IEEE ICC 2015 - Wireless Communications Symposium

Performance of Non-orthogonal Multiple Access with a Novel Interference Cancellation Method Huseyin Haci and Huiling Zhu School of Engineering and Digital Arts, University of Kent, Canterbury, CT2 7NT, United Kingdom Emails: {hh219, h.zhu}@kent.ac.uk. Abstract—In this paper, a novel interference cancellation technique is proposed for asynchronous non-orthogonal multiple access (NOMA) systems and the performance is theoretically investigated in a small cell uplink scenario. It is shown that unlike synchronous communications, at uplink transmission, NOMA users’ performance strongly depends on the relative time offset between interfering users.

I. I NTRODUCTION Mobile communications has been developing very fast [1]–[6] due to the popularity of smart devices and video applications. Wireless multiple access techniques are crucial for mobile communications performance. Multiple access to orthogonal frequency division multiplexing (OFDM)-based channel can be realized in two ways – as orthogonal multiple access (OMA) or non-orthogonal multiple access (NOMA) [7]. Orthogonal frequency division multiple access (OFDMA) [8], [9] is an OFDM-based OMA technique, which is widely adopted in current wireless systems. In OFDMA [10], [11] systems by allocating each subcarrier to a user with the best channel condition on it, it can maximize the system throughput through multiuser diversity gain. Despite high system throughput OFDMA has major problems in achieving very high datarate. The first problem is that it does not allow frequency reuse within the same cell due to strong interference [7]. This severely limits cell throughput. The second problem is the large peak-to-average power ratio (PAPR) especially when the number of subcarriers is large and/or high order modulation is used. Unlike OFDMA, NOMA techniques can allocate one subcarrier to more than one user at the same time within a cell. Reuse of subcarriers provides higher throughput. Not only the user which has the best channel state information (CSI) but also other users can use the subcarrier. Moreover, it has been shown that high PAPR problem can be overcomed with the aid of peak-clipping and compensation of NOMA signals [12]. This comes from an inherent property of NOMA receiver. Therefore NOMA can overcome the two major problems of OFDMA and is an advantageous technique for future mobile communications to achieve high data-rate. Superposition coding (SC) is an effective technique to increase capacity in the NOMA system [13]. By using SC, user multiplexing is performed at power domain and multiple users can transmit their signals simultaneously in the same subcarriers. These users are called SC users. At uplink communications, the base station (BS) detects each user’s signal, starting with the user which has highest signal to noise ratio (SNR), in a descending order. Since successive interference cancellation (SIC) algorithm suppresses interference from strong (earlier detected) signals for relatively weaker (yet to be detected) signals, it has been shown in [7] that NOMA with SC-SIC has superior performance to OFDMA in terms of total system throughput and cell-edge user throughput. [14] has proven that

978-1-4673-6432-4/15/$31.00 ©2015 IEEE

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among all possible signaling methods, SC modulation (SCM) maximizes the output signal to interference plus noise ratio (SINR) in the linear minimum mean square error (MMSE) estimation. [15] studied the optimal number of SC users on each subcarrier, and stated that there is a high probability to obtain most of the gain over OMA when few (two to three) users are superposition coded on a subcarrier. So far, the researches on NOMA only consider timesynchronous transmissions. Synchronous transmission is feasible for downlink since the BS controls transmission for all users. However perfect synchronization for all users is impractical for uplink since users are geographically distributed and the mobile environment is dynamic. Asynchronism in the received signal causes crucial disturbances to the SC-SIC. In the synchronous case, regarding a subcarrier, the OFDM symbols from SC users are aligned in time domain. However in asynchronous case, OFDM symbols from the SC users are time misaligned. Synchronous detection and succesive interference cancellation (Conv-SIC) techniques are performed based on the information on only a single symbol from each SC user. However, the asynchronous communications requires information on multiple symbols for detection and interference cancellation (IC). Otherwise, the system performance is significantly degraded if complete information of interfering signals are unknown in asynchronous communications. Therefore, it is important to investigate NOMA in asynchronous communications. To address this challenge, techniques that are able to provide complete interference information for detection and IC are needed. So far, the literature on SC-SIC uplink communications is very limited. There is no work available addressing asynchronous communications with SC-SIC. Further, it is not straightforward to apply asynchronous communication techniques proposed for OFDMA [16], [17] to SC-SIC. This is because asynchronism has different effects on OFDMA and SCSIC. Therefore, novel communication techniques are needed for future high data rate mobile communications. A novel technique that addresses asynchronous SC-SIC is proposed in this paper. It constructs so called ”IC triangles”, which contains multiple, adjacent symbols from interfering users and performs SIC to IC triangles to obtain complete information of and suppress the interference signals. With complete information, the performance of detection and SIC performance improves substantially, which leads to the improvement of reliability and capacity in uplink communications. II. S YSTEM M ODEL In this paper, an uplink NOMA communication system with a BS serving a number of geographically distributed users is considered, as shown in Fig. 1 (a). The system uses OFDM to divide the broadband channel into N narrowband subchannels. Each subchannel contains one subcarrier. Each subcarrier

IEEE ICC 2015 - Wireless Communications Symposium

Small cell environment

BS

sample transmitted from user k on subcarrier i at time n−mk . p hk,i [n] = (dk )−λ αk,i [n]ejθk,i [n] denotes the CSI of user k on subcarrier i at time n, where dk represents the distance between the BS and user k, λ is the the path loss exponent, and αk,i [n] and θk,i [n] denote magnitude and phase shift of multipath fading at time n for user k on subcarrier i. Rayleigh fading that is independent and identical for different users is assumed for characterising multipath effect. θk,i [n] is uniformly distributed over [0, 2π], at time n. The coherence time of the channel is assumed to be much larger than the symbol time and hk,i [n] is fixed during a scheduling period [19], [20]. Therefore index ”n” is omitted and hk,i is used to denote the CSI. ni [n] is the additive white Gaussian noise (AWGN) with double-side power spectral density N0 /2. 𝑦𝑛 Symbol detection for subcarrier 0

Bus for 𝑦[𝑛] Step 1: detection for user 1*

SIC

Symbol detection for subcarrier 𝑖

𝑌1∗ [𝑖, ] Symbol detection

Step K: detection for user K*

𝑌𝐾 ∗ [𝑖, ] Symbol

SIC

detection

𝑋1∗ [𝑖, ]

(t)

𝑋𝑘 [𝑖, ] ℎ𝑘

is accessed by K NOMA users. It is envisioned that NOMA is a promising multiple access technology for future mobile communications in conjuction with beamforming technology in small cell environment, where there are small number of users at each beam [18]. Therefore, if users using NOMA are served by one beam, K can be assumed to be a small number, e.g. up to three users. Due to different distance and the dynamic channel from users to the BS, the asynchronous communication is considered. Received signal structure in one subcarrier is illustrated by Fig. 1 (b), where corresponding OFDM symbols of three users are shown in time domain. In Fig. 1 (b), ς = {s − 1, s, s + 1} represents the set of index of three adjacent OFDM symbols arrived at the BS from three SC users. It can be seen that the arrival times of different SC users are not aligned. Accordingly, a symbol from a user overlaps with adjacent symbols from every other SC users. Assuming OFDM symbol duration is the same for all users, a symbol of a user overlaps with two symbols from every other SC users. For example, if user 2 is the reference user, its time offset is larger than user 1’s but smaller than user 3’s. This makes symbol s of user 2 partially overlap with symbols s and (s+1) of user 1 and with symbols (s − 1) and s of user 3. Obviously to carry out IC, the information of two symbols of other SC users is needed.

𝑋𝐾∗ [𝑖, ]

𝑋𝑘 [𝑖, ] Bus for a priori estimates 𝐗𝐤 𝐢,

Symbol detection for subcarrier (N-1)

user 1*: highest SINR user user K*: Kthth highest SINR user

users 3

Near user

Fig. 2. s

Time offset of user 1

Middle user

A beam

Time offset of user 3 2 Time offset of user 2 1

s+1

symbol at time s-1 symbol at time s symbol at time s+1

Far user

symbol time

(a) Uplink NOMA commu-(b) Received signal structure at time donications system. main. Fig. 1. Illustration of uplink NOMA communications system and structure of received symbols for SC users.

The principles of SC-SIC based transmitter and receiver are presented in the following. At the transmitter of user k, the time domain representation of the output signal is given by inverse fast Fourier transform (IFFT), N −1 p 1 X xk [n] = √ Xk [i, s]· pk [i, s]·ej2πin/N , 0 ≤ n ≤ N −1, N i=0 (1) where xk [n] is the nth time sample of the signal, Xk [i, s] is the sth complex symbol (e.g. p quadrature amplitude modulation mapped) in subcarrier i and pk [i, s] is the transmit power. Fig. 2 shows the block diagram of the BS receiver structure. At the BS receiver, the baseband received signal is represented by a time sample sequence {y[n], 0 ≤ n ≤ N − 1}, given by

y[n] =

N −1 X

yi [n], 0 ≤ n ≤ N − 1,

(2)

i=0

where yi [n] is given by X yi [n] = xk,i [n−mk ]·hk,i [n]+ni [n], 0 ≤ n ≤ N −1, (3) k∈Ωi

where Ωi denotes the set of SC users on subcarrier i, mk , 0 ≤ mk ≤ N − 1, is the discrete time offset of user k relative to the BS reference time and xk,i [n − mk ] represents signal

2913

Block diagram of the BS receiver.

At the receiver, y[n] contains all orthogonal subcarriers, so that processing for symbol detection on each subcarrier is independent and can be done in parallel. K steps of detection is applied in descending SNR order to estimate symbols of K users. Step 1 is used to detect the user, called 1∗ , which has the highest SNR, and other users (k ∈ Ωi , k 6= 1∗ ) are interfering users, which affects the accuracy of symbol detection and cause high bit errror rate (BER) for user 1∗ . Therefore, in this step, after applying fast Fourier transform (FFT) to {y[n], 0 ≤ n ≤ N − 1} to obtain frequency component Y [i, s] for symbol s on subcarrier i, the first function at frequencydomain signal processing is to apply SIC, in order to suppress interference, which requires a priori information (estimate) ˆ k [i, s] denotes estimate of symbols from interfering users. X of s interfering symbol from user k on subcarrier i. Due to asynchronism symbol information of {s−1, s+1} are required. This information is provided through a bus that stores a priori ˆ k [i, ς], 1 ≤ k ≤ ˆ k [i, ς] = {X estimated symbols of users, X K, ς ∈ {s−1, s, s+1}}. SIC reconstructs interfering signals by ˆ k [i, ς] with the CSI and time offset of interfering multiplying X user k. Reconstructed signals are then removed from Y [i, s] for user 1∗ to obtain a cleaned version, denoted as Y˜1∗ [i, s]. ˆ 1∗ [i, s] from At symbol detection, MMSE equalizer provides X ˜ Y1∗ [i, s] that minimize distortion on the received signal by the combined effect of the channel and residual interference after ˆ 1∗ [i, s] is provided to symbol de-modulator to obtain SIC. X ˆ k [i, ς]. Once output bit stream for user 1∗ and to the bus X ˆ 1∗ [i, s] is included at X ˆ k [i, ς] it can be used by SIC at X later detection steps to clean Y [i, s].This completes symbol detection in step 1. Signal processing for subcarrier i continues by detecting symbol of next user which has the second highest SNR at step 2 and then detection order continues similarly until step K. With symbols of all K users estimated, the SC-SIC based

IEEE ICC 2015 - Wireless Communications Symposium

symbol detection processing is completed for symbol s. Then signal processing advance in time to consider next symbol sequence and above procedure is repeated. III. A NALYSIS A novel technique called triangular SIC (T-SIC) is proposed in this paper for asynchronous SC-SIC systems. SIC is performed in each symbol period, before the symbol detection. Being limited to a single symbol period, only information of symbol s of interfering users can be made available to SIC. However for the sth symbol of a user there may be interference from the (s − 1)th and/or (s + 1)th symbol of other users. T-SIC aims to provide complete information of interfering signals to SIC to achieve superior performance. TSIC follows a new approach and detect symbols from multiple indexes {s, (s + 1), · · · , (s + K − 1)} of stronger users before detecting symbol of a weaker user. At SC, interference that can significantly distort the desired signal are from the symbols of users with stronger signal. Table 1 and Fig. 3 demonstrates the ”triangular” steps of T-SIC algorithm to detect symbol s of three SC users and the triangular shift to advance to the next symbol index in time, as follows. At step 1, sth symbol is detected for user 1∗ with the highest SNR. At this stage, only partial information of interference is available, i.e. the (s−1)th symbols of interfering users are a priori detected but sth symbols are not. However, since unknown signals are from weaker users, sth symbol of user 1∗ can still be correctly detected with high probability. Then, at step 2, (s + 1)th symbol of user 1∗ is detected, since in order to detect a symbol of user 2∗ all symbols of user 1∗ that overlaps with it need to be a priori detected. At step 3, sth symbol of user 2∗ is detected. To detect sth symbol of user 3∗ , (s + 1)th symbol of user 2∗ need to be a priori detected and to detect this symbol, (s + 2)th symbol of user 1∗ need to be detected. Therefore, at step 4 (s + 2)th symbol of user 1∗ is detected and at step 5 (s + 1)th symbol of user 2∗ is detected. All symbols of stronger users that overlap with sth symbol of user 3∗ have been a priori detected, so at step 6 this symbol is detected. Order of detection steps are provided at table 1 and marked with a number shown on symbols at Fig. 3. Symbols marked with number 1-6 are called as ”IC triangle” for symbol s. Once processing on IC triangle for sth symbol is completed, the IC triangle shifts (advances) in time by one symbol index. Table 1 Step Step Step Step Step Step

Detection and IC steps of T-SIC algorithm. 1. Detect sth symbol of user 1∗ . 2. Detect (s + 1)th symbol of user 1∗ . 3. Detect sth symbol of user 2∗ . 4. Detect (s + 2)th symbol of user 1∗ . 5. Detect (s + 1)th symbol of user 2∗ . 6. Detect sth symbol of user 3∗ .

user 3* user 1* m1*

m3*

6

9

3

m2*

2

4

s

s+1

s+2

11 7 s+3

+ ni [n + mk∗ ],

0 ≤ n ≤ N − 1,

(4)

where p 1 xk,i [n+mk∗ −mk ] = √ ·Xk [i, ς]· pk [i, ς]·cos (2πiτk /N ) , N (5) (s − 1), if n + mk∗ − mk < 0 ς = s, (6) if 0 ≤ n + mk∗ − mk ≤ N − 1 , (s + 1), if n + mk∗ − mk > N − 1 and τk = (N +(n+mk∗ −mk ))modN . (6) and τk provides the transmitted symbol index ς and the time instance of signals at yi [n + mk∗ ]. To obtain the frequency component for symbol s on subcarrier i, {yi [n + mk∗ ], 0 ≤ n ≤ N − 1} is passed through FFT ,given by N −1 1 X yi [n + mk∗ ] · cos (−2πin/N ) , Y [i, s] = √ N n=0 p = Xk∗ [i, s] · pk∗ [i, s] · hk∗ ,i + η[k ∗ , i] + N [i], (7)

where the first term at the right hand side (RHS) of (7) is the desired signal, η[k ∗ , i] represents the total frequency-domain interference for user k ∗ on subcarrier i, given by p −1 X NX pk [i, ς] Xk [i, ς] · √ η[k ∗ , i] = · gk,i , (8) N k∈Ωi n=0 k6=k∗

where gk,i = hk,i · cos (2πi(mk∗ − mk )/N ), and N [i] is frequency-domain AWGN on subcarrier i. The cos(·) term at (8) is due to the mismatch of FFT filter’s time component n and the incoming interference signals’ time component τk . Next operation at SIC block is to reconstruct and substract interfering signals to obtain the cleaned version of frequency component, given by X Y˜k∗ [i, s] = Y [i, s] − Iς,k · ηˆς,k [k ∗ , i], (9) Iς,k is the indicator parameter that shows if employed SIC technique exploits a priori estimated information from {(s − 1), s, (s + 1)}th symbols of interferers, given by 0, for Conv-SIC Is−1,k , Is+1,k = (10) 1, for T-SIC,

15

8

1

processing triangle

Fig. 3.

12

5

k∈Ωi k6=k∗

k∈Ωi k6=>k∗

users

user 2*

Referring to the receiver structure shown at Fig. 2, suppose signal processing is taking place for symbol s of user k ∗ on subcarrier i. T-SIC set user k ∗ as the time reference user, then N discrete time samples taken from y(t) can be expressed in terms of desired and interfering signals by X yi [n + mk∗ ] = xk∗ ,i [n]hk∗ ,i + xk,i [n + mk∗ − mk ]hk,i

time samples

triangular shift pattern

T-SIC signal processing steps.

To further present the principle and the performance of T-SIC, quantitative analysis is provided in the following.

2914

and Is,k = 1 for both SIC techniques. ηˆς,k [k ∗ , i] is the reconstructed interference signal from estimate of ς th symbol of user k on subcarrier i, given for each possible overlapping symbol {s − 1, s, s + 1} by p (mk −mk∗ )−1 X pk [i, s − 1] ∗ ˆ ηˆs−1,k [k , i] = Xk [i, s − 1] · · gk,i , N n=0 (11)

IEEE ICC 2015 - Wireless Communications Symposium

min{N −1,N −(mk∗ −mk )−1}

X

ηˆs,k [k ∗ , i] =

p ˆ k [i, s]· X

n=max{0,mk −mk∗ }

pk [i, s] ·gk,i , N (12)

+

p ˆ k [i, s+1]· pk [i, s + 1] ·gk,i . X N

(13) The theoretical analysis of SC-SIC systems are based on so called ”onion pealing” or ”stripping aided detection” [12], where it is assumed that the interference from priori detected symbols can be perfectly cancelled. Therefore Y˜k∗ [i, s] can be expressed by substituting ηˆς,k [k ∗ , i] at (11 - 13) into (9), given by p Y˜k∗ [i, s] = Xk∗ [i, s]· pk∗ [i, s]·hk∗ ,i + η˜k∗ [i, s]+N [i], (14) where η˜k∗ [i, s] represents residual interference, given by (mk −mk∗ )−1

X

X

k∈Ωi mk >mk∗

n=0

−1 Is−1,k · Xk [i, s − 1] · GK [i, ς]

min{N −1,N −(mk∗ −mk )−1}

+

+

+

X

X

k∈Ωi k>k∗

n=max{0,mk −mk∗ }

X

Xk [i, s] · GK [i, ς]

N −1 X

−1 Is+1,k · Xk [i, s + 1] · GK [i, ς]

k∈Ωi n=N −(mk∗ −mk ) mk

Performance of Non-orthogonal Multiple Access with a Novel Interference Cancellation Method Huseyin Haci and Huiling Zhu School of Engineering and Digital Arts, University of Kent, Canterbury, CT2 7NT, United Kingdom Emails: {hh219, h.zhu}@kent.ac.uk. Abstract—In this paper, a novel interference cancellation technique is proposed for asynchronous non-orthogonal multiple access (NOMA) systems and the performance is theoretically investigated in a small cell uplink scenario. It is shown that unlike synchronous communications, at uplink transmission, NOMA users’ performance strongly depends on the relative time offset between interfering users.

I. I NTRODUCTION Mobile communications has been developing very fast [1]–[6] due to the popularity of smart devices and video applications. Wireless multiple access techniques are crucial for mobile communications performance. Multiple access to orthogonal frequency division multiplexing (OFDM)-based channel can be realized in two ways – as orthogonal multiple access (OMA) or non-orthogonal multiple access (NOMA) [7]. Orthogonal frequency division multiple access (OFDMA) [8], [9] is an OFDM-based OMA technique, which is widely adopted in current wireless systems. In OFDMA [10], [11] systems by allocating each subcarrier to a user with the best channel condition on it, it can maximize the system throughput through multiuser diversity gain. Despite high system throughput OFDMA has major problems in achieving very high datarate. The first problem is that it does not allow frequency reuse within the same cell due to strong interference [7]. This severely limits cell throughput. The second problem is the large peak-to-average power ratio (PAPR) especially when the number of subcarriers is large and/or high order modulation is used. Unlike OFDMA, NOMA techniques can allocate one subcarrier to more than one user at the same time within a cell. Reuse of subcarriers provides higher throughput. Not only the user which has the best channel state information (CSI) but also other users can use the subcarrier. Moreover, it has been shown that high PAPR problem can be overcomed with the aid of peak-clipping and compensation of NOMA signals [12]. This comes from an inherent property of NOMA receiver. Therefore NOMA can overcome the two major problems of OFDMA and is an advantageous technique for future mobile communications to achieve high data-rate. Superposition coding (SC) is an effective technique to increase capacity in the NOMA system [13]. By using SC, user multiplexing is performed at power domain and multiple users can transmit their signals simultaneously in the same subcarriers. These users are called SC users. At uplink communications, the base station (BS) detects each user’s signal, starting with the user which has highest signal to noise ratio (SNR), in a descending order. Since successive interference cancellation (SIC) algorithm suppresses interference from strong (earlier detected) signals for relatively weaker (yet to be detected) signals, it has been shown in [7] that NOMA with SC-SIC has superior performance to OFDMA in terms of total system throughput and cell-edge user throughput. [14] has proven that

978-1-4673-6432-4/15/$31.00 ©2015 IEEE

2912

among all possible signaling methods, SC modulation (SCM) maximizes the output signal to interference plus noise ratio (SINR) in the linear minimum mean square error (MMSE) estimation. [15] studied the optimal number of SC users on each subcarrier, and stated that there is a high probability to obtain most of the gain over OMA when few (two to three) users are superposition coded on a subcarrier. So far, the researches on NOMA only consider timesynchronous transmissions. Synchronous transmission is feasible for downlink since the BS controls transmission for all users. However perfect synchronization for all users is impractical for uplink since users are geographically distributed and the mobile environment is dynamic. Asynchronism in the received signal causes crucial disturbances to the SC-SIC. In the synchronous case, regarding a subcarrier, the OFDM symbols from SC users are aligned in time domain. However in asynchronous case, OFDM symbols from the SC users are time misaligned. Synchronous detection and succesive interference cancellation (Conv-SIC) techniques are performed based on the information on only a single symbol from each SC user. However, the asynchronous communications requires information on multiple symbols for detection and interference cancellation (IC). Otherwise, the system performance is significantly degraded if complete information of interfering signals are unknown in asynchronous communications. Therefore, it is important to investigate NOMA in asynchronous communications. To address this challenge, techniques that are able to provide complete interference information for detection and IC are needed. So far, the literature on SC-SIC uplink communications is very limited. There is no work available addressing asynchronous communications with SC-SIC. Further, it is not straightforward to apply asynchronous communication techniques proposed for OFDMA [16], [17] to SC-SIC. This is because asynchronism has different effects on OFDMA and SCSIC. Therefore, novel communication techniques are needed for future high data rate mobile communications. A novel technique that addresses asynchronous SC-SIC is proposed in this paper. It constructs so called ”IC triangles”, which contains multiple, adjacent symbols from interfering users and performs SIC to IC triangles to obtain complete information of and suppress the interference signals. With complete information, the performance of detection and SIC performance improves substantially, which leads to the improvement of reliability and capacity in uplink communications. II. S YSTEM M ODEL In this paper, an uplink NOMA communication system with a BS serving a number of geographically distributed users is considered, as shown in Fig. 1 (a). The system uses OFDM to divide the broadband channel into N narrowband subchannels. Each subchannel contains one subcarrier. Each subcarrier

IEEE ICC 2015 - Wireless Communications Symposium

Small cell environment

BS

sample transmitted from user k on subcarrier i at time n−mk . p hk,i [n] = (dk )−λ αk,i [n]ejθk,i [n] denotes the CSI of user k on subcarrier i at time n, where dk represents the distance between the BS and user k, λ is the the path loss exponent, and αk,i [n] and θk,i [n] denote magnitude and phase shift of multipath fading at time n for user k on subcarrier i. Rayleigh fading that is independent and identical for different users is assumed for characterising multipath effect. θk,i [n] is uniformly distributed over [0, 2π], at time n. The coherence time of the channel is assumed to be much larger than the symbol time and hk,i [n] is fixed during a scheduling period [19], [20]. Therefore index ”n” is omitted and hk,i is used to denote the CSI. ni [n] is the additive white Gaussian noise (AWGN) with double-side power spectral density N0 /2. 𝑦𝑛 Symbol detection for subcarrier 0

Bus for 𝑦[𝑛] Step 1: detection for user 1*

SIC

Symbol detection for subcarrier 𝑖

𝑌1∗ [𝑖, ] Symbol detection

Step K: detection for user K*

𝑌𝐾 ∗ [𝑖, ] Symbol

SIC

detection

𝑋1∗ [𝑖, ]

(t)

𝑋𝑘 [𝑖, ] ℎ𝑘

is accessed by K NOMA users. It is envisioned that NOMA is a promising multiple access technology for future mobile communications in conjuction with beamforming technology in small cell environment, where there are small number of users at each beam [18]. Therefore, if users using NOMA are served by one beam, K can be assumed to be a small number, e.g. up to three users. Due to different distance and the dynamic channel from users to the BS, the asynchronous communication is considered. Received signal structure in one subcarrier is illustrated by Fig. 1 (b), where corresponding OFDM symbols of three users are shown in time domain. In Fig. 1 (b), ς = {s − 1, s, s + 1} represents the set of index of three adjacent OFDM symbols arrived at the BS from three SC users. It can be seen that the arrival times of different SC users are not aligned. Accordingly, a symbol from a user overlaps with adjacent symbols from every other SC users. Assuming OFDM symbol duration is the same for all users, a symbol of a user overlaps with two symbols from every other SC users. For example, if user 2 is the reference user, its time offset is larger than user 1’s but smaller than user 3’s. This makes symbol s of user 2 partially overlap with symbols s and (s+1) of user 1 and with symbols (s − 1) and s of user 3. Obviously to carry out IC, the information of two symbols of other SC users is needed.

𝑋𝐾∗ [𝑖, ]

𝑋𝑘 [𝑖, ] Bus for a priori estimates 𝐗𝐤 𝐢,

Symbol detection for subcarrier (N-1)

user 1*: highest SINR user user K*: Kthth highest SINR user

users 3

Near user

Fig. 2. s

Time offset of user 1

Middle user

A beam

Time offset of user 3 2 Time offset of user 2 1

s+1

symbol at time s-1 symbol at time s symbol at time s+1

Far user

symbol time

(a) Uplink NOMA commu-(b) Received signal structure at time donications system. main. Fig. 1. Illustration of uplink NOMA communications system and structure of received symbols for SC users.

The principles of SC-SIC based transmitter and receiver are presented in the following. At the transmitter of user k, the time domain representation of the output signal is given by inverse fast Fourier transform (IFFT), N −1 p 1 X xk [n] = √ Xk [i, s]· pk [i, s]·ej2πin/N , 0 ≤ n ≤ N −1, N i=0 (1) where xk [n] is the nth time sample of the signal, Xk [i, s] is the sth complex symbol (e.g. p quadrature amplitude modulation mapped) in subcarrier i and pk [i, s] is the transmit power. Fig. 2 shows the block diagram of the BS receiver structure. At the BS receiver, the baseband received signal is represented by a time sample sequence {y[n], 0 ≤ n ≤ N − 1}, given by

y[n] =

N −1 X

yi [n], 0 ≤ n ≤ N − 1,

(2)

i=0

where yi [n] is given by X yi [n] = xk,i [n−mk ]·hk,i [n]+ni [n], 0 ≤ n ≤ N −1, (3) k∈Ωi

where Ωi denotes the set of SC users on subcarrier i, mk , 0 ≤ mk ≤ N − 1, is the discrete time offset of user k relative to the BS reference time and xk,i [n − mk ] represents signal

2913

Block diagram of the BS receiver.

At the receiver, y[n] contains all orthogonal subcarriers, so that processing for symbol detection on each subcarrier is independent and can be done in parallel. K steps of detection is applied in descending SNR order to estimate symbols of K users. Step 1 is used to detect the user, called 1∗ , which has the highest SNR, and other users (k ∈ Ωi , k 6= 1∗ ) are interfering users, which affects the accuracy of symbol detection and cause high bit errror rate (BER) for user 1∗ . Therefore, in this step, after applying fast Fourier transform (FFT) to {y[n], 0 ≤ n ≤ N − 1} to obtain frequency component Y [i, s] for symbol s on subcarrier i, the first function at frequencydomain signal processing is to apply SIC, in order to suppress interference, which requires a priori information (estimate) ˆ k [i, s] denotes estimate of symbols from interfering users. X of s interfering symbol from user k on subcarrier i. Due to asynchronism symbol information of {s−1, s+1} are required. This information is provided through a bus that stores a priori ˆ k [i, ς], 1 ≤ k ≤ ˆ k [i, ς] = {X estimated symbols of users, X K, ς ∈ {s−1, s, s+1}}. SIC reconstructs interfering signals by ˆ k [i, ς] with the CSI and time offset of interfering multiplying X user k. Reconstructed signals are then removed from Y [i, s] for user 1∗ to obtain a cleaned version, denoted as Y˜1∗ [i, s]. ˆ 1∗ [i, s] from At symbol detection, MMSE equalizer provides X ˜ Y1∗ [i, s] that minimize distortion on the received signal by the combined effect of the channel and residual interference after ˆ 1∗ [i, s] is provided to symbol de-modulator to obtain SIC. X ˆ k [i, ς]. Once output bit stream for user 1∗ and to the bus X ˆ 1∗ [i, s] is included at X ˆ k [i, ς] it can be used by SIC at X later detection steps to clean Y [i, s].This completes symbol detection in step 1. Signal processing for subcarrier i continues by detecting symbol of next user which has the second highest SNR at step 2 and then detection order continues similarly until step K. With symbols of all K users estimated, the SC-SIC based

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symbol detection processing is completed for symbol s. Then signal processing advance in time to consider next symbol sequence and above procedure is repeated. III. A NALYSIS A novel technique called triangular SIC (T-SIC) is proposed in this paper for asynchronous SC-SIC systems. SIC is performed in each symbol period, before the symbol detection. Being limited to a single symbol period, only information of symbol s of interfering users can be made available to SIC. However for the sth symbol of a user there may be interference from the (s − 1)th and/or (s + 1)th symbol of other users. T-SIC aims to provide complete information of interfering signals to SIC to achieve superior performance. TSIC follows a new approach and detect symbols from multiple indexes {s, (s + 1), · · · , (s + K − 1)} of stronger users before detecting symbol of a weaker user. At SC, interference that can significantly distort the desired signal are from the symbols of users with stronger signal. Table 1 and Fig. 3 demonstrates the ”triangular” steps of T-SIC algorithm to detect symbol s of three SC users and the triangular shift to advance to the next symbol index in time, as follows. At step 1, sth symbol is detected for user 1∗ with the highest SNR. At this stage, only partial information of interference is available, i.e. the (s−1)th symbols of interfering users are a priori detected but sth symbols are not. However, since unknown signals are from weaker users, sth symbol of user 1∗ can still be correctly detected with high probability. Then, at step 2, (s + 1)th symbol of user 1∗ is detected, since in order to detect a symbol of user 2∗ all symbols of user 1∗ that overlaps with it need to be a priori detected. At step 3, sth symbol of user 2∗ is detected. To detect sth symbol of user 3∗ , (s + 1)th symbol of user 2∗ need to be a priori detected and to detect this symbol, (s + 2)th symbol of user 1∗ need to be detected. Therefore, at step 4 (s + 2)th symbol of user 1∗ is detected and at step 5 (s + 1)th symbol of user 2∗ is detected. All symbols of stronger users that overlap with sth symbol of user 3∗ have been a priori detected, so at step 6 this symbol is detected. Order of detection steps are provided at table 1 and marked with a number shown on symbols at Fig. 3. Symbols marked with number 1-6 are called as ”IC triangle” for symbol s. Once processing on IC triangle for sth symbol is completed, the IC triangle shifts (advances) in time by one symbol index. Table 1 Step Step Step Step Step Step

Detection and IC steps of T-SIC algorithm. 1. Detect sth symbol of user 1∗ . 2. Detect (s + 1)th symbol of user 1∗ . 3. Detect sth symbol of user 2∗ . 4. Detect (s + 2)th symbol of user 1∗ . 5. Detect (s + 1)th symbol of user 2∗ . 6. Detect sth symbol of user 3∗ .

user 3* user 1* m1*

m3*

6

9

3

m2*

2

4

s

s+1

s+2

11 7 s+3

+ ni [n + mk∗ ],

0 ≤ n ≤ N − 1,

(4)

where p 1 xk,i [n+mk∗ −mk ] = √ ·Xk [i, ς]· pk [i, ς]·cos (2πiτk /N ) , N (5) (s − 1), if n + mk∗ − mk < 0 ς = s, (6) if 0 ≤ n + mk∗ − mk ≤ N − 1 , (s + 1), if n + mk∗ − mk > N − 1 and τk = (N +(n+mk∗ −mk ))modN . (6) and τk provides the transmitted symbol index ς and the time instance of signals at yi [n + mk∗ ]. To obtain the frequency component for symbol s on subcarrier i, {yi [n + mk∗ ], 0 ≤ n ≤ N − 1} is passed through FFT ,given by N −1 1 X yi [n + mk∗ ] · cos (−2πin/N ) , Y [i, s] = √ N n=0 p = Xk∗ [i, s] · pk∗ [i, s] · hk∗ ,i + η[k ∗ , i] + N [i], (7)

where the first term at the right hand side (RHS) of (7) is the desired signal, η[k ∗ , i] represents the total frequency-domain interference for user k ∗ on subcarrier i, given by p −1 X NX pk [i, ς] Xk [i, ς] · √ η[k ∗ , i] = · gk,i , (8) N k∈Ωi n=0 k6=k∗

where gk,i = hk,i · cos (2πi(mk∗ − mk )/N ), and N [i] is frequency-domain AWGN on subcarrier i. The cos(·) term at (8) is due to the mismatch of FFT filter’s time component n and the incoming interference signals’ time component τk . Next operation at SIC block is to reconstruct and substract interfering signals to obtain the cleaned version of frequency component, given by X Y˜k∗ [i, s] = Y [i, s] − Iς,k · ηˆς,k [k ∗ , i], (9) Iς,k is the indicator parameter that shows if employed SIC technique exploits a priori estimated information from {(s − 1), s, (s + 1)}th symbols of interferers, given by 0, for Conv-SIC Is−1,k , Is+1,k = (10) 1, for T-SIC,

15

8

1

processing triangle

Fig. 3.

12

5

k∈Ωi k6=k∗

k∈Ωi k6=>k∗

users

user 2*

Referring to the receiver structure shown at Fig. 2, suppose signal processing is taking place for symbol s of user k ∗ on subcarrier i. T-SIC set user k ∗ as the time reference user, then N discrete time samples taken from y(t) can be expressed in terms of desired and interfering signals by X yi [n + mk∗ ] = xk∗ ,i [n]hk∗ ,i + xk,i [n + mk∗ − mk ]hk,i

time samples

triangular shift pattern

T-SIC signal processing steps.

To further present the principle and the performance of T-SIC, quantitative analysis is provided in the following.

2914

and Is,k = 1 for both SIC techniques. ηˆς,k [k ∗ , i] is the reconstructed interference signal from estimate of ς th symbol of user k on subcarrier i, given for each possible overlapping symbol {s − 1, s, s + 1} by p (mk −mk∗ )−1 X pk [i, s − 1] ∗ ˆ ηˆs−1,k [k , i] = Xk [i, s − 1] · · gk,i , N n=0 (11)

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min{N −1,N −(mk∗ −mk )−1}

X

ηˆs,k [k ∗ , i] =

p ˆ k [i, s]· X

n=max{0,mk −mk∗ }

pk [i, s] ·gk,i , N (12)

+

p ˆ k [i, s+1]· pk [i, s + 1] ·gk,i . X N

(13) The theoretical analysis of SC-SIC systems are based on so called ”onion pealing” or ”stripping aided detection” [12], where it is assumed that the interference from priori detected symbols can be perfectly cancelled. Therefore Y˜k∗ [i, s] can be expressed by substituting ηˆς,k [k ∗ , i] at (11 - 13) into (9), given by p Y˜k∗ [i, s] = Xk∗ [i, s]· pk∗ [i, s]·hk∗ ,i + η˜k∗ [i, s]+N [i], (14) where η˜k∗ [i, s] represents residual interference, given by (mk −mk∗ )−1

X

X

k∈Ωi mk >mk∗

n=0

−1 Is−1,k · Xk [i, s − 1] · GK [i, ς]

min{N −1,N −(mk∗ −mk )−1}

+

+

+

X

X

k∈Ωi k>k∗

n=max{0,mk −mk∗ }

X

Xk [i, s] · GK [i, ς]

N −1 X

−1 Is+1,k · Xk [i, s + 1] · GK [i, ς]

k∈Ωi n=N −(mk∗ −mk ) mk