Performance Analysis of Mixed-ADC Massive MIMO Systems ...oa.ee.tsinghua.edu.cn/dailinglong/publications/paper...feedback signaling. Therefore, the issue of imperfect channel state

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Performance Analysis of Mixed-ADC MassiveMIMO Systems over Rician Fading Channels

Jiayi Zhang, Member, IEEE, Linglong Dai, Senior Member, IEEE, Ziyan He,Shi Jin, Member, IEEE, and Xu Li

Abstract—The practical deployment of massive multiple-inputmultiple-output (MIMO) in future fifth generation (5G) wirelesscommunication systems is challenging due to its high hard-ware cost and power consumption. One promising solution toaddress this challenge is to adopt the low-resolution analog-to-digital converter (ADC) architecture. However, the practicalimplementation of such architecture is challenging due to therequired complex signal processing to compensate the coarsequantization caused by low-resolution ADCs. Therefore, fewhigh-resolution ADCs are reserved in the recently proposedmixed-ADC architecture to enable low-complexity transceiveralgorithms. In contrast to previous works over Rayleigh fadingchannels, we investigate the performance of mixed-ADC massiveMIMO systems over the Rician fading channel, which is moregeneral for the 5G scenarios like Internet of Things (IoT).Specially, novel closed-form approximate expressions for theuplink achievable rate are derived for both cases of perfect andimperfect channel state information (CSI). With the increasingRician K-factor, the derived results show that the achievablerate will converge to a fixed value. We also obtain the power-scaling law that the transmit power of each user can be scaleddown proportionally to the inverse of the number of base station(BS) antennas for both perfect and imperfect CSI. Moreover,we reveal the trade-off between the achievable rate and energyefficiency with respect to key system parameters including thequantization bits, number of BS antennas, Rician K-factor, usertransmit power, and CSI quality. Finally, numerical results areprovided to show that the mixed-ADC architecture can achievea better energy-rate trade-off compared with the ideal infinite-resolution and low-resolution ADC architectures.

Index Terms—Achievable rate, mixed-ADC receiver, massiveMIMO, Rician fading channels.

I. INTRODUCTION

The research on the fifth generation (5G) wireless commu-nication systems has been undertaken in recent years to meetthe demanding requirement of around 1000 times data traffic

Manuscript received December 15, 2016; revised March 1, 2017. Date ofpublication XX, 2017; date of current version XX, 2017.

This work was supported in part by the National Natural Science Foundationof China (Grant Nos. 61601020, 61371068 and 61571270) and the Fundamen-tal Research Funds for the Central Universities (Grant Nos. 2016RC013 and2016JBZ003).

J. Zhang and X. Li are with the School of Electronic and InformationEngineering, Beijing Jiaotong University, Beijing 100044, P. R. China (e-mail:[email protected]).

L. Dai and Z. He are with Department of Electronic Engineering, TsinghuaUniversity, Beijing 100084, P. R. China. (e-mail: [email protected])

S. Jin is with the National Mobile Communications Research Labo-ratory, Southeast University, Nanjing 210096, P. R. China (e-mail: [email protected]).

Simulation codes are provided to reproduce the results presented in thispaper: http://oa.ee.tsinghua.edu.cn/dailinglong/.

(e.g., see [1]–[3] and references therein). Massive multiple-input multiple-output (MIMO) has emerged as one of the mostpromising technologies to further improve the achievable rateand energy efficiency by ten times. By using hundreds or eventhousands of antennas at the base station (BS), the inter-userinterference in massive MIMO systems can be substantiallyreduced by simple signal processing such as maximum-ratiocombining (MRC) and zero-forcing (ZF) schemes.

For practical implementation of massive MIMO, a largenumber of antennas significantly complicate the hardwaredesign. It is difficult to use a dedicated radio frequency (RF)chain for every antenna, since the associated hardware costand power consumption is unaffordable when the numberof BS antennas becomes very large. Several massive MIMOarchitectures have been proposed to address this challengingproblem. The first one is the hybrid analog and digital pre-coding scheme, which uses different analog approaches likephase shifters [4], switches [5] or lenses [6] to substantiallyreduce the number of RF chains. However, the performance ofsuch hybrid precoding system highly depends on the accuratecontrol of the analog components. Moreover, if the beamwidthis small, the fast acquisition and alignment of the optimal beamin millimeter wave channels is challenging [7].

On a parallel avenue, the high-resolution ADC (e.g., morethan 10-12 bits for commercial use) in the RF chain is a power-hungry device, especially when large signal bandwidth is con-sidered. This is due to the factor that the power consumptionof a typical ADC roughly scales linearly with the signal band-width and exponentially with the quantization bit. Moreover, alarge demand on digital signal processing with high-resolutionADCs will induce excessive circuitry power consumptionand hardware cost. Therefore, an alternative massive MIMOarchitecture at the receiver is to reduce the high resolution(e.g., 10-12 bits) of the ADCs to low resolution (e.g., 1-3 bits)while keeping the number of RF chains unchanged. However,the severe nonlinear distortion caused by low-resolution ADCsinevitably causes several problems, including capacity loss athigh SNR [8], [9], high pilot overhead for channel estimation[10], [11], error floor for multi-user detection [12]–[14], andcomplex precoder design [15]–[17].

A. Related WorksIn order to alleviate aforementioned concerns, a mixed-ADC

architecture for massive MIMO systems has been recentlyproposed in [18], where a small number of high-resolutionADCs are employed, while the other RF chains are com-posed of one-bit ADCs. This architecture has the potential



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of designing practical massive MIMO systems while stillmaintaining a large fraction of the performance gain. Forexample, the reserved high-resolution ADCs can be utilizedto realize accurate channel estimation in a round-robin man-ner with reduced-complexity algorithm and affordable pilotoverhead [18]. Furthermore, the deduced channel estimationerror is Gaussian distributed, which facilitates the performanceanalysis and front-end designs of massive MIMO systems.

While there have been considerable works on homogeneous-ADC architectures with low ADC resolutions, very littleattention has been paid to the promising mixed-ADC mas-sive MIMO system. Only the analysis of generalized mutualinformation has been emphasized in [18] to demonstratethat the mixed-ADC architecture is able to achieve a largefraction of the channel capacity of ideal ADC architecturesover frequency-flat channels. This analysis is then extended tofrequency-selective fading channels [19]. In [20], a genericBayes detector is proposed to achieve the optimal signaldetection in the mean squared error (MSE) sense by usingthe generalized approximate message passing algorithm. Theauthors in [21] derived a closed-form approximation of theachievable rate of mixed-ADC massive MIMO systems withthe MRC detector. These pioneer works validate the merits ofthe mixed-ADC architecture for massive MIMO systems.

The common assumption of the aforementioned works isthat massive MIMO systems are operating over Rayleighfading channels. However, Rician fading, which includes thescenario of line-of-sight (LoS) signal propagation, is moregeneral and realistic than Rayleigh fading. Moreover, recentworks reveal that LoS (or near-LoS) signal propagation ismostly relied on in massive MIMO [22]–[24] or millimeter-wave communications [6], [25], [26]. Unfortunately, a Ricianmodel makes the analysis of massive MIMO systems morecomplicated, as the extension of current results in Rayleighfading channels [21] to those in Rician fading channels isnot easy. This is mainly because of the inherent difficulty inderiving the simple and mathematically tractable expressionsfor Rician fading channels. Moreover, channel estimation inmassive MIMO is a challenging problem. An erroneous chan-nel estimation may occur due to large number of estimationparameters, rapid time-varying channel fading, and imperfectfeedback signaling. Therefore, the issue of imperfect channelstate information (CSI) should also be taken into account in theperformance analysis of mixed-ADC massive MIMO systemsoperating over Rician fading channels.

B. ContributionsThis study aims to examine the mixed-ADC massive MIMO

system in terms of achievable rate and energy efficiency.Different from most of the existing works in the literature,we model the mixed-ADC massive MIMO links as moregeneral Rician fading channels for performance analysis. Wedemonstrate that the mixed-ADC architecture is practicallyuseful because it can provide comparable performance withthe ideal infinite-resolution ADC architecture, while the signalprocessing complexity and power consumption can be reducedat the same time. More specifically, the contributions of thiswork are summarized as follows:

• With the assumption of Rician fading channels, novelclosed-form approximate expressions for the achievablerate of mixed-ADC massive MIMO systems are derived.These results reveal the effects of the number of BSantennas, user transmit power, quantization bits, num-ber of high-resolution ADCs, and Rician K-factor onthe achievable rate performance. Note that our derivedresults are generalized, and can include many previouslypublished works [9], [21], [22], [27], [28] as special casesby adjusting system parameters accordingly.

• The power-scaling law of the mixed-ADC architectureunder Rician fading channels is elaborated for bothperfect and imperfect CSI cases. Our results show thatwhen the number of BS antennas, M , gets asymptoticallylarge, the transmit power of each user can be scaled downby 1/M to obtain a desirable rate for both perfect andimperfect CSI cases, if the Rician K-factor is nonzero.This new finding is different from the result in Rayleighfading channels [21], [27], [28]. In contrast to [9], wefocus on the mixed-ADC architecture and prove that thederived rate limits depend on the proportion of the high-resolution ADCs κ and the total number of low- and high-resolution ADCs.

• By adopting a generic power consumption model forthe mixed-ADC architecture, we quantify the trade-offbetween the achievable rate and energy efficiency fordifferent number of high-resolution ADCs and quantiza-tion bits. The optimal number of quantization bits andBS antennas needed to maximize the energy efficiencyare illustrated. We further prove that the mixed-ADCarchitecture can work better under stronger Rician fadingchannels and larger user transmit power.

C. Outline

The rest of this paper is organized as follows. The systemmodel is briefly introduced in Section II. Then, the close-formapproximate expressions for uplink achievable rate of mixed-ADC architectures are derived in Section III. The power-scaling laws for both perfect and imperfect CSI cases arealso derived in Section III. In Section IV, we study theenergy efficiency under a practical power consumption model.Moreover, numerical evaluations are provided in Section IV toillustrate the achievable rate and energy efficiency performanceof the mixed-ADC architecture with respect to various systemparameters. Finally, conclusions are drawn in Section V.

D. Notation

In this paper, we use x and X in bold typeface to representvectors and matrices, respectively, while scalars are presentedin normal typeface, such as x. We use XT and XH torepresent the transpose and conjugate transpose of a matrixX, respectively. IN stands for an N ×N identity matrix, and∥X∥F denotes the Frobenius norm of a matrix X. Moreover,E· is the expectation operator, and x ∼ CN (m, σ2I)denotes that x is a circularly symmetric complex Gaussianstochastic vector with mean matrix m and covariance matrixσ2I.



3

Re(.)

Im(.)

Hybrid

LO buffer

Mixer

Mixer

AGC

AGC

Re(.)

Im(.)

Hybrid

LO buffer

Mixer

Mixer

AGC

AGC

Baseband

Processor

High-res. ADC

... ...

...

0M

...

M

LNAHi h ADCHi h ADC

High-res. ADC

High-res. ADC

1M

LNAHi h ADCHi h ADC

High-res. ADC

Re(.)

Im(.) Low-res. ADCLNA

Hybrid

LO buffer

Mixer

Mixer

AGC

AGC Lo res ADCLow res ADC

Low-res. ADC

M

Low-res. ADCLNA

Low res ADCLow res ADC

Low-res. ADC

...

...

...

...

...

...

...

...

Re(.)

Im(.)

Hybrid

LO buffer

Mixer

Mixer

AGC

AGC

Fig. 1. System model of mixed-ADC massive MIMO receivers with M0

pairs of high-resolution ADCs and M1 pairs of low-resolution ADCs. Thenumber of receive antennas is M , and M = M0 +M1.

II. SYSTEM MODEL

In this paper, we consider a uplink single-cell massiveMIMO system with M antennas at the BS and N (N ≪ M)single-antenna users [1]–[3]. Since the hardware cost andenergy consumption scale linearly with the number of BSantennas, a mixed-ADC architecture as illustrated in Fig. 1 isemployed at the BS instead of costly high-resolution ADCs.Note that the transmit antenna of each user is connected withhigh-resolution digital-to-analog converters (DACs). In themixed-ADC architecture, M0 pairs of high-resolution ADCs(e.g., 10-12 bits) are connected to M0 BS antennas, whileall other M1 pairs of low-resolution ADCs (e.g., 1-3 bits)are connected to the remained M1 BS antennas. Note thatM1 = M − M0, and we define κ

∆= M0/M (0 ≤ κ ≤ 1) as

the proportion of the high-resolution ADCs in the mixed-ADCarchitecture.

As illustrated in Fig. 1, the power consumption of thereceiver is induced by the RF chain and the baseband pro-cessor. The local oscilator (LO), which is used with a mixerto change the frequency of a signal, is shared by all RF chains.Moreover, each RF chain is composed of a low-noise amplifier(LNA), a π/2 hybrid and the LO buffer. The in-phase andquadrature circuit consist of a mixer including a quadrature-hybrid coupler, an ADC, and an automatic gain control (AGC),respectively, Note that the AGC is used to amplify the receivedsignal to use the full dynamic range of the ADC. The use ofone-bit ADCs can simplify the RF chain, e.g., an AGC is notnecessary because only the sign of the input signal is output.

Let us consider the channel between each transmit-receiveantenna pair as a block-fading channel, i.e., a channel thatstays unchanged for several channel uses, and changes in-dependently from block to block [27]. In addition, G is theM × N channel matrix between the M -antenna BS and theN single-antenna users, which can be modeled as [22]

G = HD1/2, (1)

where the diagonal matrix D ∈ CN×N denotes the large-scalechannel fading (geometric attenuation and log-normal shadowfading) with the diagonal elements βn’s given by [D]nn =βn, (n = 1, · · · , N) and H ∈ CM×N presents the small-scalefading channel matrix. In contrast to [21], we consider Ricianfading channels, which includes a deterministic component H

corresponding to the LoS signal and a Rayleigh-distributionrandom component Hω accounting for the scattered signalsas [9]

H = H

√Ω(Ω+ IN )

−1+Hω

√(Ω+ IN )

−1, (2)

where Hω ∼ CN (0, IN ), and H with an arbitrary rank canbe expressed as [22][

H]mn

= exp (−j (m− 1) kd sin θn) , (3)

where θn denotes the arrival of angle (AoA) of the nth user,k = 2πd/λ with λ being the wavelength and d being theinter-antenna space. In addition, the elements of the diagonalmatrix Ω is the Rician K-factor Kn, which denotes the ratioof the power of the deterministic component to the power ofthe scattered components.

We define G0 as the M0 ×N channel matrix from the Nusers to the M0 BS antennas connected with high-resolutionADCs, and G1 as the M1 × N channel matrix from the Nusers to the M1 BS antennas connected with low-resolutionADCs. Therefore, we have

G =

[G0

G1

]. (4)

Let pu be the transmit power of each user and x ∈ CN×1 bethe transmit vector for all N users. The received signals at the2M0 high-resolution ADCs can be written as

y0 =√puG0x+ n0, (5)

where pu is the transmit power of each user, x ∈ CN×1

is the transmitted signal vector for all N users, and n0 ∼CN (0, IM0) denotes the additive white Gaussian noise(AWGN) matrix with independent and identically distributed(i.i.d.) components following the distribution CN (0, 1). Wefurther follow the general assumption that the transmittedsignal vector x is Gaussian distributed, the quantization noiseis the worst case of Gaussian distributed, and the quantizationerror of low-resolution ADCs can be well approximated asa linear gain with the additive quantization noise model(AQNM) [29]. Note that the AQNM model is accurate enoughat low and medium SNRs, which has been widely used inquantized MIMO systems [9], [28]–[31]. Thus, the quantizedreceived signals at the output of 2M1 low-resolution ADCscan be expressed as

y1 = Q (y1) ≈ αy1 + nq

=√puαG1x+ αn1 + nq, (6)

where y1 =√puG1 + n1 denotes the uplink received signal

vector at the 2M1 low-resolution ADCs, Q (·) is the scalarquantization function which applies component-wise and sep-arately to the real and imaginary parts, nq denotes the additiveGaussian quantization noise vector which is uncorrelated withy1, and α = 1− ρ is a linear gain with [30, Eq. (13)]

ρ =E∥y1 − y1∥

2

E∥y1∥

2 (7)



4

TABLE IDISTORTION FACTORS FOR DIFFERENT QUANTIZATION BITS [32]

b 1 2 3 4 5

ρ 0.3634 0.1175 0.03454 0.009497 0.002499

denoting the distortion factor of the low-resolution ADC. Theexact values of ρ have been given in Table I with respect todifferent resolution b’s [32]. For large quantization bits (e.g.,b > 5), the distortion factor ρ can be approximated as [32]

ρ ≈ π√3

22−2b. (8)

From (6) and (7), the covariance matrix of nq is given by

Rnq = αρdiag(puG1G

H1 + IM1

). (9)

By considering (5) and (6), the overall received signal at theBS can be expressed as

y =

[y0

y1

]≈[ √

puG0x+ n0√puαG1x+ αn1 + nq

]. (10)

III. ACHIEVABLE RATE

In this section, we derive approximate closed-form expres-sions for the uplink achievable rate of mixed-ADC massiveMIMO systems. Both cases of perfect and imperfect CSI atthe BS receiver are considered. The MRC receiver is assumedto be employed at the BS, as such receiver is simple and nearoptimal when the number of BS antennas becomes large [27].

A. Perfect CSI

We first consider the case of perfect CSI at the BS. By using(10), the detected signal vector after MRC is given by

r =GHy =

[G0

G1

]H [ √puG0x+ n0√

puαG1x+ αn1 + nq

],

which can be further expressed as

r =√pu

(GH

0 G0 + αGH1 G1

)x+(GH

0 n0+αGH1 n1

)+GH

1 nq.

(11)

Let gn0 and gn1 be the nth column of G0 and G1, respec-tively. Then, the nth element of r in (11) can be written as

rn =√pu(gHn0gn0 + αgH

n1gn1

)xn︸︷︷︸

desired signal

+√pu

N∑i=n

(gHn0gi0 + αgH

n1gi1

)xi︸︷︷︸

interuser interference

+(gHn0n0 + αgH

n1n1

)︸︷︷︸AWGN

+ gHn1nq︸︷︷︸

quantization noise

, (12)

where xn is the nth element of the signal vector x. For a fixedchannel realization G, the last three terms in (12) can be seenas an interference-plus-noise random variable. By assuming

the interference-plus-noise follows Gaussian distribution andis independent of x [22], [27], we can obtain a lower boundof the achievable rate of the nth user as

RMRCP,n = E

log2

(1 +

pu∣∣gH

n0gn0 + αgHn1gn1

∣∣2Ψ1

), (13)

where

Ψ1 = pu

N∑i=n

∣∣gHn0gi0 + αgH

n1gi1

∣∣2 + ∣∣gHn0n0 + αgH

n1n1

∣∣2+ αρgH

n1diag(puG1G

H1 + IM1

)gn1

= pu

N∑i=n

∣∣gHn0gi0 + αgH

n1gi1

∣∣2 + ∣∣gHn0n0

∣∣2 + α∣∣gH

n1n1

∣∣2+ αρpug

Hn1diag

(G1G

H1

)gn1, (14)

where the covariance matrix of nq in (9) has been used.For the case of perfect CSI at the BS, the approximate

achievable rate is derived in following Lemma 1.

Lemma 1. For mixed-ADC massive MIMO systems usingMRC receiver with perfect CSI over Rician fading channels,the approximate achievable rate of the nth user is given by(15) at the end of next page, where

∆j∆=

KnKiϕ2ni,j +Mj (Kn +Ki + 1)

Ki + 1j = 0, 1, (16)

ϕni,j∆=

sin (Mjkd (sin θn − sin θi)/2)

sin (kd (sin θn − sin θi)/2)j = 0, 1, (17)

∆2∆= M1

βn

(K2

n+4Kn + 2)+(Kn+1)

2N∑i=n

βi

. (18)

Proof: When M grows large, we employ [22, Lemma 1]and approximate (13) as

RMRCP,n ≈ log2

1 +puE

∣∣gHn0gn0 + αgH

n1gn1

∣∣2E Ψ1

. (19)

With the help of [22, Lemma 3], the expectations in (19) canbe derived as

E∥gnj∥2

= βnMj , (20)

E∥gnj∥4

= β2

n

(M2

j +2MjKn +Mj

(Kn + 1)2

), (21)

E∣∣gH

njgij

∣∣2=β2n

(KnKiϕ

2ni,j+Mj (Kn+Ki)+Mj

(Kn+1) (Ki+1)

).

Moreover, considering (14), the last term in the denominatorof (19) is given by [9, Eq. (15)]

EgHn1diag

(G1G

H1

)gn1

= β2

nM1K2

n + 4Kn + 2

(Kn + 1)2

+ βnM1

N∑i=n

βi. (22)



5

Substituting (21) to (22) into (19), the proof can be concludedafter some simplifications.

For the case of perfect CSI at the BS with M → ∞, theimpact of the Rician K-factor Kn, transmit power pu, large-scale fading βn, and the proportion of mixed-resolution ADCsκ on the achievable rate RMRC

P,n can be revealed in Lemma1. It is clear from (15) that the achievable rate increases byusing more BS antennas. We further show the relationshipbetween the achievable rate and key parameters by providingthe following important analysis.

Remark 1. The derived result in Lemma 1 is general. It isinteresting to note that if all users have infinite Rician K-factors, the approximate uplink achievable rate (15) approach-es a constant value as

RMRCP,n → log2

(1

+puβn(M0+αM1)

2

puN∑i=n

βi

(ϕ2ni,0+α2ϕ2

ni,1

)+M0+αM1+αρpuM1

N∑i=1

βi

),

(23)

which reveals that there is an achievable rate limit in strongLoS scenarios. When α = 1, (23) reduces to the specialcase of unquantized massive MIMO systems [22, Eq. (44)].In addition, (15) includes the achievable rate of Rayleighfading channels as a special case. More specifically, withKn = Ki = 0, (15) can be reduced to

RMRCP,n → log2

1 +M(α+ ρκ)βn

1pu

+N∑

i=1,i=n

βi +2αρ(1−κ)

α+ρκ βn

,

(24)

which is consistent with [21, Eq. (9)].

Remark 2. For the power-scaling law, let us define pu =Eu/M with a fixed Eu and a large M , then the limit of (15)converges to

RMRCP,n → log2 (1 + Euβn (ρκ+ α)) , as M → ∞. (25)

It is clear from (25) that the Rician K-factor is irrelevant tothe exact limit of the uplink rate of mixed-ADC massive MIMOsystems with MRC receivers due to the channel hardeningeffect [33]. In contrast to ideal ADCs, the proportion ofthe high-resolution ADCs κ and the distortion factor of thelow-resolution ADC ρ have effects on the limit rate whenscaling down the transmit power proportionally to 1/M . Morespecifically, the achievable rate can be improved by increasingκ. Adopting a simple transformation, ρκ+α = (1− κ)α+κ,

we can clearly see that the achievable rate is a monotonicincreasing function of α. This means that we can increase theachievable rate by using higher quantization bits in the 2M1

low-resolution ADCs.

B. Imperfect CSI

In practical massive MIMO systems, it is generally difficultto obtain accurate CSI at the BS. Therefore, for the mostpractical and general case of imperfect CSI, we considera transmission within the coherence interval T and use τsymbols for pilots. The CSI for each antenna can be obtainedby using the high-resolution ADCs in a round-robin manner,which has been clearly explained in [18]. The power of pilotsymbols is pp

∆= τpu, while the minimum mean-squared error

(MMSE) estimate of G is given by G. Let Ξ = G−G be thechannel estimation error matrix, which is independent of Gdue to the properties of MMSE estimation [27]. The elementsof Ξ has a variance of σ2

n∆= βn

(1+ppβn)(Kn+1) [22, Eq. (21)].Following a similar analysis in [27], the achievable rate of thenth user under imperfect CSI is given by

RMRCIP,n = E

log2

1 +pu

∣∣∣gHn0gn0 + αgH

n1gn1

∣∣∣2Ψ2

,

(26)where

Ψ2 = pu

N∑i=1,i=n

∣∣∣gHn0gi0 + αgH

n1gi1

∣∣∣2 + ∣∣∣gHn0n0

∣∣∣2 + α∣∣∣gH

n1n1

∣∣∣2+ pu

(∥gn0∥

2+ α2∥gn1∥

2) N∑

i=1

σ2i

+ αρpugHn1diag

((G1 −Ξ1

)(G1 −Ξ1

)H)gn1. (27)

Lemma 2. For mixed-ADC massive MIMO systems usingMRC with imperfect CSI over Rician fading channels, theapproximate achievable rate of the nth user is given by (28)at the end of this page, where

ηn∆=

ppβn

1 + ppβn, (29)

∆3∆=

βi

Ki + 1KnKi

(ϕ2ni,0 + α2ϕ2

ni,1

)+

βi

(M0 + α2M1

)Ki + 1

(Kiηn +Knηi + ηnηi) , (30)

∆4∆= βn

(K2

n + 4Knηn + 2η2n)

+ (Kn + 1) (Kn + ηn)N∑i=n

βi (Ki + ηi)

Ki + 1. (31)

RMRCP,n ≈ log2

(1+

puβn

[(2Kn+1)

(M0 + α2M1

)+(Kn+1)

2(M0+αM1)

2]

pu (Kn+1)N∑i=n

βi (∆0+α2∆1)+(Kn+1)2(M0+αM1)+αρpu∆2

), (15)



6

Proof: When the number of BS antennas M growswithout bound, we employ [22, Lemma 1] to approximate(26) as

RMRCIP,n ≈ log2

1 +

puE∣∣∣gH

n0gn0 + αgHn1gn1

∣∣∣2E Ψ2

. (32)

Utilizing [22, Lemma 5], the expectations in (32) can be foundas

E∥gnj∥2

= βn

(MjKn

Kn + 1+

MjηnKn + 1

)(33)

E∥gnj∥4

=

β2n

(Kn + 1)2

[M2

j K2n +

(M2

j +Mj

)η2n

+(2MjKn + 2M2

j Kn

)ηn

](34)

E∣∣gH

nj gij

∣∣2 =βnβi

(Kn + 1) (Ki + 1)

[KnKiϕ

2ni,j

+MjKiηn +MjKnηi +Mjηnηi

]. (35)

Furthermore, with the help of the known variance and meanof the elements of Ξ, and [9, Eq. (22)], we can easily derivethe expectation of the last term in the denominator of (26) as

EgHn1diag

((G1 −Ξ1

)(G1 −Ξ1

)H)gn1

= E

gHn1diag

(G1G1

H)gn1

+ E

gHn1diag

(Ξ1Ξ1

H)gn1

=

M1β2n

(Kn + 1)2

(K2

n + 4Knηn + 2η2n)

+M1βn (Kn + ηn)

Kn + 1

N∑i=1,i=n

βi (Ki + ηi)

Ki + 1

+M1βn (Kn + ηn)

Kn + 1

N∑i=1

σ2i . (36)

Substituting (33) to (36) into (26), the proof can be concludedafter some simplifications.

Note that Lemma 2 presents a closed-form approximationfor the achievable rate of mixed-ADC massive MIMO systemswith imperfect CSI over Rician fading channels. The derivedapproximate rate expressions are more and more accurate asthe number of antennas increases and the Rician K-factordecreases. This finding coincides with the one presented in[22, Figs. 2-3]. It is clear that the channel estimation errorhas a baneful effect on the achievable rate. We now performfurther analysis based on the uplink rate approximation (28).

Remark 3. For unquantized massive MIMO systems with

ideal ADCs (α = 1) over Rician fading channels, (28) canreduce to [22, Eq. (82)]. For the special case of Rayleighfading channels, (28) reduces to (37) at the end of nextpage, where σ2

i = βn

1+ppβn, ∆3 = βiηi

(M0 + α2M1

), and

∆4 = βnηn +N∑i=1

βiηi. To the best of our knowledge, (37) is

new and has not been derived before.

Remark 4. With pu = Eu/Mγ and M → ∞, the limit of

(28) converges to

RMRCIP,n → log2

(1 + (ρκ+ α)

Euβn (MγKn + τEuβn)

M2γ−1 (Kn + 1)

),

as M → ∞. (38)

It is worth pointing out that the power scaling law withimperfect CSI depends on the value of nth user’s Rician K-factor Kn. For Rayleigh fading channels (Kn = 0), the usertransmit power pu can be at most cut down by a factor of1/

√M . If there is a LoS component (κ > 0), the transmit

power of each user can be scaled down proportionally to 1/M .For the special case of low-resolution ADC architectures

(κ = 0), (38) reduces to

RMRCIP,n → log2

(1 +

αEuβn (MγKn + τEuβn)

M2γ−1 (Kn + 1)

),

as M → ∞. (39)

which is consistent with [9, Eq. (23)]. For the unquantizedmassive MIMO systems (κ = 1, α = 1), (38) converges to aconstant value as

RMRCIP,n → log2

(1 +

Euβn (MγKn + τEuβn)

M2γ−1 (Kn + 1)

),

as M → ∞, (40)

which is the exact achievable rate of unquantized massiveMIMO systems as derived in [22].

Remark 5. In contrast to the case of perfect CSI, RMRCIP,n is

affected by the Rician K-factor Kn. When γ = 1, (38) reducesto a constant value as

RMRCIP,n → log2

(1 +

(ρκ+ α)EuβnKn

Kn + 1

), as M → ∞.

(41)Note that (41) converges to (25) for very strong LoS scenarios.i.e., Kn → ∞, where the channel estimation becomes far morerobust. This is because items in the fading matrix that wererandom before becomes deterministic now. Also, similar to theperfect CSI case (25), (41) clearly indicates that as either thenumber of high-resolution ADCs (κ) or the quantization bit oflow-resolution ADCs (α) gets larger, the achievable rate canbe improved monotonously.

RMRCIP,n ≈ log2

1 +puβn

[(M0 + αM1)

2(Kn + ηn)

2+(M0 + α2M1

) (η2n + 2Knηn

)](M0 + αM1) (Kn + ηn) (Kn + 1)

(1 + pu

N∑i=1

σ2i

)+ pu (Kn + 1)

N∑i=n

∆3 + αρpuM1∆4

, (28)



7

-10 -5 0 5 10 15 20 25 30

User Transmit Power (dB)

0

10

20

30

40

50

60S

um A

chie

vabl

e R

ate

(bits

/s/H

z)Simulated (M

0=200,M

1=0)

Analytical (M0=200,M

1=0)

Simulated (M0=100,M

1=100)


1=100)

Simulated (M0=0,M

1=200)

Analytical (M0=0,M

1=200)

Simulated (M0=128,M

1=0)


1=0)

Fig. 2. Sum achievable rate of mixed-ADC massive MIMO systems overRician fading channels against the user transmit power for K = 10 dB,N = 10 and b = 1.

IV. NUMERICAL RESULTS

In this section, we provide simulated and analytical resultson the uplink sum achievable rate of mixed-ADC massiveMIMO systems, which is defined as R =

∑Nn=1 Rn. The

energy efficiency is also examined in detail. First, we assumethe users are uniformly distributed in a hexagonal cell with aradius of 1000 meters, while the minimum distance betweenthe user to the BS is rmin = 100 meters. Furthermore, thepathloss is expressed as r−v

n with rn denoting the distancebetween the nth user to the BS and v = 3.8 be thepathloss exponent, respectively. The shadowing is modeledas a log-normal random variable sn with standard deviationδs = 8 dB. Therefore, the large-scale fading is given byβn = sn(rn/rmin)

−v . Finally, θn are assumed to be uniformlydistributed within the interval [−π/2, π/2].

A. Achievable rate

In Fig. 2, the simulated and the analytical achievable rate(15) of mixed-ADC massive MIMO systems with perfect CSIare plotted against the user transmit power pu. Herein, weconsider the following four cases: 1)M0 = 200, M1 = 0;2)M0 = 100, M1 = 100; 3)M0 = 0, M1 = 200; 4)M0 =128, M1 = 0. Fig. 2 shows that the analytical and simulatedcurves are very tight in all considered cases, which confirmsthe correctness of our derived results. Moreover, the sumachievable rates in four cases are similar at low SNR. While aspu increases, the gap among different cases becomes relativelylarge. It is clear that the massive MIMO systems with idealADCs (Case 1) gains superior achievable rate performancecompared to the one with mixed-ADCs (Case 2) and the one

1 2 3 4 5 6 7 8 9 10

ADC Quantization Bits (b)

15

16

17

18

19

20

21

Sum

Ach

ieva

ble

Rat

e (b

its/s

/Hz)

Simulated (M0=50,M

1=150)

Analytical (M0=50,M

1=150)

Simulated (M0=10,M

1=190)

Analytical (M0=10,M

1=190)

High-resolation ADC

K = 10

K = 0

Fig. 3. Sum achievable rate of mixed-ADC massive MIMO systems overRician fading channels against the ADC quantization bits for N = 10, andpu = 10 dB.

with low-resolution ADCs (Case 3). With similar hardwarecost as Case 2, the achievable rate of Case 4 is lower due toa smaller number of BS antennas are used.

Fig. 3 presents the simulated and approximate sum achiev-able rate of mixed-ADC massive MIMO systems for variousnumbers of ADC quantization bits. Without loss of generality,we assume that all users have the same Rician K-factor asKn = K. The simulation results notably coincide with thederived results for all ADC quantization bits. We also findfrom Fig. 3 that higher sum rate can be achieved by employ-ing more high-resolution ADCs. Furthermore, the achievablerate increases with the number of quantization bits (b), andconverges to a limited achievable rate with high-resolutionADCs. For Rayleigh fading channels (K = 0), the mixed-ADC architecture can achieve the same sum achievable rate byemploying 5 bits, while for Rician fading channels (K = 10),more ADC quantization bits are needed, which is in agreementwith Remark 1. This is true because the quantization noise islarger with more received power in LoS dominating scenarios.

In Fig. 4, we investigate the power scaling law of mixed-ADC massive MIMO systems over Rician fading channelswith perfect CSI. The proportions of the number of high-resolution ADCs in the mixed-ADC architecture are con-sidered as κ = 0, 1/2, and 1, respectively. As predictedin Remark 2, a higher proportion of the number of high-resolution ADCs improves the achievable rate. For fixedvalues of pu = 10 dB, all curves grow without bound byincreasing M ; while for variable values of pu = Eu/M , thecorresponding curves eventually saturate with an increased M .These results validate that we can scale down the transmittedpower of each user as Eu/M for the perfect CSI case over

RMRCIP,n ≈ log2

1 +puβnηn

[(M0 + αM1)

2+(M0 + α2M1

)](M0 + αM1)

(1 + pu

N∑i=1

σ2i

)+ pu

N∑i=n

∆3 + αρpuM1∆4

, (37)



8

101 102 103

Number of BS Antennas (M)

0

10

20

30

40

SimulatedAnalytical

101 102 103


5

10

15

Sum

Ach

ieva

ble

Rat

e (b

its/s

/Hz)

SimulatedAnalytical

κ = 0, 1/2, 1pu = 10 dB

κ = 0, 1/2, 1pu = Eu/M

Fig. 4. Sum achievable rate of mixed-ADC massive MIMO systems overRician fading channels against the number of BS antennas for K = 10dB,N = 10, and b = 1.

-10 -5 0 5 10 15 20Rician K-Factor (dB)

15

16

17

18

19

20

21

Sum

Ach

ieva

ble

Rat

e (b

its/s

/Hz)

SimulatedAsymtopicAnalytical

M0 = 200,M1 = 0

M0 = 0,M1 = 200

M0 = 100,M1 = 100

Fig. 5. Sum achievable rate of mixed-ADC massive MIMO systems overRician fading channels against the Rician K-factor for pu = 10 dB, N = 10,and b = 1.

Rician fading channels.A beneficial sum achievable rate improvement arising with

a higher Rician K-factor is illustrated in Fig. 5. Here, thefollowing three cases considered in Fig. 2 are investigated:1)M0 = 200, M1 = 0; 2)M0 = 100, M1 = 100; 3)M0 =0, M1 = 200. The three constant curves are obtained bythe analytical expression (23). As expected, the sum rateapproach a fixed value as K → ∞. In addition, placing morehigh-resolution ADCs at the BS greatly enhances the overallperformance of the sum achievable rate.

Fig. 6 presents the sum achievable rate of different ADCarchitectures with both perfect and imperfect CSI over Ricianfading channels. As can be seen, the sum achievable rategrows obviously without bound as the user transmit powerpu increases for both perfect and imperfect CSI. An insightfulobservation is that the sum achievable rates of all cases aresimilar at low SNR. However, the gaps become large whenthe SNR increases.

-10 -5 0 5 10 15 20

User Transmit Power (dB)

0

5

10

15

20

25

30

35

Sum

Ach

ieva

ble

Rat

e (b

its/s

/Hz)

Perfect CSI, SimulatedPerfect CSI, AnalyticalImperfect CSI, SimulatedImperfect CSI, Analytical

κ = 1, 1/2, 0

Fig. 6. Sum achievable rate of mixed-ADC massive MIMO systems overRician fading channels against the user transmit power for K = 0dB, M =200, N = 10, and b = 1.

B. Energy Efficiency

Until now, we have investigated the achievable rate ofmixed-ADC massive MIMO systems over Rician fading chan-nels. As expected, the sum rate of unquantized massive MIMOsystems outperforms the one with mixed-ADCs, at the costof higher hardware cost and power consumption. Therefore,there should be a fundamental trade-off between the energy ef-ficiency and power consumption for practical massive MIMOsystems. Due to this reason, the energy efficiency of mixed-ADC massive MIMO systems over Rician fading channels isstudied in this section.

Let us first consider a generic power consumption modelof the mixed-ADC architecture. The energy efficiency ηEE isdefined as [31]

ηEE =RW

Ptotalbit / Joule, (42)

where R denotes the sum rate, W denotes the transmissionbandwidth assumed to be 1 GHz and Ptotal is the totalconsumed power, which can be expressed as [5]

Ptotal = PLO +M (PLNA + PH + 2PM)

+ 2M0

(PAGC + PH

ADC

)+ 2M1

(cPAGC + PL

ADC

)+ PBB,

(43)

where PLO, PLNA, PH, PM, PAGC, PHADC, PL

ADC, PBB denotethe power consumption in the LO, LNA, π/2 hybrid andLO buffer, Mixer, AGC, high-resolution ADCs, low-resolutionADCs, and baseband processor, respectively. In addition, c isthe flag related to the quantization bit of low-resolution ADCsand is given by

c =

0, b = 1,1, b > 1.

(44)

Furthermore, the power consumed in the ADCs can be ex-pressed in terms of the number of quantization bits as

PADC = FOMW · fs · 2b, (45)

where fs is the Nyquist sampling rate, b is the number of



9

1 2 3 4 5 6 7 8 9 10 11

ADC Quantization Bits (b)

10

15

20

25

30

35

40

45

50

55

60E

nerg

y E

ffici

ency

(M

bit/J

)

M0=5, M

1=123

M0=10, M

1=118

M0=0, M

1=128

M0=128, M

1=0

Fig. 7. Energy efficiency of mixed-ADC massive MIMO systems over Ricianfading channels against different ADC quantization bits for K = 10 dB,N = 10, and pu = −10 dB.

quantization bits, and FOMW is Walden’s figure-of-merit forevaluating the power efficiency with ADC’s resolution andspeed [34]. In the simulation, the consumed power in theRF components are assumed to be PLO = 22.5mW [35],PLNA = 5.4mW [36], PH = 3mW [37], PAGC = 2mW [36],PM = 0.3mW [38], PBB = 200mW [5]. With state-of-the-arttechnology, the power consumption value of FOMW at 1 GHzbandwidth is FOMW = 5 ∼ 15 fJ/conversion-step [39].

With the power consumption model (43), the energy ef-ficiency of massive MIMO systems with different ADC ar-chitectures and perfect CSI is illustrated in Figs. 7-10. Wefind that the energy efficiency of the mixed-ADC architecturecan be significantly improved compared with ideal high-resolution ADCs. Moreover, the receiver adopting only low-resolution ADCs has the highest energy efficiency among allarchitectures. This implies that the energy efficiency decreaseswith the proportion of the number of high-resolution ADCs(κ) in the mixed-ADC structure. Although the low-resolutionADC architecture can achieve better energy efficiency than themixed-ADC architecture, the spectral efficiency of the low-resolution ADC architecture is much lower than that of themixed-ADC architecture. Moreover, the channel estimation inthe mixed-ADC architecture are more tractable than that inthe low-resolution ADC architecture due to the use of partialhigh-resolution ADCs. With all results, it is clear that we canachieve a better achievable rate meanwhile obtain a relativelyhigh energy efficiency by using the mixed-ADC architecture.

In Fig. 8, we analyze the effect of the number of receiveantennas on the energy efficiency. Due to the fact that eachantenna is connected with one RF chain, it may be wastefulto use more antennas at the BS. The energy efficiency oflow-resolution ADCs is largest among others. Indeed, if theBS has only around 30 antennas, the mixed-ADC architectureachieves its optimal energy efficiency for the selecting systemparameters.

Next, we present some numerical results in Figs. 10-12 to il-lustrate the trade-off between energy efficiency and achievable

101

102

103

0

50

100

150

200

250

300

350


Ene

rgy

Effi

cien

cy (

Mbi

t/J)

κ = 1

κ = 1/2

κ = 0

Fig. 8. Energy efficiency of mixed-ADC massive MIMO systems over Ricianfading channels against different numbers of antennas for K = 10 dB, N =10, and pu = 0 dB.

11.5 12 12.5 13 13.5 14 14.5 15 15.5

Sum Achievable Rate (bits/s/Hz)

0

5

10

15

20

25

30

35

Pow

er C

onsu

mpt

ion

at th

e R

ecei

ver

(Wat

t)

M0=32, M

1=96

M0=64, M

1=64

M0=0, M

1=128

Increasing ADC's resolution

Fig. 9. Trade-off between power consumption and achievable rate of mixed-ADC massive MIMO systems over Rician fading channels for K = 10 dB,N = 10, and pu = 10 dB.

rate of the mixed-ADC architecture for different portions ofhigh-resolution ADCs (κ), Rician K-factor, and quantizationbits of low-resolution ADCs (b). In addition, for each figure,we plot curves representing the trade-off performance as weincrease the number of ADC quantization bits from 1 to 12,at the increment of 1. Note that the largest value of theachievable rate is given at the rightmost points, while thehighest points in the figure correspond to the largest valueof the energy efficiency. Therefore, it is better to reach apoint to the top-right corner for the corresponding architecture.Moreover, if the area contained at the left of the curve, whichcan be interpreted as an “operating region”, is bigger, thecorresponding architecture is more versatile as a function ofthe ADC quantization bit.

The first insight obtained from Fig. 9 is that the mixed-ADC architecture requires more power than the one with purelow-resolution ADCs, but with a relatively big increase in



10

11 12 13 14 15 16 17


0

1

2

3

4

5

6

7

8

9

10

11E

nerg

y E

ffici

ency

(G

bit/J

)

M0=5, M

1=123

M0=10, M

1=118

M0=0, M

1=128

K=10

K=0

Fig. 10. Trade-off between energy efficiency and achievable rate of mixed-ADC massive MIMO systems over Rician fading channels for N = 10 andpu = 10 dB.

8 9 10 11 12 13 14 15


0

1

2

3

4

5

6

7

8

9

10

Ene

rgy

Effi

cien

cy (

Gbi

t/J)

M0=5, M

1=123

M0=10, M

1=118

M0=0, M

1=128

Imperfect CSI

Perfect CSI

Fig. 11. Trade-off between energy efficiency and achievable rate of mixed-ADC massive MIMO systems over Rician fading channels for imperfect andperfect CSI, K = 10 dB, N = 10 and pu = 0 dB.

the achievable rate for small quantization bits. In addition,the gap of power consumption decreases with the increas-ing ADC’s resolution. For the mixed-ADC architecture, theachievable rate significantly increases when the quantizationbit increases from 1 to 4, with a negligible increase in thereceiver power consumption. However, the power consumptionincreases significantly when the quantization bit going from 4to 12 bits. This means that the mixed-ADC architecture canachieve a better trade-off between the power consumption andachievable rate by using 4 bits.

Fig. 10 shows the trade-off between energy efficiency andachievable rate of mixed-ADC architectures for different val-ues of the Rician K-factor. We also plot the curves of the purelow-resolution ADC architecture as the evaluation baselines.Note that the signal processing in the pure low-resolution ADCarchitecture is very complex and time-consuming comparedwith the mixed-ADC architecture. It is clear from Fig. 10

10.5 11 11.5 12 12.5 13 13.5 14 14.5 15


0

1

2

3

4

5

6

7

8

9

10

Ene

rgy

Effi

cien

cy (

Gbi

t/J)

M0=5, M

1=123

M0=10, M

1=118

M0=0, M

1=128

imperfect CSI perfect CSI

Fig. 12. Trade-off between energy efficiency and achievable rate of mixed-ADC massive MIMO systems over Rician fading channels for imperfect andperfect CSI, K = 10 dB, N = 10 and pu = 10 dB.

that the optimal ADC quantization bit is influenced by boththe portion of high-resolution ADCs and the Rician K-factor.For the mixed-ADC architecture, the energy efficiency onlyincreases up to a certain number of quantization bits, while itdecreases at higher ADC quantization bits. This is due to thefact that the achievable rate is a sub-linear increasing functionof the quantization bits, whereas the power consumption ofADCs increases exponentially with b. As expected, the mixed-ADC architecture can achieve larger operating region whenoperating over Rician fading channels with stronger LoScomponent (large values of Kn) due to higher achievable rateshown in Fig. 5.

The effect of imperfect CSI and user transmit power onthe trade-off between energy efficiency and achievable rateof mixed-ADC massive MIMO systems has been investigatedin Figs. 11 and 12. We observe that the operating region ofimperfect CSI is smaller than the one of perfect CSI. However,this gap is reduced by improving the user transmit power puform 0 dB to 10 dB. This means that more user transmit poweris needed to combat the effect of channel estimation error.

V. CONCLUSIONS

In this paper, the performance of mixed-ADC massiveMIMO systems over Rician fading channels is investigated.We derive novel and closed-form approximate expressions forthe achievable rate for large-antenna limit. The cases of bothperfect and imperfect CSI are incorporated in our analysis.With similar hardware cost, the mixed-ADC architecture canachieve larger sum rate than the ideal-ADC architecture.For mixed-ADC massive MIMO systems over Rician fadingchannels, the user transmit power can be at most cut down by afactor of 1/M . In contrast to the case of perfect CSI, the powerscaling law in the imperfect CSI case is related to the RicianK-factor. For both perfect and imperfect CSI, the achievablerate limit converges to a constant as K → ∞. In addition,the mixed-ADC architecture can have a large operating regionwith few high-resolution ADCs. More energy efficiency can



11

be achieved when operating over stronger LoS scenarios. Itis worth mentioning that the derived results are general andcan include many previously reported ones as special cases.Finally, we conclude that practical massive MIMO can achievea considerable performance with small power consumption byadopting the mixed-ADC architecture for 5G.

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Jiayi Zhang (S’08–M’14) received the B.Sc. andPh.D. degree of Communication Engineering fromBeijing Jiaotong University, China in 2007 and 2014,respectively. Since 2016, he has been a Professorwith School of Electronic and Information Engineer-ing, Beijing Jiaotong University, China. From 2014to 2016, he was a Postdoctoral Research Associatewith the Department of Electronic Engineering, Ts-inghua University, China. From 2014 to 2015, hewas also a Humboldt Research Fellow in Institutefor Digital Communications, University of Erlangen-

Nuermberg, Germany. From 2012 to 2013, he was a visiting Ph.D. student atthe Wireless Group, University of Southampton, United Kingdom. His currentresearch interests include Massive MIMO, unmanned aerial vehicle systemsand performance analysis of generalized fading channels.

He was recognized as an exemplary reviewer of the IEEE COMMUNICA-TIONS LETTERS in 2015 and 2016. He was also recognized as an exemplaryreviewer of the IEEE TRANSACTIONS ON COMMUNICATIONS in 2017.He serves as an Associate Editor for IEEE COMMUNICATIONS LETTERSand IEEE ACCESS.

Linglong Dai (M’11–SM’14) received the B.S. de-gree from Zhejiang University in 2003, the M.S.degree (with the highest honor) from the China A-cademy of Telecommunications Technology (CATT)in 2006, and the Ph.D. degree (with the highesthonor) from Tsinghua University, Beijing, China, in2011. From 2011 to 2013, he was a PostdoctoralResearch Fellow with the Department of Electron-ic Engineering, Tsinghua University, where he hasbeen an Assistant Professor since July 2013 and thenan Associate Professor since June 2016. His current

research interests include massive MIMO, millimeter-wave communications,multiple access, and sparse signal processing. He has published over 50 IEEEjournal papers and over 30 IEEE conference papers. He also holds 13 grantedpatents. He co-authored the book “mmWave Massive MIMO: A Paradigm for5G” (Academic Press, Elsevier, 2016). Dr. Dai has received the OutstandingPh.D. Graduate of Tsinghua University Award in 2011, the Excellent DoctoralDissertation of Beijing Award in 2012, the IEEE ICC Best Paper Awardin 2013, the National Excellent Doctoral Dissertation Nomination Award in2013, the IEEE ICC Best Paper Award in 2014, the URSI Young ScientistAward in 2014, the IEEE Transactions on Broadcasting Best Paper Awardin 2015, the IEEE RADIO Young Scientist Award in 2015, the URSI AP-RASC 2016 Young Scientist Award in 2016, the WCSP Best Paper Awardin 2016, the Exemplary Reviewer of IEEE Communications Letters in 2016,and the Second Prize of Science and Technology Award of China Instituteof Communications in 2016. He currently serves as an Editor of the IEEETransactions on Communications, an Editor of the IEEE Transactions onVehicular Technology, an Editor of the IEEE Communications Letters, aGuest Editor of the IEEE Journal on Selected Areas in Communications(the Special Issue on Millimeter Wave Communications for Future MobileNetworks), the Leading Guest Editor of the IEEE Wireless Communications(the Special Issue on Non-Orthogonal Multiple Access for 5G), and co-chairof the IEEE Special Interest Group (SIG) on Signal Processing Techniquesin 5G Communication Systems. He is an IEEE Senior Member. Particularly,he is dedicated to reproducible research and has made a large amount ofsimulation code publicly available (refer to his homepage for more details:http://oa.ee.tsinghua.edu.cn/dailinglong/).

Ziyan He is currently working towards the B.Eng.degree in Electronic Engineering from TsinghuaUniversity, Beijing, China. His research interests in-clude massive MIMO systems and signal processingfor wireless communications.

Shi Jin (S’06–M’07) received the B.S. degree incommunications engineering from Guilin Universityof Electronic Technology, Guilin, China, in 1996, theM.S. degree from Nanjing University of Posts andTelecommunications, Nanjing, China, in 2003, andthe Ph.D. degree in communications and informationsystems from the Southeast University, Nanjing, in2007. From June 2007 to October 2009, he was aResearch Fellow with the Adastral Park ResearchCampus, University College London, London, U.K.He is currently with the faculty of the National

Mobile Communications Research Laboratory, Southeast University. Hisresearch interests include space time wireless communications, random matrixtheory, and information theory. He serves as an Associate Editor for theIEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, and IEEECOMMUNICATIONS LETTERS, and IET Communications. Dr. Jin andhis co-authors have been awarded the 2011 IEEE Communications SocietyStephen O. Rice Prize Paper Award in the field of communication theoryand a 2010 Young Author Best Paper Award by the IEEE Signal ProcessingSociety.

Xu Li received the B.Sc. degree from Jilin Uni-versity, China in 1991 and the Ph.D. degree fromNortheastern University, China in 1997. Since 2003,she has been a Professor and Head of WirelessSelf-Organized Communications Group, School ofElectronic and Information Engineering, BeijingJiaotong University, China. She owns more than40 patents. Her research interest includes wirelessself-organized communications, sensor networks andunmanned aerial vehicle systems.

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Performance Analysis of Mixed-ADC Massive MIMO Systems ...oa.ee.tsinghua.edu.cn/dailinglong/publications/paper...feedback signaling. Therefore, the issue of imperfect channel state