analysis of the impact of agc on cyclic prefix length for

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 10, OCTOBER 2018 4783

Analysis of the Impact of AGC on Cyclic PrefixLength for OFDM SystemsHao Wu , Member, IEEE, Jun Li, Bo Dai, and Yuan Liu

Abstract— In some orthogonal frequency division multiplex-ing (OFDM) systems, a number of OFDM symbols form one sub-frame and consecutive subframes may be allocated to differentusers. The power estimation and the gain adjustment need to becarried out within the cyclic prefix (CP) of the first OFDM symbolin a subframe. After passing through the multipath channel,the CP of the first OFDM symbol in a subframe contains aportion of the power of the last OFDM symbol in the priorsubframe. When these two subframes are allocated to distinctusers with different received powers, the gain adjustment isinaccurate and the system performance is degraded. To combatthe inter-user interference at the boundary of subframes, the CPof the first OFDM symbol in a subframe is proposed to includean adjustment portion (AP). The overhead of the AP is amortizedover the OFDM symbols in a subframe and is negligible whenthe number of OFDM symbols in a subframe is large. A modelis given to calculate the optimal length of the AP in this paper.The model uses an information theory to formulate the tradeoffbetween the accuracy of power measurement and the overheadof the AP.

Index Terms— AGC, ADC, OFDM, cyclic prefix.

I. INTRODUCTION

ORTHOGONAL frequency division multiplex-ing (OFDM) is adopted in many communication

systems because of its high spectral efficiency. In wiredscenarios, OFDM has been developed into the asymmetricdigital subscriber line (ADSL), the very-high-bit-rate digitalsubscriber line (VDSL), etc. In wireless scenarios, OFDM hasbeen developed into the digital audio broadcasting (DAB),the digital video broadcasting (DVB), the IEEE 802.11, theIEEE 802.16, the 3rd generation partnership project (3GPP)long term evolution (LTE), etc.

Due to the varying path loss and the different transmitpowers, the power of the received signal in OFDM systems

Manuscript received October 26, 2017; revised February 23, 2018 andApril 23, 2018; accepted April 28, 2018. Date of publication May 8, 2018;date of current version October 16, 2018. This paper was presented in partat the 2017 IEEE 85th Vehicular Technology Conference, Sydney, Australia,June 2017 [1]. The associate editor coordinating the review of this paperand approving it for publication was S. Muhaidat. (Corresponding author:Hao Wu.)

H. Wu is with the State Key Laboratory of Mobile Network and MobileMultimedia Technology, ZTE Corporation, Shenzhen 518055, China, and alsowith the Department of Wireless Product Research and Development Institute,ZTE Corporation, Shenzhen 518055, China (e-mail: [email protected]).

J. Li, B. Dai, and Y. Liu are with the Department of Wire-less Product Research and Development Institute, ZTE Corporation,Shenzhen 518055, China (e-mail: [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCOMM.2018.2834408

can vary over a large dynamic range. Automatic gain con-trol (AGC) is needed for regulating the power of the receivedsignal at a desired level. If the power of the received signal isweak, AGC boosts the gain to decrease the quantization noise.If the power of the received signal is strong, AGC attenuatesthe gain to avoid the clipping. Thus the quantization noise andthe clipping of the received signal introduced by the analog-to-digital converter (ADC) are minimized.

The AGC strategy depends on subframe structure of OFDMsystems. In general, the subframe structure can be classifiedinto two categories. The first category is that the subframeconsists of preamble and payload OFDM symbols [2]–[4].The preamble is designed to facilitate timing and frequencysynchronization. Based on the power of the received pream-ble, gain is adjusted before receiving the payload OFDMsymbols [5]–[7]. The length of the preamble is usually longenough for the gain to be obtained accurately. The secondcategory is that the subframe only consists of payload OFDMsymbols [8], [9]. Timing and frequency synchronization arenormally achieved by the cell search procedure and the ran-dom access procedure instead of the preamble. The powerestimation and the gain adjustment need to be carried outwithin the cyclic prefix (CP) of the first OFDM symbol ina subframe [10], [11]. There is inter-carrier interference (ICI)when the gain is adjusted within the useful portion of theOFDM symbol. To reduce the overhead of the CP, the lengthof the CP is usually equal to the delay spread of the multipathchannel in the traditional scheme [12]. After passing throughthe multipath channel, the CP of the first OFDM symbol in asubframe contains a portion of the power of the last OFDMsymbol in the prior subframe. Consecutive subframes may beallocated to distinct users with different received powers. Theinter-user interference (IUI) at the boundary of subframes mayresult in inaccurate power measurement and inappropriate gainadjustment. To combat the IUI at the boundary of subframes,the CP of the first OFDM symbol in a subframe is proposedto include an adjustment portion (AP). Since the IUI at theboundary of subframes does not exist from the second OFDMsymbol to the last OFDM symbol, the AP is only present in thefirst OFDM symbol. The overhead of the AP is amortized overthe OFDM symbols in a subframe and is negligible when thenumber of OFDM symbols in a subframe is large. In this paper,we focus on the second category of the subframe structure.

There are many proposed improvements to the CP-OFDM,such as known symbol padding OFDM (KSP-OFDM),windowed OFDM (W-OFDM), filtered OFDM (F-OFDM),generalized frequency division multiplexing (GFDM),

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4784 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 10, OCTOBER 2018

Fig. 1. A homogeneous deployment where UE1 and UE2 are served by themacro cell. UE1 is located near to the base station. UE2 is located far fromthe base station.

Fig. 2. A heterogeneous deployment where UE1 is served by the macrocell and UE2 is served by the small cell. To prevent the severe inter-cellinterference in the macro-small deployment, certain subframes of one cell aremuted.

Fig. 3. A relay deployment where UE1 is served by the relay cell.

universal filtered multi-carrier (UFMC), filter-bandmulti-carrier (FBMC), etc. [13], [14]. The IUI at the boundaryof subframes also degrades the system performance whenthese waveforms are adopted. And the system performance isexpected to be improved if the AP is introduced.

Fig. 1 to Fig. 3 show three scenarios where there may bea large difference in the received powers between consecutivesubframes. Fig. 1 shows a homogeneous deployment whereuser equipment 1 (UE1) and UE2 are served by the macrocell. UE1 with high modulation order and code rate is locatednear to the base station. UE2 with low modulation order andcode rate is located far from the base station. When UE1 andUE2 are assigned to transmit in consecutive uplink subframes,there may be a large difference in the received powers of themacro base station. Fig. 2 shows a heterogeneous deploymentwhere UE1 is served by the macro cell and UE2 is servedby the small cell. To prevent the severe inter-cell interferencein the macro-small deployment, certain subframes of one cellare muted (e.g., almost blank subframes [15], [16]). However,the IUI at the boundary of subframe can not be avoided in thisway. Fig. 2 demonstrates two cases. In the first case, the smallcell is located close to the macro cell edge. UE1 is in thevicinity of the small cell. When UE1 and UE2 are assigned

to transmit in consecutive uplink subframes, there may bea large difference in the received powers of the small basestation. In the second case, the small cell is located close tothe macro cell center. The transmit power of the macro basestation is high and that of the small base station is low. Whenthe macro base station and the small base station are assignedto transmit in consecutive downlink subframes, there may bea large difference in the received powers of UE2. Fig. 3 showsa relay deployment where UE1 is served by the relay cell. Thelink between the base station and the relay node is referred tobackhaul link and the link between the relay node and the UEis referred to access link [17]. For the time division duplexoperation, the subframes allocated to the backhaul link andthe access link must be mutually compatible. When the accessuplink subframe and the backhaul downlink subframe are theconsecutive subframes, there may be a large difference in thereceived powers of the relay node.

In the LTE standard, each frame consists of 10 subframesand each subframe consists of 14 OFDM symbols in thecase of the normal CP [8]. The length of the CP of the firstOFDM symbol and the eighth OFDM symbol is 160Ts andthat of the remaining OFDM symbols is 144Ts, where Ts isequal to 1/30.72M seconds. If 16Ts of the CP of the eighthOFDM symbol is moved to the CP of the first OFDM symbol,the adverse effect of the IUI at the boundary of subframe ismitigated. And a better performance can be achieved. In the802.16m standard, the CP length of all the OFDM symbols ina subframe is GTb, where Tb is the useful portion length of theOFDM symbol and G is equal to 1/4, 1/8 or 1/16 [9]. A portionof the idle time can be given to the CP of the first OFDMsymbol to mitigate the IUI at the boundary of subframes.The adoption of the proposed scheme in the existing OFDMsystems would require significant changes and hence is quiteunlikely. The proposed scheme can be a candidate for the newOFDM systems.

Many AGC schemes have been proposed for the secondcategory of the subframe structure. The scheme proposed by[18] and [19], called AGC-UP, may adjust the gain withinthe useful portion of the OFDM symbol. The ICI degradesthe system performance. The scheme proposed by [20], calledAGC-SP, suggests that the gain should be adjusted within theinter-frame silence period based on the received signal of theprior frame. The power of the received signals may vary sig-nificantly between subframes. It is difficult to ensure that thegain is appropriate for all the subframes in a frame. In addition,the statistics of the received signals between frames are notnecessary the same. The gain may be appropriate for the priorframe but not the present frame. The scheme proposed by[11] and [21], called AGC-CP, suggests that the gain shouldbe adjusted within the CP. As mentioned earlier, the IUI at theboundary of subframes degrades the system performance.

The main contribution of the paper is two-fold:1) We propose a new subframe structure to simplify the

implementation of the AGC for the second category of thesubframe structure. The CP of the first OFDM symbol in asubframe is proposed to include an AP. The overhead of theAP is amortized over the OFDM symbols in a subframe andis usually negligible.

WU et al.: ANALYSIS OF THE IMPACT OF AGC ON CP LENGTH FOR OFDM SYSTEMS 4785

2) A model is given to calculate the optimal length ofthe AP. The model uses information theory to formulate thetradeoff between the accuracy of power measurement and theoverhead of the AP. Also, we derive a closed-form expressionfor the distribution of the estimation of the received power.

The rest of the paper is organized as follows. In section II,we give the OFDM system model and propose the newsubframe structure. Two AGC strategies are illustrated insection III. We derive the normalized channel capacity of theOFDM system with the AP and without the AP in Section IVand Section V respectively. Section VI presents the simulationresults to compare the system performance of the proposedscheme and the traditional schemes. And the conclusion isgiven in Section VII.

Notation: Uppercase boldface letters and lowercase bold-face letters represent matrices and vectors respectively. A �0 and A � 0 denote A is a positive definite matrixand a positive semi-definite matrix respectively. (·)−1, (·)−,rank(·), (·)t, and (·)∗ stand for inverse, generalized inverse,rank, transpose, and Hermitian transpose of a matrix respec-tively. diag(a1, a2, . . . , aj) denotes a diagonal matrix withdiagonal elements a1, a2, . . . , aj . E[·], Q[·] and |·| represent theexpectation operator, the quantizer operator, and the absoluteoperator respectively. rvec(·) stands for concatenating the rowsof a matrix into a row vector. Ij and 0j×k represent theidentity matrix of size j × j and the zero matrix of sizej×k respectively. We use the notations of R to denote the setof all real numbers and ⊗ to denote the Kronecker product.a ∼ CN (u,v) denotes the circularly symmetric complexGaussian random vector with mean vector u and covariancematrix v. Aj,k is the (j, k)th entry of the matrix A. aj is thejth entry of the vector a. Matrix A with j row partitions andk column partitions is

A =

⎡⎢⎢⎣A00 A01 . . . A0k

A10 A11 . . . A1k

. . . . . . . . . . . .Aj0 Aj1 . . . Ajk

⎤⎥⎥⎦ (1)

Finally, i �√−1.

II. SYSTEM MODEL

Zero intermediate-frequency (IF) receiver is widely used inOFDM systems. The block diagram of the zero IF receiver isshown in Fig. 4. Signal is received and filtered by the antennaand the bandpass filter first, and then the signal is amplifiedby a variable gain low noise amplifier (LNA). Following,the radio-frequency signal is down converted to the basebandby a mixer and the baseband signal is amplified by a variablegain amplifier (VGA). By using the ADC, the baseband signalis converted to the digital domain. By measuring the power ofthe signal after the ADC, the gains of the LNA and the VGAare adjusted accordingly.

We assume that the useful portion of the OFDM symbolhas N samples x = [x0, x1, . . . , xN−1]t. The N -point inversediscrete Fourier transform (IDFT) of x yields the time domainsignal

x = Ux, Uj,k =1√Ne

i2πjkN (2)

Fig. 4. Block diagram of the zero IF receiver for OFDM systems.By measuring the power of the received signal after the ADC, the gainsof the LNA and the VGA are adjusted accordingly.

where j, k = 0, 1, . . . , N − 1 and x = [x0, x1, . . . , xN−1]t.When N � 1, it is reasonable to assume thatx ∼ CN (0N×1, NxIN ) [22], [23], where Nx is the averageenergy of the time domain signal. After the addition ofthe CP, the time domain signal is xCP = [xN−L+1, . . . ,xN−1, x0, . . . , xN−1]t, where L − 1 is the length ofthe CP. After passing through the multipath channel,the received signal of the first OFDM symbol in a subframe,y = [y0, y1, . . . , yN+L−2]t, can be expressed as (the index ofthe antenna is dropped for simplicity)

y = Hx + HxCP + w (3)

x = [x0, x1, . . . , x �D−2]t is the last D− 1 samples of the time

domain signal of the prior subframe. Also, it is reasonableto assume that x ∼ CN (0( �D−1)×1, NpI �D−1), where Np

is the average energy of the time domain signal of theprior subframe. w = [w0, w1, . . . , wN+L−2]t is the additivewhite Gaussian noise (AWGN) at the receiver. If the receiverapplies gain a just before receiving yn+1, then we havew ∼ CN (0(N+L−1)×1,Rw), where

Rw =[

N0In+1 0(n+1)×(N+L−2−n)

0(N+L−2−n)×(n+1) a2N0IN+L−2−n

](4)

and N0 is the average energy of the AWGN. Assuming thatthe multipath channel filter taps of the present subframeand the prior subframe are h = [h0, h1, . . . , hD−1]t andh = [h0, h1, . . . , h �D−1]

t respectively, we have

Hj,k =

⎧⎪⎨⎪⎩

hj−k 0 ≤ j − k < D, j ≤ n

ahj−k 0 ≤ j − k < D, j > n

0 otherwise

(5)

where j, k = 0, 1, . . . , N + L− 2, and

Hj,k =

⎧⎪⎨⎪⎩

h�D−1+j−k 0 ≤ k − j < D, j ≤ n

ah�D−1+j−k 0 ≤ k − j < D, j > n

0 otherwise

(6)

where j = 0, 1, . . . , N + L − 2 and k = 0, 1, . . . , (D − 2).OFDM systems is usually designed to ensure that L is notsmaller than D and D.

Due to the addition of the CP, we have yUP =HTx + wUP, where yUP = [yL−1, yL, . . . , yL+N−2]t and


Fig. 5. IUI occurs at the boundary of the subframes. To avoid the IUI, the CPof the first OFDM symbol in a subframe is proposed to include an AP. TheUP in the figure means the useful potion of the OFDM symbol.

wUP = [wL−1, wL, . . . , wN+L−2]t. There is no ICI if andonly if U∗HTU is a diagonal matrix. If n < L−1, the gain isadjusted within the CP. HT is given by the following equation

HT|j,k =

{ahmod(j−k,N) mod(j − k,N) < D

0 mod(j − k,N) ≥ D(7)

where j, k = 0, 1, . . . , N − 1. HT in (7) is a circulantmatrix, which is diagonalizable by the discrete Fourier trans-form (DFT). Thus there is no ICI when the gain is adjustedwithin the CP. HT can be written as UΛU∗, where Λ =diag(aH0, aH1, . . . , aHN−1) and Hj =

∑D−1k=0 hke

− i2πjkN .

If n ≥ L − 1, the gain is adjusted within the useful portion.HT is given by the following equation

HT|j,k =

⎧⎪⎨⎪⎩

hmod(j−k,N) mod(j−k,N)<D, j ≤ n−L+1ahmod(j−k,N) mod(j−k,N)<D, j > n−L+10 otherwise

(8)

where j, k = 0, 1, . . . , N − 1. HT in (8) is an non-normalmatrix, which is not diagonalizable by the DFT [24]. Thusthere is ICI when the gain is adjusted within the useful portion.In the following, we assume that n+ 1 = L− 1.

From (3) it is known that the first D−1 samples of the firstOFDM symbol in a subframe contain a portion of the power ofthe last OFDM symbol in the prior subframe. This is illustratedin Fig. 5. When these two subframes are allocated to distinctusers with different received powers, the gain adjustment isinaccurate and the system performance is degraded. To solvethis problem, the CP of the first OFDM symbol in a subframeis proposed to include an AP. The length of the CP of theother OFDM symbols in a subframe remains the same. If thelargest delay spread in the majority of scenarios is D� and thelength of the AP is M , then the length of the CP of the firstOFDM symbol is D� +M−1 and the length of the CP of theother OFDM symbols is D� − 1. In the following, we focuson the first OFDM symbol. For the other OFDM symbols,the analysis is similar.yj is converted into the digital domain by the ADC. The

clipping ratio of yj is defined as cj = O/(Nyj /2)1/2, where

O is the span of the ADC and Nyj is the average energy of yj .

Without loss of generality, O is set equal to 1. The optimalclipping ratio copt depends on the ADC resolution [25].

Let T� = Nx

∑D−1l=0 |hl|2, T� = Np

∑ �D−1l=0 |hl|2, and

Tj = Nx

j∑k=0

|hk|2 +Np

�D−1∑k=j+1

|hk|2 (9)

where j = 0, 1, . . . , D�−2, hk = 0 when k ≥ D, and hk = 0when k ≥ D. Then we have

Nyj =

⎧⎪⎨⎪⎩

N0 + Tj j < D� − 1N0 + T� D� − 1 ≤ j ≤ D� +M − 2a2N0 + a2T� j > D� +M − 2

(10)

where j = 0, 1, . . . , N +D� + M − 2. In order to make theclipping ratio of the useful portion of the OFDM symbol cUP

closes to copt, the gain a should be set to (2/P )1/2/copt,where P is the estimation of the received power. Then

cUP =1a

√2

N0 + T�= copt

√P

N0 + T�(11)

Assume that R is divided by a B-bit ADC into R disjointsubsets: ψ0 = (q0, q1], ψ1 = (q1, q2], . . . , ψR−1 = (qR−1, qR),where B = log2(R). In the case of mid-raiser uniform quan-tization with step size = 2/R, qj is equal to (j − R/2)when j = 1, 2, . . . , R−1. In addition, we have q0 = −∞ andqR = ∞. yj is mapped to vk = (k − R/2) − /2 whenyj ∈ ψk−1. yj is a Gaussian random variable since it is alinear combination of Gaussian random variables. Accordingto the Bussgang theorem [26], the quantization of yj canbe decomposed into Q(yj) = sjyj + dj , where sj is thescaling factor and dj is the distortion component. And dj isuncorrelated with yj . It is shown that [25]

sj =

√1

πNyj

R−1∑k=0

vk+1(e−c2j q2

k2 − e−

c2j q2k+12 ) (12)

and

Ndj =

R−1∑k=0

v2k+1(erfc(

cjqk√2

) − erfc(cjqk+1√

2)) − s2jN

yj (13)

where erfc is the complementary error function and Ndj is the

average energy of dj . Nyj is constant over the ranges [D�−1,

D� + M − 2] and [D� + M − 1, N + D� + M − 2]. LetsAP and Nd

AP be the scaling factor and the average energyof the distortion component of the AP respectively. Also, letsUP and Nd

UP be the scaling factor and the average energy ofthe distortion component of the useful portion of the OFDMsymbol respectively. Applying the DFT to the output of theADC, we obtain

y = sUPU∗HTUx + sUPU∗wUP + U∗d(1)= sUPΛx + wUP (14)

where wUP � sUPU∗wUP + U∗d and d =[dD�+M−1, dD�+M , . . . , dN+D�+M−2]t. In step (1) we usethe fact that U∗U = IN . Since wUP ∼ CN (0N×1, a

2N0IN ),we have

sUPU∗wUP ∼ CN (0N×1, a2s2UPN0IN ) (15)


Fig. 6. The AGC strategies. The upper part is the first strategy. The lower partis the second strategy. S is the number of the OFDM symbols in a subframe.The UP in the figure means the useful potion of the OFDM symbol.

There are usually a large number of subcarriers in OFDMsystems [8], [9]. Applying the central limit theory, U∗d iswell approximated by CN (0N×1, N

dUPIN ) [27], [28]. Then

we have wUP ∼ CN (0, (a2s2UPN0 + NdUP)IN ). Assuming

the perfect channel state information at the receiver side,the channel capacity of the OFDM system can be written as

C(h, h, P ) = Eh,�h,P

∑j∈Θ

log2(1 +a2s2UPNx|Hj |2a2s2UPN0 +Nd

UP

) (16)

where Θ is the allocated subcarriers and Nx is the averageenergy of the frequency domain signal. The average is overthe stationary distributions of the multipath channel and theestimation power.

III. THE AGC STRATEGIES

In general, there are two AGC strategies for the secondcategory of the subframe structure, which are shown in Fig. 6.The first strategy is that the receiver obtains the gain of theuseful portion of all the OFDM symbols based on the receivedsignal of the CP of the first OFDM symbol. If there is a pre-defined power difference between the first OFDM symbol anda subsequent OFDM symbol, the gain of the correspondingOFDM symbol is adjusted accordingly. The second strategyis that the receiver obtains the gain of the useful portion ofthe first OFDM symbol based on the received signal of theCP of the first OFDM symbol. A new AGC gain is applied tothe useful portion of the second OFDM based on the receivedsignal of the useful portion of the first OFDM symbol. Andthe remaining OFDM symbols in a subframe is processedsimilarly.

The advantage of the first strategy is the low complexityreceiver: the received powers of the second OFDM symbolto the last OFDM symbol do not need to be estimated. Thedisadvantage of the first strategy is that the performance ofthe subsequent OFDM symbols decreases if the received pow-ers are measured inaccurately. This problem is significantlymitigated by the introduction of the AP. The advantage ofthe second strategy is that the received powers of the secondOFDM symbol to the last OFDM symbol are measuredaccurately and the performance of these OFDM symbols isoptimal. However, this increase in performance comes at theexpense of the higher implementation complexity.

IV. NORMALIZED CHANNEL CAPACITY OF

THE OFDM SYSTEM WITH THE AP

It is easier to obtain an accurate estimation of the receivedpower of the first OFDM symbol when the subframe containsthe AP. As a result, cUP is close to copt and the channelcapacity of the OFDM system is increased. On the other hand,the AP introduces an additional overhead. There is a tradeoffbetween the accuracy of power measurement and the overheadof the AP. The received power of the AP of the first OFDMsymbol is measured as

PAP =1M

D�+M−2∑j=D�−1

|Q(yj)|2 (17)

The received power of the useful portion of the first OFDMsymbol is measured as

PUP0 =

1N

N+D�+M−2∑j=D�+M−1

|Q(yj)|2 (18)

N is usually much larger than 1. PUP0 is approximately equal

to the average energy of the useful portion of the first OFDMsymbol. PUP

1 , PUP2 , . . . , PUP

S−2 are obtained similarly, where Sis the number of the OFDM symbols in a subframe.

The normalized channel capacity of the first AGC strategyis

RS1AP =

S · C(h, h, PAP)S(N +D� − 1) +M

(19)

The normalized channel capacity of the second AGC strategyis

RS2AP =

C(h, h, PAP)+C(h, h, PUP0 )+ . . .+C(h, h, PUP

S−2)S(N +D� − 1) +M

(20)

The overhead of the AP is amortized over the OFDM symbolsin a subframe and is negligible when the number of OFDMsymbols in a subframe is large. Let the optimal length of theAP be Mopt. When M is smaller than Mopt, the decreasein channel capacity mainly comes from the quantization error.When M is larger than Mopt, the decrease in channel capacitymainly comes from the overhead of the AP. We now derivethe distribution of PAP.

A. The Distribution of PAP

From (17) it can be shown that

PAP =1M

x∗APGxAP (21)

where G = IM×M ⊗ (hAPh∗AP); hAP = [sAPh0, sAPh1, . . . ,

sAPhD−1, 1]t; and

x∗AP =

rvec

⎛⎜⎜⎝

⎡⎢⎢⎣

xCP|D�−1 . . . xCP|D�−D wAP|0xCP|D� . . . xCP|D�−D+1 wAP|1. . . . . . . . . . . .

xCP|D�+M−2 . . . xCP|D�−D+M−1 wAP|M−1

⎤⎥⎥⎦

⎞⎟⎟⎠

(22)


Tj,k =

⎧⎪⎨⎪⎩

1 mod(j,D + 1) = D, k = D − 1 − mod(j,D + 1) + �j/(D + 1)�1 mod(j,D + 1) = D, k = D − 2 +M + (j + 1)/(D + 1)0 otherwise

(25)

wAP = [sAPwD�−1 + dD�−1, . . . , sAPwD�+M−2 +dD�+M−2]t is the sum of the scaled AWGN plusthe quantization error. The additive quantization noisemodel (AQNM) treats dAP = [dD�−1, . . . , dD�+M−2]t

as the AWGN to simplify the analysis [29]–[31]. Thisapproximation is used to derive the distribution of PAP. ThenwAP ∼ CN (0M×1, N

tAPIM ), where N t

AP = s2APN0 +NdAP.

The unique elements in x∗AP form

xAU = [xCP|D�−D, . . . ,xCP|D�+M−2,

wAP|0, . . . ,wAP|M−1]∗ (23)

We have xAU ∼ CN (0(D+2M−1)×1,RAU), where

RAU =[NxID+M−1 0(D+M−1)×M

0M×(D+M−1) N tAPIM

](24)

There exists a transformation matrix T such thatTxAU = xAP. T is given by (25), as shown at thetop of this page, where j = 0, 1, . . . , (D + 1)M − 1 andk = 0, 1, . . . , D + 2M − 2.

Then PAP = x∗AUT∗GTxAU/M . Let RAS = (RAU)1/2

and xAU = RASxAS, so that xAS = R−1ASxAU. PAP is

expressed as

PAP =1M

x∗ASR

∗AST

∗GTRASxAS

=1M

x∗AU(R−1

AS)∗R∗

AST∗GTRASR−1

ASxAU (26)

We will show later that R∗AST

∗GTRAS/M has M positiveeigenvalues λ0, λ1, . . . , λM−1 and D+M−1 zero eigenvalues.Then

PAP = x∗AU(R−1

AS)∗Ψdiag(λ0, . . . , λM−1, 0, . . . , 0)

×Ψ∗R−1ASxAU

= x∗ANdiag(λ0, . . . , λM−1, 0, . . . , 0)xAN (27)

where xAN = Ψ∗R−1ASxAU and Ψ is an orthogonal matrix

of the eigenvectors of R∗AST

∗GTRAS/M . It follows thatxAN ∼ CN (0(D+2M−1)×1, ID+2M−1). Then

PAP =M−1∑j=0

λjx∗AN|jxAN|j (28)

Since xAN|j ∼ CN (0, 1), we have that λjx∗AN|jxAN|j

∼ Exp(1/λj), where Exp(1/λj) means exponential distrib-ution with parameter 1/λj . PAP is the sum of independentexponentially distributed variables. The probability densityfunction (PDF) of the sum of the independent exponentiallydistributed variables is given in [32].

B. The Eigenvalues of R∗AST

∗GTRAS/M

In this subsection, we show that R∗AST

∗GTRAS/M hasM positive eigenvalues and D + M − 1 zero eigenvalues.

We define a (D+M − 1)× (D+M − 1) matrix V with the(j, k)th entry

Vj,k =

⎧⎪⎨⎪⎩

1 j = 0, k = D +M − 21 j = k + 10 otherwise

(29)

It follows that V∗V = ID+M−1. Let

hAE = [sAPhD−1, sAPhD−2, . . . , sAPh0,01×(M−1)]t (30)

and HAE = [hAE,VhAE, . . . ,VM−1hAE]. T∗GT is givenby (31), as show at the top of the next page, whereD• = D+1.From (25), we have

T∗GT =[HAEH∗

AE HAE

H∗AE IM

](32)

Then

R∗AST

∗GTRAS =[A00 A01

A10 A11

](33)

where A00 = NxHAEH∗AE, A01 = A∗

10 =(N t

APNx)1/2HAE, and A11 = N tAPIM . The following

lemmas are needed to derive the eigenvalues ofR∗

AST∗GTRAS/M .

Lemma 1: Let B00 represent a j × j matrix, B01 a j × kmatrix, B10 a k × j matrix, and B11 a k × k matrix. Then

rank([

B00 B01

B10 B11

])= rank(X) + rank(Y) + rank(Z)

+ rank(B11) (34)

where X = (Ik −B11B−11)B10, Y = B01(Ik −B−

11B11), andZ = (Ik − YY−)(B00 − B01B−

11B10)(Ik − X−X). [24]Lemma 2: If B and C are positive semi-definite Hermitian

matrix, then so is B⊗ C [24].Lemma 3: Suppose B is a positive semi-definite Hermitian

matrix. If rank(B) = j, B has j positive eigenvalues. Andthe remaining eigenvalues are zero [33].

Lemma 4: Suppose B is j × k and C is k × j, bothcomplex matrices. Then BC and CB have the same nonzeroeigenvalues, counting algebraic multiplicities [24].

Since A11 is nonsingular, A11A−11 = A−

11A11 = IM .Also, we have that A01(A11)−A10 = A00. It follows fromLemma 1 that rank(R∗

AST∗GTRAS) = rank(A11) = M .

From Lemma 2 we conclude that G � 0, so thatR∗

AST∗GTRAS � 0. From Lemma 3 we can con-

clude that R∗AST

∗GTRAS/M has M positive eigenvaluesλ0, λ1, . . . , λM−1 and D +M − 1 zero eigenvalues.

Let Φ = [(Nx)1/2H∗AE (N t

AP)1/2IM ], so that Φ∗Φ/M =R∗

AST∗GTRAS/M . It follows from Lemma 4 that the non-

zero eigenvalues of ΦΦ∗/M and R∗AST

∗GTRAS/M areequal. And ΦΦ∗ is given by (35), as shown at the top ofthe next page.


T∗GT = T∗

⎡⎢⎢⎣hAPh∗

AP 0D•×D• . . . 0D•×D•

0D•×D• 0D•×D• . . . 0D•×D•

. . . . . . . . . . . .0D•×D• 0D•×D• . . . 0D•×D•

⎤⎥⎥⎦T + . . .+ T∗

⎡⎢⎢⎣0D•×D• 0D•×D• . . . 0D•×D•

0D•×D• 0D•×D• . . . 0D•×D•

. . . . . . . . . . . .0D•×D• 0D•×D• . . . hAPh∗

AP

⎤⎥⎥⎦T (31)

ΦΦ∗ = N tAPIM +Nx

⎡⎢⎢⎣

h∗AEhAE h∗

AEVhAE . . . h∗AEVM−1hAE

h∗AE(V)∗hAE h∗

AEhAE . . . h∗AEVM−2hAE

. . . . . . . . . . . .h∗

AE(VM−1)∗hAE h∗AE(VM−2)∗hAE . . . h∗

AEhAE

⎤⎥⎥⎦ (35)

V. NORMALIZED CHANNEL CAPACITY OF THE OFDMSYSTEM WITHOUT THE AP

If the CP of the first OFDM symbol in a subframe doesnot include the AP, the received power of the CP of the firstOFDM symbol is measured as

PCP =1

D� − 1

D�−2∑j=0

|Q(yj)|2 (36)

The received power of the useful portion of the first OFDMsymbol is measured as

PUP

0 =1N

N+D�−2∑j=D�−1

|Q(yj)|2 (37)

PUP

0 is also approximately equal to the average energy of theuseful portion of the first OFDM symbol. P

UP

1 ,PUP

2 ,…, andP

UP

S−2 are obtained similarly.The normalized channel capacity of the AGC first strategy

is

RS1CP =

C(h, h, PCP)(N +D� − 1)

(38)

Due to the IUI at the boundary of subframes, there may be alarge difference between PCP and N0 + T� when consecutivesubframes are allocated to distinct users with different receivedpowers. As a result, the channel capacity of the OFDM systemis decreased. The normalized channel capacity of the secondAGC strategy is

RS2CP =

C(h, h, PCP)+C(h, h, PUP

0 )+ . . .+C(h, h, PUP

S−2)S(N +D� − 1)

(39)

In this case, only the first OFDM symbol suffers from theIUI at the boundary of subframes. The IUI at the boundary ofsubframes has no impact on the channel capacity of the secondOFDM symbol to the last OFDM symbol. We now derive thedistribution of PCP.

A. The Distribution of PCP

From (36) it can be shown that

PCP =1

D� − 1x∗

CTGxCT (40)

where x∗CT is given by (41), as shown at the bottom of

this page and D+ is the maximum value of D and D. xj

and xCT|j are equal to 0 when j < 0. wCT = [s0w0 +d0, . . . , sD�−2wD�−2 + dD�−2]t is the sum of the scaledAWGN plus the quantization error. G is

G =

⎡⎢⎢⎣

h0CP(h0

CP)∗ 0D◦×D◦ . . . 0D◦×D◦

0D◦×D◦ h1CP(h1

CP)∗ . . . 0D◦×D◦

. . . . . . . . . . . .

0D◦×D◦ 0D◦×D◦ . . . hD�−2CP (hD�−2

CP )∗

⎤⎥⎥⎦

(42)

where D◦ = D+ + 1 and

hjCP =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

[sjh0, . . . , sjhj , sj hj+1, . . . , sj hD+−1, 1]t

j ≤ D+ − 2[sjh0, . . . , sjhD+−1, 1]t

j ≥ D+ − 1

(43)

Similar to wAP, we have wCT ∼ CN (0(D�−1)×1,Kw), whereKw = diag(N0

CP, N1CP , . . . , N

D�−2CP ) and N j

CP = s2jN0+Ndj .

The unique elements in xCT form

xCU = [x�D−D+ , . . . , x �D−2,

xCP|0, . . . ,xCP|D�−2,wCT|0, . . . ,wCT|D�−2]∗ (44)

We have xCU ∼ CN (0(D++2D�−3)×1,RCU), where

RCU =⎡⎣

NpID+−1 0(D+−1)×(D�−1) 0(D+−1)×(D�−1)

0(D�−1)×(D+−1) NxID�−1 0(D�−1)×(D�−1)

0(D�−1)×(D+−1) 0(D�−1)×(D�−1) Kw

⎤⎦

(45)

There exists a transformation matrix T such that TxCU =xCT. T is given by (46), as shown at the top of the next

x∗CT = rvec

⎛⎜⎜⎜⎜⎜⎜⎝

⎡⎢⎢⎢⎢⎢⎢⎣

xCP|0 x�D−2 . . . x

�D−D+ wCT|0. . . . . . . . . . . . . . .

xCP|D+−2 . . . xCP|0 x�D−2 wCT|D+−2

xCP|D+−1 . . . xCP|1 xCP|0 wCT|D+−1

. . . . . . . . . . . . . . .xCP|D�−2 . . . xCP|D�−D+ xCP|D�−D+−1 wCT|D�−2

⎤⎥⎥⎥⎥⎥⎥⎦

⎞⎟⎟⎟⎟⎟⎟⎠

(41)


Tj,k =

⎧⎪⎨⎪⎩

1 mod(j,D+ + 1) = D+, k = D+ − 1 − mod(j,D+ + 1) + �j/(D+ + 1)�1 mod(j,D+ + 1) = D+, k = D+ − 2 +M + (j + 1)/(D+ + 1)0 otherwise

(46)

T∗GT = T

∗

⎡⎢⎢⎣h0

CP(h0CP)∗ 0D◦×D◦ . . . 0D◦×D◦

0D◦×D◦ 0D◦×D◦ . . . 0D◦×D◦

. . . . . . . . . . . .0D◦×D◦ 0D◦×D◦ . . . 0D◦×D◦

⎤⎥⎥⎦T + . . .+ T

∗

⎡⎢⎢⎣

0D◦×D◦ 0D◦×D◦ . . . 0D◦×D◦

0D◦×D◦ 0D◦×D◦ . . . 0D◦×D◦

. . . . . . . . . . . .

0D◦×D◦ 0D◦×D◦ . . . hD∗−2CP (hD∗−2

CP )∗

⎤⎥⎥⎦T (50)

page, where j = 0, 1, . . . , (D+ + 1)(D� − 1) − 1 andk = 0, 1, . . . , D+ + 2D� − 4. We will show later thatR∗

CST∗GTRCS/(D� − 1) has D� − 1 positive eigenvalues

ϕ0, ϕ1, . . . , ϕD�−2 and D+ +D� −2 zero eigenvalues, whereRCS = (RCU)1/2. Similar to the analysis of the distributionof PAP, PCP is equal to

PCP =D�−2∑j=0

ϕjx∗CN|jxCN|j (47)

where xCN ∼ CN (0(D++2D�−3)×1, ID++2D�−3). The PDFof PCP is obtained similar to PAP.

B. The Eigenvalues of R∗CST

∗GTRCS/(D� − 1)

In this section, we show that R∗CST

∗GTRCS/(D�−1) has

D�−1 positive eigenvalues and D++D�−2 zero eigenvalues.We define a (D+ +D� − 2)× (D+ +D� − 2) matrix V withthe (j, k)th entry

Vj,k =

⎧⎪⎨⎪⎩

1 j = 0, k = D+ +D� − 31 j = k + 10 otherwise

(48)

It follows that V∗V = ID++D�−2. Let

hjCE =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

sj [hD+−1, . . . , hj+1, hj , . . . , h0,01×(D�−2)]t

j ≤ D+ − 2sj [hD+−1, . . . , h0,01×(D�−2)]t

j ≥ D+ − 1

(49)

and HCE = [h0CE,Vh1

CE, . . . ,VD�−2

hD�−2CE ]. T

∗GT is

given by (50), as shown at the top of this page. From (46),we have

T∗GT =

[HCEH∗

CE HCE

H∗CE ID�−1

](51)

Then

R∗CST

∗GTRCS =

[A00 A01

A10 A11

](52)

where A00 = (Kx)1/2HCEH∗CE(Kx)1/2, A01 = A

∗10 =

(Kx)1/2HCE(Kw)1/2, A11 = Kw, and

Kx =[

NpID+−1 0(D+−1)×(D�−1)

0(D�−1)×(D+−1) NxID�−1

](53)

For simplicity, let Ω = R∗CST

∗GTRCS. Since A11 is non-

singular, A11(A11)− = (A11)−A11 = ID�−1. Also, we havethat A01(A11)−A10 = A00. It follows from Lemma 1 thatrank(Ω) = rank(A11) = D� − 1. Since hj

CP(hjCP)∗ � 0,

we conclude that G � 0, so that Ω � 0. From Lemma 3 wecan conclude that Ω/(D�−1) has D�−1 positive eigenvaluesϕ0, ϕ1, . . . , ϕD�−2 and D+ +D� − 2 zero eigenvalues.

Let Φ = [H∗CE(Kx)1/2 (Kw)1/2], so that

Φ∗Φ/(D�−1) = Ω/(D�−1). It follows from Lemma 4 that

the non-zero eigenvalues of Ω/(D� − 1) and ΦΦ∗/(D� − 1)

are equal. And ΦΦ∗

is given by (54), as shown at the bottomof this page.

VI. PERFORMANCE EVALUATION

This section applies the analytical results to evaluate the sys-tem performance. The simulation is carried out in the uplinkdirection. The channel model is the extended vehicular A70Hz (EVA70) with low spatial correlation [27]. The numberof receive antennas and the number of transmit antennas are2 and 1 respectively. The considered OFDM system has abandwidth of 5MHz with N = 512, 300 of which are active.All active subcarriers are allocated to one user in a subframeand consecutive subframes are allocated to distinct users. Theratio of the received power of the prior subframe to that ofthe present subframe is T�/T� = 30dB. The sampling rateis 7.68MHz and D� is equal to 20. Each subframe consistsof 14 OFDM symbols. The fourth OFDM symbol and theeleventh OFDM symbol are used for demodulation refer-ence signals (DMRS) transmission and the remaining OFDMsymbols are used for data transmission. After attaching a24-bit cyclic redundancy check (CRC), the size of data fromthe media access control (MAC) layer is 18360. The data issegmented into 3 equal size code blocks (CBs). A further

ΦΦ∗

= Kw +

⎡⎢⎢⎢⎣

(h0CE)∗Kxh0

CE (h0CE)∗KxVh1

CE . . . (h0CE)∗KxV

D�−2hD�−2

CE

(Vh1CE)∗Kxh0

CE (Vh1CE)∗KxVh1

CE . . . (Vh1CE)∗KxV

D�−2hD�−2

CE

. . . . . . . . . . . .

(VD�−2

hD�−2CE )∗Kxh0

CE (VD�−2

hD�−2CE )∗KxVh1

CE . . . (VD�−2

hD�−2CE )∗KxV

D�−2hD�−2

CE

⎤⎥⎥⎥⎦ (54)


Fig. 7. Received signal of the first two OFDM symbols in a subframe afterthe AGC, where B = 8 and M = 20. The introduction of the AP makes thepower of the received signal of OFDM system with a high degree of accuracy.Top: the first AGC strategy; Bottom: the second AGC strategy.

24-bit CRC is appended to each CB. The turbo encoderemploys a systematic parallel concatenated convolutional codewith two 8-state constituent encoders and one contention-freequadratic permutation polynomial internal interleaver [34].The generator polynomial of the 8-state constituent encodeis [1,1011/1101]. The output of turbo encoder is followed byrate matching to adjust the code rate. 64QAM modulation withGray mapping is used for the bit to symbol mapping. Twotypes of mapping of modulation symbols onto the allocatedresources are considered in this paper: frequency-first (e.g.,physical uplink shared channel in [35]) and time-first (e.g.,physical uplink shared channel in [8]). Each mapping typehas its own pros and cons [36].

A. Accuracy of Measurement

From (28), it can be shown that

EPAP

(1)=

M−1∑j=0

λj(2)= s2APNx

D−1∑j=0

|hj|2 +N tAP (55)

where step (1) follows since the mean of an exponentiallydistributed with parameter 1/λj is λj and step (2) followssince the trace of a matrix is equal to the sum of allits eigenvalues. PAP is an unbiased estimation of the powerof the quantized received signal. From (47), we obtain that

EPCP =M−1∑j=0

ϕj =1

D� − 1

D�−2∑j=0

(N jCP + s2jTj) (56)

PCP is a biased estimation of the power of the quantizedreceived signal. As expected, the introduction of the AP makesthe power of the received signal of OFDM system with a highdegree of accuracy.

Fig. 7 shows the received signal of the first two OFDMsymbols in a subframe after the AGC. For the OFDM systemwithout the AP, some OFDM symbols have large quantizationerror, resulting in a loss of performance. For the OFDM systemwith the AP, the dynamic range of the ADC is fully used byall the OFDM symbols.

Fig. 8. The ratio of the normalized channel capacity of the OFDM systemwith the AP to Rideal as a function of M , where SNR = 10dB.

Fig. 9. The ratio of the normalized channel capacity of the OFDM systemwith the AP to Rideal as a function of M , where SNR = 30dB.

B. Optimal Length of the AP

In the ideal situation when T�/T� is always equal to 0dB,the received power can be estimated accurately without theAP and the length of the CP of all the OFDM symbols in asubframe only needs to be equal to D� − 1. Let

Rideal =C(h, h, N0 + T�)N +D� − 1

(57)

be the normalized channel capacity of the ideal OFDM system.The ratio of the normalized channel capacity of the OFDMsystem with the AP to Rideal as a function of M is plottedin Fig. 8 and Fig. 9, where SNR = Nx

∑D−1l=0 |hl|2/N0.

ST1 and ST2 mean the first AGC strategy and the secondAGC strategy respectively. As SNR increases, the ratio of thenormalized channel capacity of the OFDM system with theAP to Rideal decreases.Mopt is chosen to be 20 to balance the accuracy of power

measurement and the overhead of the AP. The channel capacitychanges slowly when M is in the vicinity of Mopt. Theoverhead of the AP is only 0.27%. The ratio of the normalizedchannel capacity of the OFDM system with the AP to Rideal

is larger than 0.98 in all scenarios.

C. Channel Capacity of the OFDM System

The ratio of the normalized channel capacity of the OFDMsystem without the AP to Rideal as a function of SNR is plottedin Fig. 10. From the figure, we conclude that the channelcapacity loss of the first OFDM symbol is large in some


Fig. 10. The ratio of the normalized channel capacity of the OFDM systemwithout the AP to Rideal as a function of SNR.

scenarios regardless of the AGC strategies and the channelcapacity loss of the second OFDM symbol to the last OFDMsymbol is mitigated by the second AGC strategy. To simplifythe implementation of the encoder and decoder, data fromthe MAC layer is usually segmented into smaller CBs. Thecode rates of all the CBs are the same. If the frequency-firstmapping is implemented, each CB is restricted to a few OFDMsymbols in the subframe. The channel capacity loss of the firstOFDM symbol significantly degrades the performance of thefirst CB when a large part of the first CB is mapped to thefirst OFDM symbol. Since the data from the MAC layer isdecoded in error if any CB is decoded in error, the channelcapacity loss of the first OFDM symbol can have a significantimpact on the system performance.

The ratio of the normalized channel capacity of the OFDMsystem with the AP to Rideal as a function of SNR is plottedin Fig. 11. From the figure, we see that the OFDM systemwith the AP can achieve most of the channel capacity in allscenarios regardless of the AGC strategies. The first AGCstrategy can be adopted to simplify the implementation ofthe receiver. There are usually some unnecessary resourceswhen designing OFDM systems in practical systems (such as16Ts of the first OFDM symbol and the eighth OFDM symbolin [8] and idle time in [9]). These unnecessary resources can beallocated to the AP in these systems, and the channel capacityloss due to the AP can be partly avoided.

D. BLER Performance of the OFDM System

In this subsection, the block error ratio (BLER) of variousAGC schemes is compared in the uplink direction. We assume

Fig. 11. The ratio of the normalized channel capacity of the OFDM systemwith the AP to Rideal as a function of SNR.

that the data traffic only exists in the odd frames. Theeven frames are silent. It is a reasonable assumption whenthere is a little active users in the cell. BLER as a func-tion of SNR for various AGC schemes is plotted fromFig. 12 to Fig. 13.

Under the considered scenario, the performance of theAGC-SP scheme and the AGC-UP scheme is far inferior tothat of the proposed scheme. The AGC-SP scheme makes anerroneous decision on the gain of the odd frames based onthe received power of the even frames. Most of the receivedsignals are saturated in the odd frames. The clipping degradesthe performance significantly. The AGC-UP scheme adjuststhe gain within the useful portion of the OFDM symbol. TheICI leads to a very degraded performance.

The performance of the AGC-CP scheme is inferior to thatof the proposed scheme. The performance difference betweenthe AGC-CP scheme and the proposed scheme decreases withthe resolution of the ADC. For the OFDM system with theAP, the performance of the first AGC strategy is almost thesame as that of the second AGC strategy. The first AGCstrategy is preferred to simplify the implementation. For theOFDM system without the AP, the performance of the firstAGC strategy is worse than that of the second AGC strategy.The second AGC strategy is preferred to improve the perfor-mance at the price of higher computational complexity of thereceiver.

For the OFDM system without the AP, the frequency-first mapping is more susceptible to the performance loss ofthe first OFDM symbol compared to the time-first mapping,particularly when the resolution of the ADC is low. When


Fig. 12. BLER as a function of SNR of various AGC schemes (time-first mapping).

Fig. 13. BLER as a function of SNR of various AGC schemes (frequency-first mapping).

the frequency-first mapping is implemented, the performanceloss of the first OFDM symbol significantly degrades theperformance of the first CB. When the time-first mapping isimplemented, the impact of the performance loss of the firstOFDM symbol on BLER is shared between all the CBs.

VII. CONCLUSION

In this paper, we propose a new subframe structure tocombat the IUI at the boundary of subframes. The CP of thefirst OFDM symbol in a subframe is proposed to include anAP. The overhead of the AP is amortized over the OFDMsymbols in a subframe and is usually negligible. The pro-posed scheme simplifies the implementation of the AGC. Thesimulation results show that the proposed scheme can providean advantage compared to the traditional schemes.

Minimizing power consumption is a goal of many systems[37], [38]. The power consumption of an ADC grows exponen-tially with the resolution. With the proposed subframe struc-ture, the resolution of the ADC needed by the OFDM systemscan be reduced. The proposed scheme also improves energyefficiency. As the cellular network evolves, the complexityof the architecture grows. It is more likely that there is alarge difference in the received powers between consecutivesubframes. The proposed scheme can guarantee the systemperformance in these challenging environments with a smalloverhead.

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Hao Wu received the M.S. degree in communicationand information systems from Tianjin Universityin 2009. He is currently a Senior Engineer withZTE, Inc., Shenzhen, China. His research interestsinclude wireless communications systems, digitalsignal processing, and error control coding. He hasauthored or co-authored several papers in interna-tional conference and journal. He is the inventor ofa number of patents.

Jun Li received the M.S. degree from the Nan-jing University of Science and Technology, Nanjing,China, in 2006. Since 2006, he has been a SeniorCommunication Engineer with ZTE, Inc., Shen-zhen, China. His research interests include digitalsignal processing, array processing, and basebandalgorithms.

Bo Dai received the M.S. degree from the HarbinInstitute of Technology, Harbin, China, in 2006. Heis currently with ZTE, Inc., where he is responsiblefor the standardization of the Internet of Things.Since 2006, he has been participating in the stan-dardizations of LTE R8/9/10/11/12/13/14/15 andNR in 3GPP. His main research interests includelink adaptation, access technology, control channeldesign, location technology, and power saving.

Yuan Liu received the B.S. and M.S. degrees fromthe Nanjing University of Science and Technology,Nanjing, China, in 2007 and 2009, respectively. Heis currently a Senior Engineer with ZTE, Inc., Shen-zhen, China. Since 2009, he has been participatingin the algorithm development of 3G/4G/5G. Hisresearch interests include signal processing, wirelesscommunications, channel estimation, and channelcoding.

analysis of the impact of agc on cyclic prefix length for

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