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IEICE TRANS. COMMUN., VOL.E100–B, NO.1 JANUARY 2017177
PAPERJoint Maximum Likelihood Detection in Far User ofNon-Orthogonal Multiple Access∗
Kenji ANDO†a), Student Member, Yukitoshi SANADA†b), and Takahiko SABA††c), Senior Members
SUMMARY Non-orthogonal multiple access (NOMA) enables multi-ple mobile devices to share the same frequency band. In a conventionalNOMA scheme, the receiver of a far user detects its desired signal withoutcanceling the signal for a near user. However, the signal for the near useracts as interference and degrades the accuracy of likelihood values for thefar user. In this paper, a joint maximum likelihood detection scheme forthe far user of the NOMA downlink is proposed. The proposed schemetakes the interference signal into account in calculating the likelihood val-ues. Numerical results obtained through computer simulation show that theproposed scheme improves the performance by from 0.2 dB to 3.1 dB forpower allocation coefficients of 0.2 to 0.4 at a bit error rate (BER) of 10−2
relative to the conventional scheme.key words: non-orthogonal multiple access, joint maximum likelihooddetection, successive interference cancelation
1. Introduction
Due to the rise in the penetration rate of mobile devices suchas smartphones and tablet PC, demands for higher data ratesand larger capacity have been increasing in cellular systems.The report released by ITU-R has shown that the amountof mobile data traffic will increase 1000 times by 2020 [1].Technical solutions to resolve the problems caused by thisexplosive traffic growth have been investigated, and candi-date system concepts for future radio access beyond LTE-Advanced have been discussed. One solution for increas-ing the capacity is non-orthogonal multiple access (NOMA)[2]–[16]. NOMA enables multiple mobile users to sharethe same frequency band. By sending signals with differenttransmission powers, a receiver can extract its desired signal.It has been shown that the total channel capacity increases ifa receiver can remove the overlaid interference signal [17].
In NOMA, mobile users that are located near and farfrom a base station are assigned the same frequency resourceand allowed to share it through a scheduling algorithm. Sincethe amount of propagation loss depends on the distance fromthe base station, the base station transmits the signal for thefar user with larger power than the signal for the near user.
Manuscript received March 11, 2016.Manuscript revised June 17, 2016.Manuscript publicized July 29, 2016.†The authors are with the Dept. of Electronics and Electrical
Engineering, Keio University, Yokohama-shi, 223-8522 Japan.††The author is with the Dept. of Computer Science, Chiba
Institute of Technology, Narashino-shi, 275-0016 Japan.∗The part of this paper is submitted to IEEE APWCS 2015.
a) E-mail: [email protected]) E-mail: [email protected]) E-mail: [email protected]
DOI: 10.1587/transcom.2016EBP3098
The receiver of the near user cancels the signal for the faruser by means of successive interference cancelation (SIC)and then detects its desired signal [6]–[15]. On the otherhand, the receiver of the far user demodulates the signalwithout canceling the signal for the near user and employsmaximum likelihood detection (MLD). This is because thesignal for the near user is expected to be attenuated and it isnot regarded as interference by the receiver of the far user.
However, the signal for the near user actually interfereswith the signal for the far user and degrades the accuracy oflikelihood values in the MLD. Thus, a joint detection schemein the receiver of the far user has been proposed [16]. In [16],the sum of the constellation constrained capacities (CCCs)of a NOMA downlink with the joint detection scheme in boththe near and the far users is derived. In deriving the CCCs,the signal for the near user is treated as probabilistic inter-ference. However, the derivation of CCCs does not assumethe superposition of the constellation points of the signalsfor the near and the far users. Thus, this paper investigatesdirect effects of the joint MLD in the far user of the NOMAsystem on the link-level performance with specific settingsof transmission parameters including modulation schemes,coding rates, and power allocation coefficients. These nu-merical results show that the joint MLD in the far user of theNOMA system works effectively with various transmissionparameter values.
This paper is organized as follows. Section 2 describesthe system model and the proposed scheme. In Sect. 3,the bit error rate (BER) curves obtained through computersimulation are presented. Sect. 4 gives our conclusions.
2. System Model
2.1 Non-Orthogonal Multiple Access Model
In this paper, a NOMA downlink is assumed as a systemmodel, in which two mobile users share the same frequencyband. A base station and each of mobile terminals areequipped with a single antenna. A block diagram of the basestation is presented in Fig. 1. In the LTE standard, a sys-tematic parallel concatenated convolutional code is adopted[18]. In a turbo encoder, two 8-state encoders and one inter-leaver are used. With the input of Ns bits, the turbo encodergenerates three length-Ns streams, d (0)
n , d (1)n , and d (2)
n . Theyare referred as the “Systematic”, “Parity 1”, and “Parity 2”streams, respectively. At the end of each stream, four tailbits for trellis termination are appended.
Copyright © 2017 The Institute of Electronics, Information and Communication Engineers
178IEICE TRANS. COMMUN., VOL.E100–B, NO.1 JANUARY 2017
Fig. 1 Block diagram of base station.
In order to support a higher data rate, bit puncturing isimplemented in the turbo codes. In the LTE standard, punc-turing is conducted in a rate matching (RM) block [18]. Inthe RM block, each of the three output streams is rearrangedin a sub-block interleaver. Afterward, a single output bufferwith the length of 3(Ns + 4) is filled by placing the rear-ranged “Systematic” bit stream in the beginning, followedby the two rearranged bit streams of “Parity 1” and “Par-ity 2” interlaced in a bit-by-bit fashion. The contents of thebuffer are then passed to a circular buffer for bit selection andpuncturing. The output of the circular buffer forms a singlebit stream with the length of 3(Ns +4). After bit puncturing,the RM block generates a single bit stream with the lengthof (Ns + 4)/r , where r is the code rate and the minimum ofr is 1/3. The outputs of the RM blocks for the near and thefar users are mapped to 2MnQAM and 2M f QAM symbolsthrough Gray coding, where Mn and Mf are the numbers ofbits per symbol of the near and the far users, respectively.
After symbol mapping, they are put into serial-to-parallel (S/P) converters and summed together on each sub-carrier. Here, Sn[k] and Sf [k] are the symbols to be trans-mitted for the near and the far users on the kth subcarrier.The transmit power is divided with the coefficients of α and(1 − α). The symbol to be transmitted on the kth subcarrieris composed of the sum of the symbols of the near and thefar users as follows:
S[k] =√αSn[k] +
√1 − αSf [k] (0 ≤ k ≤ N − 1),
(1)
where N is the size of the IDFT. After the IDFT andthe parallel-to-serial (P/S) conversion, the non-orthogonalOFDM signal is generated. The last part of each OFDMsymbol is replicated and inserted at the beginning of thesymbol as a guard interval (GI). The generated OFDM sig-nal is put into a transmit filter and is transmitted. At thereceiver side, the received signal first goes through a receivefilter. In an analog-to-digital (A/D) converter, the receivedsignal is digitized to discrete samples. The signal on the kthsubcarrier after the removal of the GI and the N-sample DFTis given as
Y [k] =N−1∑n=0y[n] exp
(− j
2πnkN
)= H[k]S[k] +W [k], (2)
Fig. 2 Conventional detection scheme in far user.
where y[n] is the nth received signal in the time domain,Y [k] is the received signal, H[k] is the frequency response,and W [k] is the noise in the frequency domain on the kthsubcarrier, respectively. The output of the DFT on the kthsubcarrier is sent to a detector to obtain soft information fora turbo decoder.
At the detector, the likelihood values for turbo decodingare calculated. After the likelihood calculation in the detec-tor, bit depuncturing is carried out. The likelihood sequenceis then passed to an inverse circular buffer. Afterward, thelikelihood sequence is divided into three streams that corre-spond to “Systematic”, “Parity 1”, and “Parity 2” streams,respectively. Each of the three output streams is rearrangedin a sub-block deinterleaver and is then put into the turbodecoder to obtain information bits.
2.2 Conventional Detection Scheme
In the NOMA system, the signals for the near and the farusers are superposed on each subcarrier. Since the signalpower of the far user is larger than that of the near user, theconventional detection scheme in the far user employs MLD.In the conventional detection scheme, the signal for the nearuser is expected to be attenuated and it is not regarded asinterference by the receiver of the far user.
The block diagram of the conventional detectionscheme in the far user is shown in Fig. 2. The likelihoodcalculations by the MLD are given as,
∆MLDf ,1 [k] =
∑S f [k]∈{S f } |
bfm=1
exp(− 1N0∥Y [k]
−H[k]√
1 − αSf [k]∥2), (3)
ANDO et al.: JOINT MAXIMUM LIKELIHOOD DETECTION IN FAR USER OF NON-ORTHOGONAL MULTIPLE ACCESS179
∆MLDf ,0 [k] =
∑S f [k]∈{S f } |
bfm=0
exp(− 1N0∥Y [k]
−H[k]√
1 − αSf [k]∥2), (4)
where∆MLDf ,1 [k] and∆MLD
f ,0 [k] are the sums of the likelihoodvalues for the mth (1 ≤ m ≤ Mf ) bit being “1” and “0” in thesymbol for the far user Sf [k] on the kth subcarrier, N0 is thepower spectrum density of the white Gaussian noise, Sf [k]is the symbol candidate for the far user on the kth subcarrier,and {Sf }|b f
m=1and {Sf }|b f
m=0are the sets of symbols of which
the mth bit is equal to “1” and “0”, respectively. FromEqs. (3) and (4), the log likelihood ratio (LLR) is calculatedas
L(bfm |Y [k]) = log
∆MLDf ,1 [k]
∆MLDf ,0 [k]
, (5)
where L(bfm |Y [k]) is the LLR of the mth bit of the symbol
obtained from the received signal Y [k] on the kth subcarrier.The LLR calculated as above is passed to the turbo decoderand then the information bits are recovered.
2.3 Codeword Level SIC in the Far User
The conventional detection scheme with the MLD in the faruser neglects the signal for the near user. However, when thesignal power for the near user is larger than the noise power atthe far user, interference owing to the signal for the near userdegrades the accuracy of the likelihood values. Meanwhile,in [6]–[15], the codeword level SIC is implemented in thereceiver of the near user. Thus, it is assumed here that thecodeword level SIC is also applied to the far user.
The block diagram of the codeword level SIC in thefar user is presented in Fig. 3. The receiver of the far useremploys the MLD and then obtains the decoded bits for thefar user. From the decoded bits, the receiver generates areplica signal for the far user. The receiver then subtracts thereplica signal for the far user from the received signal. Thereceived signal after the interference cancelation is given as
Y SICn [k] = Y [k]−H[k]
√1 − αSf [k], (6)
where Y SICn [k] is the received signal after the codeword level
SIC and Sf [k] is the replica signal for the far user on the kthsubcarrier.
The receiver of the far user carries out the MLD againstthe remaining signal. The likelihood calculations for thesignal for the near user are given as,
∆MLDn,1 [k] =
∑Sn[k]∈{Sn } |bn
m=1
exp(− 1N0∥Y SIC
n [k]
−H[k]√αSn[k]∥2), (7)
∆MLDn,0 [k] =
∑Sn[k]∈{Sn } |bn
m=0
exp(− 1N0∥Y SIC
n [k]
Fig. 3 Codeword level SIC in far user.
−H[k]√αSn[k]∥2), (8)
where∆MLDn,1 [k] and∆MLD
n,0 [k] are the sums of the likelihoodvalues for the mth (1 ≤ m ≤ Mn) bit of Sn[k] for the near useron the kth subcarrier, Sn[k] is the symbol candidate for thenear user on the kth subcarrier, and {Sn}|bn
m=1and {Sn}|bn
m=0are the sets of symbols of which the mth bit is equal to “1”and “0”, respectively. From the sum of the likelihood values,the LLR is calculated. The LLR is passed to the decoder andthen the decoded bits for the near user are obtained.
The codeword level SIC generates the replica signal forthe near user. Applying the codeword level SIC again, thereceived signal after the interference cancelation is given as
Y SICf [k] = Y [k]−H[k]
√αSn[k], (9)
where Y SICf
[k] is the received signal after the codeword levelSIC for the far user and Sn[k] is the replica signal for thenear user on the kth subcarrier. The receiver of the far usercarries out the MLD against the remaining signal to obtainthe decoded bits for the far user. The likelihood calculationsfor the far user are given as,
DMLDf ,1 [k] =
∑S f [k]∈{S f } |
bfm=1
exp(− 1N0∥Y SIC
f [k]
−H[k]√
1 − αSf [k]∥2), (10)
DMLDf ,0 [k] =
∑S f [k]∈{S f } |
bfm=0
exp(− 1N0∥Y SIC
f [k]
−H[k]√
1 − αSf [k]∥2), (11)
180IEICE TRANS. COMMUN., VOL.E100–B, NO.1 JANUARY 2017
where DMLDf ,1 [k] and DMLD
f ,0 [k] are the sums of the likeli-hood values for the mth bit being “1” and “0” in the symbolSf [k] on the kth subcarrier, respectively. From the sumof the likelihood values, the LLR is calculated as the samemanner as Eq. (5). The decoded bits for the far user are thendecoded.
2.4 Proposed Joint MLD Scheme
In the conventional scheme, the receiver of the far user em-ploys the MLD by neglecting the signal for the near user.Alternatively, as described in Sect. 2.3, the receiver may em-ploy the codeword level SIC by treating the signal for thenear user as the interference. On the other hand, in the pro-posed scheme, the receiver of the far user applies joint MLDto the received signal. The joint MLD treats the receivedsignal as the superposed signal of the near and the far userswith a larger number of constellation points. In the jointMLD, the signal for the near user is taken into account in thelikelihood calculation. The LLR is calculated with the coor-dinates of the candidate constellation points and the receivedsignal point in each symbol. It does not depend on the coderate of the signal for the near user because the far user doesnot decode the received signal for the near user. Thus, theperformance of the far user depends only on the code rate ofthe signal for the far user and the modulation schemes of thesignals for the near and the far users.
The block diagram of the proposed detection scheme inthe far user is shown in Fig. 4. The likelihood calculationsof the joint MLD are given as,
DJMLDf ,1 [k] =
∑Sn[k]∈{Sn },S f [k]∈{S f } |
bfm=1
exp(− 1
σ2 ∥Y [k]−H[k](√αSn[k])
+√
1 − αSf [k])∥2), (12)
DJMLDf ,0 [k] =
∑Sn[k]∈{Sn },S f [k]∈{S f } |
bfm=0
exp(− 1
σ2 ∥Y [k]−H[k](√αSn[k])
+√
1 − αSf [k])∥2), (13)
where DJMLDf ,1 [k] and DJMLD
f ,0 [k] are the sums of the likeli-hood values for the mth bit being “1” and “0” in the symbol
Fig. 4 Proposed joint MLD scheme in far user.
Sf [k] on the kth subcarrier, respectively. Since the signalsfor the near and the far users are taken into account at thesame time, the likelihood values are more accurate throughthe joint MLD. From Eqs. (12) and (13), the LLR is calcu-lated as
LJMLD (bfm |Y [k]) = log
DJMLDf ,1 [k]
DJMLDf ,0 [k]
, (14)
where LJMLD (bfm |Y [k]) is the LLR of the mth bit in the
received symbol of the far user obtained from the receivedsignal Y [k] on the kth subcarrier. The LLR calculated asabove is passed to the decoder and then the information bitsfor the far user are recovered.
2.5 Detection Complexity and Processing Delay
The difference of the detection complexity between the MLDand the joint MLD is the number of the candidate constella-tion points to be considered. The number of the constellationpoints in the MLD is equal to the modulation order of thesignal for the far user whereas the number of the constella-tion points in the joint MLD is the product of the modulationorders of the signals for the near and the far users.
Meanwhile, the MLD is also employed in the codewordlevel SIC. Even though it is applied three times, the detectioncomplexity of the MLD in the codeword level SIC is smallerthan that of the joint MLD. However, the codeword levelSIC also requires the turbo decoding three times and thereplica generation two times. These processes at least causea delay which is larger than that caused by the proposedscheme though the amount of delay depends largely on theimplementation of the decoding process.
3. Numerical Results
3.1 Simulation Conditions
Numerical results obtained through computer simulation arepresented in this section. Simulation conditions are shownin Table 1. An 8-state memory turbo code is employed andthe size of the interleaver is 4800 [18]. The code rates of thesignals for the near and the far users are selected from 1/3,1/2, 2/3, and 5/6 through the RM function. Encoded bits aremodulated with QPSK, 16QAM or 64QAM for the near userand QPSK for the far user on each subcarrier†. The powerallocation coefficient has been examined in a range of up to0.4 in [15]. Thus, the link-level performance of the receiverof the far user is evaluated under power allocation coefficientsof 0.1 to 0.4. In this paper, the power allocation coefficient,α, is set to 0.2 or 0.35 unless it is specified. The signals forthe near and the far users are superposed on the subcarrier toform the non-orthogonal signal. Other specifications such asthe channel bandwidth, the subcarrier spacing, the number†Different combinations of modulation orders in the near and
the far users are also examined, but the observed results show thesame tendency as those presented in the following sections.
ANDO et al.: JOINT MAXIMUM LIKELIHOOD DETECTION IN FAR USER OF NON-ORTHOGONAL MULTIPLE ACCESS181
Table 1 Simulation conditions.Forward error coding turbo codeInterleaver size 4800Code rate 1/3, 1/2, 2/3, 5/6Modulation scheme QPSK/16QAM/64QAMfor near user +OFDMModulation scheme QPSKfor far user +OFDMPower allocation α = 0.2, 0.35coefficientChannel Bandwidth 2.5 MHzSubcarrier spacing 15 kHzNumber of subcarriers 256Number of 151data subcarriersSampling frequency 3.84 MHzGI length 5.21 µs (1st symbol)
4.69 µs (2nd-7th symbols)Decoding algorithm Log-MAP algorithmDecoding iterations 8Channel model 6 Taps GSM-TU ModelChannel estimation IdealNumber of trials 4.8 × 105 bits
of DFT/IDFT points, and the sampling frequency followthose of the LTE standard. The channel bandwidth is set to2.5 MHz and the subcarrier spacing is set to 15 kHz. Thenumber of DFT/IDFT points is set to 256 and 151 subcarriersare used for data transmission. The sampling frequency isset to 3.84 MHz. The guard interval is set to 5.21 µs forthe first symbol and 4.69 µs for the following six symbols.The Log-MAP algorithm is employed for decoding and thenumber of decoding iterations is eight. The channel model isassumed to be the 6-tap GSM typical urban (TU) model [19].The channel response on each subcarrier is assumed to beideally estimated. As detection schemes, MLD, codewordlevel SIC, and joint MLD are employed. The number oftrials is set to 4.8 × 105 bits for each plot. Furthermore,the performance of an orthogonal multiple access (OMA)scheme without the superposition of the signal for the nearuser is also presented for comparison [15].
3.2 Comparison of BER Performance
The BER performance versus Eb/N0 in the far user ispresented in Figs. 5–8. Encoded bits are modulated with16QAM or 64QAM for the near user and QPSK for the faruser on each subcarrier. The power allocation coefficient, α,is set to 0.2 or 0.35 in Figs. 5–8.
The BER performance versus Eb/N0 in the far user isshown in Fig. 5. The code rate of the signal for the far useris set to 1/3. The proposed scheme outperforms the MLD by0.2 dB at a BER of 10−2. This is because the joint MLD takesthe signal for the near user into account when calculating thelikelihood values, whereas the MLD neglects it. On the otherhand, the performance of the codeword level SIC with a coderate of 1/3 in the near user is worse by 0.2 dB at a BER of10−2 as compared with that of the MLD. Different code ratesof the signals for the near user such as 1/2 and 5/6 are alsoexamined and the same BER tendency has been observed.
Fig. 5 BER vs. Eb/N0 in far user (near user: 16QAM, far user: QPSK,code rate of far user: 1/3, power allocation coefficient α = 0.2).
Fig. 6 BER vs. Eb/N0 in far user (near user: 16QAM, far user: QPSK,code rate of far user: 1/3, power allocation coefficient α = 0.35).
Although the MLD is also employed in the codeword levelSIC, the likelihood values are not accurate, which results inincorrect replica signals. This is due to the attenuation ofthe signal power as well as the residual interference aftercancelation. Thus, the cancelation of the signal for the nearuser increases the interference to the signal for the far user.
The BER performance versus Eb/N0 in the far user witha power allocation coefficient of 0.35 is shown in Fig. 6. The
182IEICE TRANS. COMMUN., VOL.E100–B, NO.1 JANUARY 2017
Fig. 7 BER vs. Eb/N0 in far user (near user: 16QAM or 64QAM,far user: QPSK, code rate of far user: 1/2, power allocation coefficientα = 0.2).
code rate of the signal for the far user is set to 1/3. For apower allocation coefficient of 0.35, the proposed schemeoutperforms the MLD by 1.5 dB at a BER of 10−2. Theimprovement in Eb/N0 due to the proposed scheme with apower allocation coefficient of 0.35 is larger than that with apower allocation coefficient of 0.2. This is because when thepower allocation coefficient increases, the interference to thesignal for the far user becomes large. The receiver with theMLD suffers from the interference while the receiver with thejoint MLD can calculate the likelihood values accurately. Onthe other hand, the performance of the codeword level SICwith a power allocation coefficient of 0.35 is worse by 2.8 dBat a BER of 10−2 as compared with that of the MLD. Theamount of the degradation with a power allocation coefficientof 0.35 is larger than that with a power allocation coefficientof 0.2. This is because the MLD is also employed at the firststage in the codeword level SIC and then decoding errorsoccur due to the large interference. In the codeword levelSIC, decoding errors increase the residual interference aftercancelation.
The BER performance versus Eb/N0 in the far userwith a code rate of 1/2 in the signal for the far user is shownin Fig. 7. For a code rate of 1/2, the proposed scheme out-performs the MLD by 0.5 dB at a BER of 10−2. On theother hand, the performance of the codeword level SIC witha code rate of 1/2 in the signal for the near user is worse by0.8 dB at a BER of 10−2 as compared with that of the MLD.The performance of the codeword level SIC for the case of64QAM in the signal for the near user is worse by 0.6 dB at aBER of 10−2 as compared with that of the MLD. The BER isworse for the case of 16QAM in the signal for the near user.The residual interference after cancelation due to decoding
Fig. 8 BER vs. Eb/N0 in far user (near user: 16QAM, far user: QPSK,code rate of far user: 5/6, power allocation coefficient α = 0.2).
errors is smaller for the case of 64QAM than for the caseof 16QAM though the BERs of the signal for the near userafter the MLD are almost equivalent as shown in Fig. 13 inSect. 3.5. This is because the minimum distance between thesignal constellation points is smaller for the case of 64QAMin terms of the same symbol power. Thus, the influence ofdecoding errors for the case of 64QAM is smaller than thatfor the case of 16QAM.
The BER performance versus Eb/N0 in the far user witha code rate of 5/6 is also shown in Fig. 8. For a code rate of5/6, the proposed scheme outperforms the MLD by 0.5 dB ata BER of 10−2. The performance of the codeword level SICis worse and the BER curve shows the error floor with theincrease in Eb/N0. The reason is that the error correctioncapability is too low for a code rate of 5/6 and bit errorsremain after decoding of the signal for the near user.
3.3 Effect of Code Rate
The required Eb/N0 at a BER of 10−2 versus the code rateis shown in Fig. 9. As the code rate increases, the con-ventional detection scheme requires more Eb/N0 than theproposed scheme. This is because when the code rate in-creases, the error correction capability becomes low. Asshown in Sect. 3.2, the performance of the codeword levelSIC is worse than that of the MLD.
3.4 Effect of Power Allocation Coefficient
The required Eb/N0 at a BER of 10−2 versus the power al-location coefficient, α, is shown in Fig. 10. When the powerallocation coefficient is large, the signal for the near userinterferes with the signal for the far user more significantlyand the required Eb/N0 increases. The improvement in the
ANDO et al.: JOINT MAXIMUM LIKELIHOOD DETECTION IN FAR USER OF NON-ORTHOGONAL MULTIPLE ACCESS183
Fig. 9 Required Eb/N0 at BER of 10−2 versus code rate (near user:16QAM, far user: QPSK, power allocation coefficient α = 0.2).
Fig. 10 Required Eb/N0 at BER of 10−2 versus power allocation coef-ficient α (near user: 16QAM, far user: QPSK, code rate: 1/3).
required Eb/N0 due to the joint MLD becomes larger whenthe power allocation coefficient increases. Concretely, theamount of the improvement is 0.2 dB under the conditionthat the power allocation coefficient is set to 0.2 and it be-comes 0.8 dB, 1.5 dB, and 3.1 dB when the power allocationcoefficient is set to 0.3, 0.35, and 0.4, respectively. It is clearthat the proposed scheme is more effective when larger inter-ference is caused by the signal for the near user. The amountof the performance deterioration of the codeword level SICis especially large when the power allocation coefficient isat around 0.3. With a power allocation coefficient of 0.3,
Fig. 11 Constellation points of superposed signals for near and far users(near user: 16QAM, far user: QPSK, power allocation coefficient α = 0.3).
Fig. 12 Required Eb/N0 at BER of 10−2 versus modulation schemes fornear user (power allocation coefficient α = 0.2, code rate: 1/2).
some of the constellation points in the superposed signal areclose to each other as shown in Fig. 11. Therefore, decodingerrors occur easily, which results in incorrect interferencecancelation.
3.5 Effect of Modulation Scheme of Near User
The required Eb/N0 at a BER of 10−2 versus the variousmodulation schemes for the near user is presented in Fig. 12.The amount of the improvement due to the joint MLD forthe case of 16QAM in the signal for the near user is largerthan that for the case of QPSK. The amplitude of QPSK isconstant while that of 16QAM varies. The receiver of thefar user occasionally suffers from larger interference owingto 16QAM symbols even though the mean power of the in-terference is the same. The variation of the interference am-
184IEICE TRANS. COMMUN., VOL.E100–B, NO.1 JANUARY 2017
Fig. 13 BER performance after first codeword level SIC vs. Eb/N0 (faruser: QPSK, power allocation coefficient α = 0.2, code rate: 1/2).
plitude deteriorates the BER performance due to the MLD.This phenomenon is also observed in the case with 64QAM.The proposed scheme is then more effective when a higherorder modulation scheme is employed for the near user.
As for the codeword level SIC, the required Eb/N0 forthe case of QPSK in the signal for the near user is smaller thanthose for the cases of 16QAM and 64QAM in Fig. 12. TheBER performance for the case of 64QAM in the signal for thenear user is better than that for the case of 16QAM as shownin Fig. 7 and the required Eb/N0 for the case of 64QAM issmaller than that for the case of 16QAM in Fig. 12. Thefollowing two factors affect the performance of the requiredEb/N0 versus modulation schemes in the signal for the nearuser in the codeword level SIC.
The BER performance after the first codeword levelSIC versus Eb/N0 is shown in Fig. 13. As shown in Fig. 13,the BER performance of the signal for the near user for thecases of 16QAM and 64QAM is worse than that for the caseof QPSK. The amplitude of the QPSK signal is constant,whereas those of the 16QAM and the 64QAM signals vary.For the cases of 16QAM and 64QAM in the signal for thenear user, the receiver of the far user suffers from largeramplitude symbols as compared with the receiver for thecase of QPSK even though the mean power of the signal isthe same at the input of the codeword level SIC. Therefore,for the cases of 16QAM and 64QAM, decoding errors occurmore easily than for the case of QPSK, which results inincorrect interference cancelation.
Furthermore, the minimum distance between the signalconstellation points is another factor as explained in Sect. 3.2.The BER performance is better for the case of 64QAM inthe signal for the near user than for the case of 16QAM inFig. 7. This is because the minimum distance between the
Table 2 Conditions of system-level simulation.
Cell layout 19 hexagonal cell siteInter-site distance 500 mMinimum distance 35 m
between users and cell siteDistance dependent path loss 128.1+37.6log10(r) dB
r : Distance [km]Shadowing standard deviation 8 dB
Shadowing correlation 0.5Channel model Six-path Rayleigh
Number of users per cell U = 5, 10, 20, 30Scheduling algorithm PF scheduling
Time interval 100Transmit power 42 dBm
Power allocation coefficient 0.05–1.00 (0.05 step)Receiver noise density −174 dBm/Hz
System bandwidth 4.32 MHzResource block bandwidth 180 kHz
Number of RBs 24Modulation scheme QPSK, 16QAM,
64QAMUser drop 400
Trial per user drop 30Number of symbols per trial 100
signal constellation points is smaller for the case of 64QAMin terms of the same symbol power in average. Thus, the in-fluence of decoding errors for the case of 64QAM is smallerthan that for the case of 16QAM.
3.6 System-Level Aspect
The system-level simulation of the NOMA downlink withthe joint detection scheme in both the near and the far usersis conducted as described in [20]. The conditions of thesystem-level simulation are presented in Table 2. A 19-hexagonal macrocell model is assumed. The cell radius ofthe macrocells is set to 289 m (inter-site distance = 500 m).Users are dropped randomly with a uniform distribution. Asa propagation model, distance-dependent path loss with a de-cay factor of 3.76 and lognormal shadowing with a standarddeviation of 8 dB are assumed. The shadowing correlationbetween the sites is set to 0.5. A six-path Rayleigh fadingchannel model with an exponential decay profile is assumed.The root-mean-square (RMS) delay spread is set to 1 µs andthe maximum Doppler frequency is set to 5.55 Hz. Thetransmit power is set to 42 dBm and the receiver noise den-sity is set to −174 dBm/Hz. The power allocation coefficientis selected from between 0 and 1 with a step size of 0.05. Inthe OMA scheme, it is set to 1.0. The throughputs of theconventional and proposed schemes are evaluated with CCCthrough Monte Calro simulation [16]. Proportional fairness(PF) scheduling is applied and the time interval of the PFscheduling is set to 100 [21]. The number of resource blocks(RBs) is 24 and the number of subcarriers in one RB is 12.The system bandwidth is 4.32 MHz. A QPSK, 16QAM, or64QAM symbol is transmitted on each subcarrier. The num-ber of user drops is 400 and the number of trials per user
ANDO et al.: JOINT MAXIMUM LIKELIHOOD DETECTION IN FAR USER OF NON-ORTHOGONAL MULTIPLE ACCESS185
Fig. 14 Number of users in each cell vs. system throughput.
Fig. 15 PDF of power allocation coefficient with the NOMA scheme(Transmit power: 42 dBm, 30 users).
drop is 30. The channel response is renewed each trial. Thenumber of transmitted symbols per trial is 100 and the last80 symbols are used for throughput evaluation.
The relationship between the number of users in eachcell versus the system throughput per subcarrier is shownin Fig. 14. Here, 19 hexagonal cell sites are assumed andproportional fairness scheduling is employed for user assign-ment. The numerical results obtained through system-levelsimulation show that the joint MLD in the far user increasesthe system throughput by 0.3 bit/subcarrier.
The probability distribution function (PDF) of thepower allocation coefficient, α, is presented in Fig. 15. Theprobability that the power allocation coefficient is within therange of 0.25 to 0.5 is higher in the far user with the jointMLD whereas it is 0 in the far user without joint MLD. The
reason is that the required Eb/N0 reduces with the proposedscheme for the same BER in that range of the power allo-cation coefficient as presented in Fig. 10. The PF schedul-ing then selects the power allocation coefficient with higherprobabilities at the range of 0.25 to 0.5.
4. Conclusions
In this paper, a joint MLD scheme in the NOMA downlinkfor the far user has been proposed and its BER performanceinvestigated. In the conventional NOMA system, the receiverof the far user employs the MLD and neglects the signal forthe near user even though its interference degrades the accu-racy of likelihood values. On the other hand, the proposedjoint MLD scheme takes the signal for the near user intoaccount when calculating the likelihood values. It improvesthe accuracy of the likelihood values for the signal for the faruser and thus improves its BER. Numerical results obtainedthrough computer simulation have shown that the proposedscheme improves the performance by from 0.2 dB to 3.1 dBfor power allocation coefficients of 0.2 to 0.4 at a BER of10−2 relative to the conventional scheme the conventionalscheme. In addition, the proposed scheme is more effectiveif the power allocation coefficient increases or a higher ordermodulation scheme is employed for the near user.
Acknowledgments
This work is supported in part by a Grant-in-Aid for ScientificResearch (C) under Grant No.25420382 from the Ministryof Education, Culture, Sport, Science, and Technology inJapan.
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Kenji Ando was born in Shizuoka, Japan in1992. He received his B.E. degree in electron-ics engineering from Keio University, Japan in2015. Since April 2015, he has been a gradu-ate student in School of Integrated Design Engi-neering, Graduate School of Science and Tech-nology, Keio University. His research interestsare NOMA system.
Yukitoshi Sanada was born in Tokyo in1969. He received his B.E. degree in electricalengineering from Keio University, YokohamaJapan, his M.A.Sc. degree in electrical engi-neering from the University of Victoria, B.C.,Canada, and his Ph.D. degree in electrical engi-neering from Keio University, Yokohama Japan,in 1992, 1995, and 1997, respectively. In 1997he joined the Faculty of Engineering, Tokyo In-stitute of Technology as a Research Associate.In 2000 he joined Advanced Telecommunica-
tion Laboratory, Sony Computer Science Laboratories, Inc., as an associateresearcher. In 2001 he joined Faculty of Science and Engineering, KeioUniversity, where he is now a professor. He received the Young EngineerAward from IEICE Japan in 1997. His current research interests are insoftware defined radio, cognitive radio, and OFDM systems.
Takahiko Saba was born in Tokyo in 1969.He received his B.E., M.E., and Ph.D. degrees allin electrical engineering from Keio University,Yokohama, Japan in 1992, 1994, and 1997, re-spectively. From 1994 to 1997, he was a SpecialResearcher of Fellowships of the Japan Societyfor the Promotion of Science for Japanese Ju-nior Scientists. From 1997 to 1998, he was withthe Department of Electrical and Computer En-gineering, Nagoya Institute of Technology, Na-goya, Japan, as a Research Assistant. From 1998,
he joined the Department of Computer Science, Chiba Institute of Technol-ogy, Narashino, Japan, where is now a Professor. In 2008, he was a Visit-ing Associate Professor of University of British Columbia, B.C., Canada.From 2015, he is a Vice President of Chiba Institute of Technology. He re-ceived Distinguished Contributions Award from Communications Societyof IEICE in 2009 and 2013. From 2013 to 2015, he was an Editor-in-Chiefof IEICE Transactions on Communications (Japanese Ed.). His currentresearch interests include wireless communications and physical layer se-curity. He is a member of IEEE.
