoT in thesmart home: Architecture, challenges, and countermeasures[J]. IEEEWireless Commun., 2018, 25(6): 53-59.

[20] PROAKIS J. Digital communications[M]. New York: McGraw-Hill,1983.

[21] NGO H Q. Massive MIMO: Fundamentals and System Designs[M].Linkoping: LiU-Tryck, 2015.

[22] SHEN P H, QI Y H, YU W, et al. An RTS-based near-field MIMOmeasurement solutionła step toward 5G[J]. IEEE Trans. Microw. The-ory Techn., 2019, 67(7): 2884-2893.

[23] DAO M T, NGUYEN V A, IM Y T, et al. 3D polarized channel mod-eling and performance comparison of MIMO antenna configurationswith different polarizations[J]. IEEE Trans. Antennas Propag., 2011,59(7): 2672-2682.

[24] SHEN P H, QI Y H, YU W, et al. A decomposition method for MIMOOTA performance evaluation[J]. IEEE Trans. Veh. Technol., 2019,67(9): 8184-8191.

ABOUT THE AUTHORS

Penghui Shen received his B.S. and M.S. degrees inelectronic information and technology from the HunanUniversity, Changsha, China, in 2013 and 2016. Heis currently working toward his Ph.D. degree in elec-tronics from the same university. His research interestsinclude SISO, MIMO and 5G array measurements forwireless devices, EMC, and antenna design.

Yihong Qi [corresponding author] received his B.S.degree in electronics from National University of De-fense Technologies, Changsha, China, in 1982, hisM.S. degree in electronics from China Academy ofSpace Technology, Beijing, China, in 1985, and hisPh.D. degree in Electronics from Xidian University,Xi’an, China, in 1989. From 1989 to 1993, he wasa postdoctoral fellow and then an associate professorwith Southeast University, Nanjing, China. From 1993

to 1995, he was a postdoctoral researcher at McMaster University, Hamilton,ON, Canada. From 1995 to 2010, he was with Research in Motion (Black-berry), Waterloo, ON, where he was the director of Advanced Electromag-netic Research. Currently, he is the president and a chief scientist with Gen-eral Test Systems, Inc.; he founded DBJay in 2011. He is also an adjunctprofessor in EMC Laboratory, Missouri University of Science and Technol-ogy, Rolla, MO and an adjunct professor in Hunan University, Changsha,China. He is an honorary professor and the dean of Behivioral Big Data In-stitute in Southwest University. He is an inventor of more than 400 published

and pending patents. Dr. Qi was a distinguished lecturer of IEEE EMC Soci-ety for 2014 and 2015, and serves as the chairman of IEEE EMC TC-12. Hehas received an IEEE EMC Society Technical Achievement Award in August2017. He is a fellow of Canadian Academy of Engineering.

Xianbin Wang is a professor and Tier 1 Canada Re-search Chair at Western University, Canada. He re-ceived his Ph.D. degree in electrical and computer en-gineering from National University of Singapore in2001.

Prior to joining Western, he was with Communi-cations Research Centre Canada (CRC) as a researchscientist/senior research scientist between July 2002and December 2007. From January 2001 to July 2002,

he was a system designer at STMicroelectronics. His current research in-terests include 5G and beyond, Internet-of-things, communications security,machine learning and intelligent communications. Dr. Wang has over 400peer-reviewed journal and conference papers, in addition to 30 granted andpending patents and several standard contributions.

Dr. Wang is a fellow of Canadian Academy of Engineering, a fellow ofEngineering Institute of Canada, a fellow of IEEE and an IEEE distinguishedlecturer. He has received many awards and recognitions, including CanadaResearch Chair, CRC President’s Excellence Award, Canadian Federal Gov-ernment Public Service Award, Ontario Early Researcher Award and 6 IEEEBest Paper Awards. He currently serves as an editor/associate editor for IEEETransactions on Communications, IEEE Transactions on Broadcasting, andIEEE Transactions on Vehicular Technology. He was also an associate editorfor IEEE Transactions on Wireless Communications between 2007 and 2011,and IEEE Wireless Communications Letters between 2011 and 2016. Hewas involved in many IEEE conferences including GLOBECOM, ICC, VTC,PIMRC, WCNC and CWIT, in different roles such as symposium chair, tu-torial instructor, track chair, session chair and TPC co-chair. Dr. Wang iscurrently serving as the chair of ComSoc Signal Processing for Communica-tions and Computing Technical Committee.

Wei Zhang received his Ph.D. degree in electronic en-gineering from the Chinese University of Hong Kong,Hong Kong, China in 2005. He was a research fellowwith the Hong Kong University of Science and Tech-nology from 2006 to 2007. Currently, he is a professorwith the University of New South Wales, Sydney, Aus-tralia. His current research interests include 5G, spaceinformation networks, and network security. He is anarea editor for IEEE Transactions on Wireless Com-

munications and the editor-in-chief of Journal of Communications and Infor-mation Networks. He is the vice director of IEEE Communications SocietyAsia Pacific Board and the chair of IEEE Wireless Communications TechnicalCommittee. He is a member of Board of Governors of IEEE CommunicationsSociety and an IEEE fellow.

Wei Yu received his B.S. degree in electrical engineer-ing from Xi’an Jiaotong University, Xi’an, China, in1991, his M.S. degree in electrical engineering fromChina Academy of Space Technology (CAST), Bei-jing, China, in 1994, and his Ph.D. degree in electricalengineering from Xidian University, Xi’an, China, in2000. From 2001 to 2003, he was a postdoctoral fel-low with University of Waterloo, Canada. He was aCTO with Sunway Communications Ltd., from 2008

to 2012. He founded Autonovation Electronics Inc. in 2004 and cofoundedGeneral Test Systems Inc., Shenzhen, China, in 2012. He is now with DBJTechnologies as COO. His current research interests include signal process-ing and mobile device test system. He is an inventor of 91 published andpending patents.


Documents

2 MIMO Throughput Analytical Model for RF Front End