This letter considers the architecture of distributed antenna system, which
is made up of a massive number of single-antenna remote radio heads (RRHs),
some with full-resolution but others with low-resolution analog-to-digital
converter (ADC) receivers. This architecture is greatly motivated by its high
energy efficiency and low-cost implementation. We derive the worst-case uplink
spectral efficiency (SE) of the system assuming a frequency-flat channel and
maximum-ratio combining (MRC), and reveal that the SE increases as the number
of quantization bits for the low-resolution ADCs increases, and the SE
converges as the number of RRHs with low-resolution ADCs grows. Our results
furthermore demonstrate that a great improvement can be obtained by adding a
majority of RRHs with low-resolution ADC receivers, if sufficient quantization
precision and an acceptable proportion of high-to-low resolution RRHs are used.Comment: 4 pages, to be published in IEEE Wireless Communications Letter

Jin, Shi

Wen, Chao-Kai

Wong, Kai-Kit

Yuan, Jide

English

arXiv

This letter considers the architecture of a distributed antenna system, which is made up of a massive number of single-antenna remote radio heads (RRHs), some with full-resolution but others with low-resolution analog-to-digital converter (ADC) receivers. This architecture is greatly motivated by its high energy efficiency and low-cost implementation. We derive the worst-case uplink spectral efficiency (SE) of the system assuming a frequency-flat channel and maximum-ratio combining, and reveal that the SE increases as the number of quantization bits for the low-resolution ADCs increases, and the SE converges as the number of RRHs with low-resolution ADCs grows. Our results furthermore demonstrate that a great improvement can be obtained by adding a majority of RRHs with low-resolution ADC receivers, if sufficient quantization precision and an acceptable proportion of high-to-low resolution RRHs are used

Yuan, J

Jin, S

Wen, C-K

Wong, K-K

UCL Discovery

1The Distributed MIMO Scenario: Can Ideal ADCs BeReplaced by Low-resolution ADCs?Jide Yuan, Student Member, IEEE, Shi Jin, Member, IEEE,Chao-Kai Wen, Member, IEEE, and Kai-Kit Wong, Fellow, IEEEAbstract—This letter considers the architecture of distributedantenna system, which is made up of a massive number of single-antenna remote radio heads (RRHs), some with full-resolutionbut others with low-resolution analog-to-digital converter (ADC)receivers. This architecture is greatly motivated by its high energyefficiency and low-cost implementation. We derive the worst-case uplink spectral efficiency (SE) of the system assuming afrequency-flat channel and maximum-ratio combining (MRC),and reveal that the SE increases as the number of quantizationbits for the low-resolution ADCs increases, and the SE convergesas the number of RRHs with low-resolution ADCs grows. Ourresults furthermore demonstrate that a great improvement can beobtained by adding a majority of RRHs with low-resolution ADCreceivers, if sufficient quantization precision and an acceptableproportion of high-to-low resolution RRHs are used.Index Terms—Distributed antenna system, low-resolution ADCreceiver, massive MIMO, spectral efficiency.I. INTRODUCTIONMASSIVE multiple-input multiple-output (MIMO) anten-nas are widely anticipated as one key 5G technology [1,2]. A distributed setup, with antennas spread over a large areaconnecting to a baseband unit (BBU) via a fronthaul network,has considerable advantages in both spectral efficiency (SE)and energy efficiency (EE) due to reduced distances betweenusers and the remote radio heads (RRHs) as well as the richdiversity against shadow fading [3,4]. In [3], it was revealedthat enormous gains can be achieved by distributed massiveMIMO antennas if compared to the centralized counterpart. Arecent work [4] presented the cell-free massive MIMO system,with all RRHs serving all users, outperforming the traditionalcentralized massive MIMO in terms of throughput.Nevertheless, the hardware expenditure and power con-sumption grows with the number of antennas. This hasmotivated the adoption of low-resolution analog-to-digitalconverters (ADCs) in antennas to save cost [5,6]. In [6], theSE for a multi-user massive MIMO with arbitrary quantizationwas studied. The result can be applied into frequency-selectiveMIMO channel, and demonstrated that the antenna with 3-bits quantization can unleash most of the performance gainsthat the setup with all full-resolution ADC has. Mixed-ADCarchitectures have since been proposed, e.g., [7,8], where onlya fraction of the antennas are equipped with full-resolutionADCs, with the rest low-resolution ADCs. In [7], a mixed-ADC framework for massive MIMO uplink was establishedJ. Yuan and S. Jin (corresponding author) are with the National MobileCommunications Research Laboratory, Southeast University, Nanjing 210096,P. R. China (e-mail: {yuanjide, jinshi}@seu.edu.cn).C. Wen is with the Institute of Communications Engineering, National SunYat-sen University, Kaohsiung 804, Taiwan (e-mail: ckwen@ieee.org).K. K. Wong is with the Department of Electronic and ElectricalEngineering, University College London, London WC1E 7JE, UnitedKingdom (e-mail: kai-kit.wong@ucl.ac.uk).This work was supported in part by the National Science Foundation(NSFC) for Distinguished Young Scholars of China with Grant 61625106 andthe National Natural Science Foundation of China under Grant 61531011.BBU poolL-RRH F-RRH Fronthaul networkFig. 1. The diagram of the distributed massive MIMO with mixed-ADCreceivers, where some of the RRHs are equipped with full-resolution ADCsand others with low-resolution ADCs. All RRHs belong to one BBU.by developing a family of detectors via probabilistic Bayesianinference. The results showed that using just a small numberof full-resolution ADCs can achieve a significant gain.In this letter, the focus is on the distributed massive MIMOsetup, where RRHs with mixed ADC receivers are deployed.In particular, the RRHs with full-resolution ADCs (F-RRHs)or low-resolution ADCs (L-RRHs) are randomly distributedin the area. Our aim is to analyze the uplink SE performanceassuming perfect knowledge of channel statistics and the useof a maximal-ratio combining (MRC) receiver. The effects ofthe user transmit SNR and the number of quantization bits ofthe low-resolution ADCs on the achievable performance areexamined using the derived lower bounds of SE. Our resultsdemonstrate that distributed massive MIMO with mixed-ADCreceivers possesses much higher SE than the centralizedcounterpart, and can realize most of the performance gainsat much lower cost than the configuration with all F-RRHs.II. SYSTEM MODELConsider a multi-user distributed massive MIMO uplinkwith K users and M RRHs (see Fig. 1), in which each RRHand user has a single antenna. All of the RRHs in the networkserve all users simultaneously. We assume that only a fractionof RRHs (e.g., Mf) are F-RRHs, while the rest (Ml =M−Mf)are L-RRHs. The locations of RRHs and users are randomlygenerated, and all of the RRHs are connected to a BBU.We model the complex propagation coefficient between themth RRH and the kth user bygmk = hmk√βmk, (1)2where hmk denotes the fast fading coefficient assumed to havezero-mean and unit-variance, and βmk is the large scale fadingwhich can be factored into βmk = zmkd−γmk, where zmk is alog-normal random variable with standard deviation σshad, dmkis the distance between the mth RRH and the kth user, and γ isthe path-loss exponent. We use gf,mk and gl,mk to specify thechannel propagation from F-RRHs and L-RRHs, respectively.In the uplink, the received signals of the Mf F-RRHs canbe packed into a vectoryf =√ρGfx+ ωf, (2)where x is the K × 1 vector, whose kth element is the kthuser symbol, xk, with E[|xk|2] = 1. Also, ωf ∼ CN (0, I) isthe additive white Gaussian noise (AWGN), ρ is the systemSNR, and Gf is the Mf×K channel matrix between the Mf F-RRHs and the K terminals with [Gf]mk = gf,mk. Assuming afrequency-flat channel, the quantization signal of Ml L-RRHswith each a B-bit quantizer can be approximately depicted bythe additive quantization noise model (AQNM) given by [9]y˜l ≈ αyl + ωq = α√ρGlx+ αωl + ωq, (3)where ωl ∼ CN (0, I), ωq is the quantization noise vector thatis uncorrelated with y˜l. For the non-uniform scalar minimummean squared error (MMSE) quantizer of a Gaussian randomvariable, the values of α, obtained by numerical computation,increase with B and are upper bounded by 1 [5]. In addition,Gl is the Ml ×K propagation matrix between the Ml L-RRHsand the K terminals, whose (i, j)th entry is [Gl]mk = gl,mk.Combining (2) and (3), the overall received signals can bemodelled asy =[yTf y˜Tl]T. (4)Adopting an unbiased channel estimator at each RRH whichcan provide the exact mean of the statistic, we haveE[gˆHf,mkgf,mk]= βmk and E[gˆHl,m′kgl,m′k]= βm′k, (5)where gˆf,mk and gˆl,m′k are the estimated channel coefficientsfrom the kth user to the mth F-RRH and the m′th L-RRH,respectively.In this letter, we consider that the MRC receiver is adoptedbecause of its significantly low complexity. From (4), thereceived signal vector after MRC processing is given asr ≈ r˜ =[GˆHf GˆHl]y. (6)From (6), the kth element of r˜ can be expressed asr˜k =√ρ(gˆHf,kgf,k + αgˆHl,kgl,k)xk+√ρ∑i6=k(gˆHf,kgf,i + αgˆHl,kgl,i)xi+(gˆHf,kωf + αgˆHl,kωl)+ gˆHl,kωq, (7)where gf,k, gl,k, gˆf,k and gˆl,k are the kth columns of Gf , Gl,Gˆf and Gˆl, respectively.III. SE ANALYSISIn this section, we derive the achievable SE of the network.Given that the unbiased channel estimators are employed atthe RRHs, the received signal in (7) is rewritten asr˜k = (FSk+LSk)xk + (FUk+LUk)xk+ (FIk + LIk)xi +QNk +Nk, (8)whereFSk =√ρ∑Mfm=1E[gˆHf,mkgf,mk], (9)LSk = α√ρ∑Mlm′=1E[gˆHl,m′kgl,m′k], (10)FIk =√ρK∑i=1,i6=kgˆHf,kgf,i, LIk = α√ρK∑i=1,i6=kgˆHl,kgl,i, (11)FUk =√ρ∑Mfm=1(gˆHf,mkgf,mk − E[gˆHf,mkgf,mk]), (12)LUk = α√ρMl∑m′=1(gˆHl,m′kgl,m′k − E[gˆHl,m′kgl,m′k]), (13)QNk = gˆHl,kωq, Nk = gˆHf,kωf + αgˆHl,kωl, (14)and each represents the desired signals contributed from theF-RRHs (FS) and that from the L-RRHs (LS), the interferencecaused by other users at the F-RRHs (FI) and that at the L-RRHs (LI), the interference due to the channel estimationuncertainty at the F-RRHs (FU) and the L-RRHs (LU), thequantization noise (QN) and the AWGN (N), respectively.In (8), we treat the sum of the second to the fifth terms inthe right hand side as the noise-plus-interference (NPI) power,to which the desired signal is uncorrelated, i.e.,E [(FSk+LSk)×NPIk] = 0. (15)Given that uncorrelated Gaussian noise represents the worstcase, the achievable SE of the kth user for the architecturecan be derived by (16), see top of next page.Theorem 1: The worst-case achievable uplink SE for thekth user in the distributed massive MIMO system with mixed-ADC receivers is lower bounded by (17), see top of next page.Proof: Given that an unbiased channel estimator isemployed at each RRH, we have|FSk|2 = ρ(∑Mfm=1βmk)2, (18)|LSk|2 = α2ρ(∑Mlm′=1βm′k)2, (19)E[|FIk|2]= ρ∑Mfm=1∑Ki 6=k βmkβmi, (20)E[|LIk|2]= α2ρ∑Mlm′=1∑Ki 6=k βm′kβm′i, (21)E[|Nk|2]=∑Mfm=1βmk + α2∑Mlm′=1βm′k, (22)and E [FIk]E [LIk] = 0.Due to the independence among the channel paths to the MfF-RRHs, the channel estimation uncertainty at the F-RRHs,E[|FUk|2], can be derived asE[|FUk|2]= ρMf∑m=1(E[∣∣gˆHf,mkgf,mk∣∣2]− E2 [gˆHf,mkgf,mk])a= ρ∑Mfm=1β2mk, (23)where a is obtained since E[|gˆHf,mkgf,mk|2] = 2β2mk. Similarly,E[|LUk|2]= α2ρ∑Mlm′=1β2m′k. (24)We then calculate the power of the quantization noise termQNk. From [5], we haveE[|QNk|2]= E[∣∣gHl,kRωqgl,k∣∣] , (25)where Rωq=α (1− α) diag(ρGlGˆHl + I) is the3Rk = log21 + |FSk+LSk|2E[|FUk+LUk|2]+ E[|FIk + LIk|2]+ E[|QNk|2]+ E[|Nk|2]. (16)Rk = log21 +(Mf∑m=1βmk)2+2αMf∑m=1Ml∑m′=1βmkβm′k+α2(Ml∑m′=1βm′k)2Mf∑m=1K∑i=1βmkβm′i+(2α−α2)Ml∑m′=1β2m′k+αMl∑m′=1K∑i=1,i 6=kβm′kβm′i+1ρ(Mf∑m=1βmk+αMl∑m′=1βm′k). (17)E[∣∣∣gˆHl,kdiag (ρGlGˆHl + I)gl,k∣∣∣]=∑M1m′=1E[∣∣gˆHl,m′kgl,m′k∣∣]+ ρ∑M1m′=1∑Ki 6=k E[∣∣gˆHl,m′kgl,m′k∣∣]E [∣∣gˆHl,m′igl,m′i∣∣]+ ρ∑M1m′=1E[∣∣gˆHl,m′kgl,m′k∣∣2]=∑M1m′=1βm′k + ρ∑M1m′=1∑Ki 6=k βm′kβm′i + 2ρ∑M1m′=1β2m′k. (26)covariance matrix of ωq. Since the m′th diagonalelement of diag(ρGlGˆHl + I) can be expressed as1+ρ∑Ki=1 |gˆHl,m′igl,m′i|, we can obtain the power quantizationnoise as (26). Substituting (26) into (25), and combining theresults from (18) to (25) obtain the result.Based on Theorem 1, the achievable SE is dependent on thetransmit SNR, the number of quantization bits B, the numbersof F-RRHs and L-RRHs, and the positions of each RRH.The SE obviously increases as the transmit power increases,whereas it has a ceiling due to interference as ρ→∞. Also,with ∂SINRk/∂α > 0 for α ∈ [0, 1], we conclude that theSE is a monotonically increasing function of the resolution ofthe receiver and consistent with the trend for the mixed-ADCarchitecture. To enhance our understanding of achievable SE,we consider the following two extreme cases.Remark 1: The SE for the case that all RRHs are equippedwith low-resolution ADCs, i.e., Mf = 0, givesRMf=0k = log21 + α(∑Mm=1 βmk)2J+ (1− α)∑Mm=1 β2mk, (27)where J =M∑m=1β2mk +M∑m=1K∑i 6=kβmkβmi +1ρM∑m=1βmk. Thispure low-resolution ADC architecture can effectively reducethe power consumption and hardware expenditure but sufferperformance loss. Note that when α→ 1, (27) becomesRMl=0k = log2(1 +(∑Mm=1βmk)2/J), (28)which represents the case that all RRHs are F-RRHs. Thus,(28) is a closed-form expression given when no quantizationnoise is introduced by the L-RRHs. This case was consideredin most existing works on massive MIMO, despite thehigh power consumption and hardware cost. Moveover, theexpression has a similar structure as the result in [4], whichwas obtained assuming that the channel statistic is estimatedvia a MMSE detector. Therefore, the result in (17) can beregarded as the generalized expression of the achievable SEfor distributed MIMO systems with MRC receiver.Remark 2: In the centralized massive MIMO case whereβmk = βm′k = βk for m = 1, . . . ,Mf, m′ = 1, . . . ,Ml, theachievable SE is reduced toRk=log21+M (κ+ α (1− κ))βk1ρ +K∑i=1,i6=kβi +κ+(1−κ)(2α−α2)κ+α(1−κ) βk,(29)where κ , Mf/M . We note that when all the RRHs areequipped with full-resolution ADC receivers, i.e., α = 1,the expression is consistent with the result in [10]. Hence,summarizing the results of (28) and (29), the achievable SEexpression in (17) can be regarded as the generalized result ofthe existing works on massive MIMO with MRC receviers.Uplink throughput per user (Mbits/s)0 5 10 15 20 25 30 35Cumulativedistributionfunction00.20.40.60.81distibuted layout B = 1 bitdistibuted layout B = 3 bitsdistibuted layout B = 8 bitscentralized layout B = 1 bitcentralized layout B = 3 bitscentralized layout B = 8 bitsFig. 2. The cumulative distribution function (CDF) of the uplink throughputper user, with M = 100, K = 20, κ = 0.2 and ρ = 10 dB.IV. NUMERICAL RESULTSIn our simulations, 100 RRHs and 20 users were randomlydistributed in a 1 km2 area. We also set a guard zone of50 meters for each user, i.e., the distance between any RRHand the user is no less than 50 m. The decay exponent, shadow-fading standard deviation, and bandwidth were set to γ = 3.8,σshad = 8 dB, and W = 10MHz, respectively.4We first compare the performance of centralized againstdistributed massive MIMO setups under mixed-ADC receivers.In Fig. 2, the results for centralized MIMO correspond to thosein (29), in which users are randomly distributed as well. Aswe can see, the distributed setup significantly outperforms thecentralized counterpart, e.g., the 95%-likely throughput of thearchitecture with distributed MIMO with 3-bits quantizer isabout 11 Mbits/s, 14 times more than that of the centralizedsetup (about 0.8 Mbits/s). This is mainly because of the spatialdiversity and the enhanced signal strength due to reduceddistance between the RRHs and the users. More remarkably,the results for L-RRHs with 3-bit ADCs are very close tothose for L-RRHs with 8-bit ADCs, indicating that deployingthe L-RRHs with a resolution higher than 3 bits is unnecessary.Uplink throughput per user (Mbits/s)0 5 10 15 20 25 30Cumulativedistributionfunction00.20.40.60.81κ = 1/2, B = 1 bitκ = 1/2, B = 2 bitsκ = 1/3, B = 1 bitκ = 1/3, B = 2 bitsκ = 1/6, B = 1 bitκ = 1/6, B = 2 bitswithout L-RRHsMf = 60 without L-RRHsFig. 3. The CDF of the uplink throughput per user for distributed massiveMIMO with mixed-ADC receivers against with different κ and B. Resultsare shown for Mf = 20 and ρ = 10 dB.Now study the impact of adding L-RRHs on the throughputperformance. Fig. 4 shows the CDF of the uplink throughputper user at 10 dB with 20 F-RRHs in the system. Comparedwith the result of the pure F-RRHs case, adding a certainnumber of L-RRHs can significantly improve the systemthroughput, e.g., the 95%-likely throughput is increased byabout 30%, 100%, and 300% for adding 20, 40, 100 L-RRHs with 2-bit ADCs, respectively. Also, we find that themixed 120 RRHs architecture with 20 F-RRHs outperformsthe pure 60 F-RRHs architecture (denoted by dotted line)about 4 Mbits/s, indicating that distributed massive MIMOwith less full-resolution ADC receivers can achieve superiorperformance if a large number of L-RRHs can be deployed.Finally, we compare the cost of adding RRHs with thatof increasing the resolution bits based on the EE, which isdefined as η=WR/(Pf + Pl) with P(·) =M(·)(c022B + c1),where c0=10−4 Watt and c1=2Watt [5]. W is the bandwidthset to 10 MHz, and R is the sum rate. In Fig. 4, we seta total throughput threshold as 100Mbits/s to guarantee therequirement of users. Adopting the achievable rate in (17),we observe that the proposed architecture can hardly meet thedesired requirement if the number of L-RRHs is less than 20or the L-RRH is equipped with 1-bits quantizer. We also notethe there is a tradeoff between adding L-RRHs and increasingresolution bits of L-RRHs, e.g., adding 60 L-RRHs with 1-bit quantizer and adding 25 L-RRHs with 3-bits quantizercan both meet the throughput requirement, whereas we canoptimize the L-RRH configuration based on the EE.Ml10 20 30 40 50 60QuantizationbitB123456700.10.20.30.40.50.60.70.80.9Fig. 4. The average energy efficiency (in Mbits/Joule) of distributed massiveMIMO with mixed-ADC receiver against with quantization bits B and thenumber of L-RRHs Ml, with ρ = 10 dB, Mf = 20, K = 20.V. CONCLUSIONThis letter investigated the uplink achievable SE of a multi-user distributed massive MIMO with mixed-ADC receivers.We derived the worst-case achievable SE considering theeffect of ADCs. Our results revealed the effects of the systemparameters, such as the transmit power and the quantizationbits of the low-resolution ADCs, on the achievable SE. Thenumerical results revealed that the distributed mixed-ADCarchitecture is an energy-efficient architecture that significantlyoutperforms the centralized massive MIMO system and canachieve outstanding throughput via deployment of a largenumber of L-RRHs with appropriate quantization resolution.REFERENCES[1] F. Boccardi, R. W. Heath, A. Lozano, T. L. Marzetta, and P. Popovski,“Five disruptive technology directions for 5G,” IEEE Commun. Mag.,vol. 52, no. 2, pp. 74–80, Feb. 2014.[2] V. Raghavan, J. Cezanne, S. Subramanian, A. Sampath, and O. Koymen,“Beamforming tradeoffs for initial UE discovery in millimeter-waveMIMO Systems,” IEEE J. Sel. Topics Signal Process., vol. 10, no. 3,pp. 543–559, Apr. 2016.[3] L. Dai, “A comparative study on uplink sum capacity with co-locatedand distributed antennas,” IEEE J. Sel. Areas Commun., vol. 29, no. 6,pp. 1200–1213, Jun. 2011.[4] H. Q. Ngo, A. E. Ashikhmin, H. Yang, E. G. Larsson, and T. L. Marzetta,“Cell-free massive MIMO versus small cells,” Available:http://arxiv.org/abs/1602.08232, [Online].[5] L. Fan, S. Jin, C. K. Wen, and H. Zhang, “Uplink achievable ratefor massive MIMO systems with low-resolution ADC,” IEEE Commun.Lett., vol. 19, no. 12, pp. 2186–2189, Dec. 2015.[6] C. Molle´n, J. Choi, E. G. Larsson, and R. W. Heath, “Achievableuplink rates for massive MIMO with coarse quantization,” CoRR, 2016.[Online]. Available: http://arxiv.org/abs/1611.05723[7] T. C. Zhang, C. K. Wen, S. Jin, and T. Jiang, “Mixed-ADC massiveMIMO detectors: Performance analysis and design optimization,” IEEETrans. Wireless Communi., vol. 15, no. 11, pp. 7738–7752, Nov. 2016.[8] N. Liang and W. Zhang, “Mixed-ADC massive MIMO uplink infrequency-selective channels,” IEEE Trans. Commun., vol. 64, no. 11,pp. 4652–4666, Nov. 2016.[9] O. Orhan, E. Erkip, and S. 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The Distributed MIMO Scenario: Can Ideal ADCs Be Replaced by Low-Resolution ADCs?

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The Distributed MIMO Scenario: Can Ideal ADCs Be Replaced by Low-resolution ADCs?

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