SCMA for Downlink Multiple Access of 5G Wireless Networks
Hosein Nikopour, Eric Yi, Alireza Bayesteh, Kelvin Au, Mark Hawryluck, Hadi Baligh, and Jianglei Ma Huawei Technologies Canada Co., LTD., Ottawa, Ontario, Canada
{hosein.nikopour, zhihang.yi, alireza.bayesteh, kelvin.au, mark.hawryluck, hadi.baligh, jianglei.ma}@huawei.com Abstract²Sparse code multiple access (SCMA) is a new
frequency domain non-orthogonal multiple-access technique which can improve spectral efficiency of wireless radio access.
With SCMA, different incoming data streams are directly mapped to codewords of different multi-dimensional cookbooks, where each codeword represents a spread transmission layer.
Multiple SCMA layers share the same time-frequency resources of OFDMA. The sparsity of codewords makes the near-optimal detection feasible through iterative message passing algorithm (MPA). Such low complexity of multi-layer detection allows excessive codeword overloading in which the dimension of multiplexed layers exceeds the dimension of codewords.
Optimization of overloading factor along with modulation-coding levels of layers provides a more flexible and efficient link- adaptation mechanism. On the other hand, the signal spreading feature of SCMA can improve link-adaptation as a result of less colored interference. In this paper a technique is developed to enable multi-user SCMA (MU-SCMA) for downlink wireless access. User pairing, power sharing, rate adjustment, and scheduling algorithms are designed to improve the downlink throughput of a heavily loaded network. The advantage of SCMA spreading for lightly loaded networks is also evaluated.
Keywords²SCMA; LDS; non-orthogonal multiple-access;
multi-dimensional constellation; 5G; LTE I. INTRODUCTION
Future fifth generation (5G) wireless networks are expected to support better quality of service, higher throughput, and lower latency [1]. Recent research activities [2], [3] emerge toward new technologies providing solutions to meet the requirements of the next generation of wireless communication networks in 2020 and beyond.
Multi-user MIMO (MU-MIMO) is a well-known multiple access technique to share given time-frequency and power resources among multiple users in a downlink wireless access network [4]. The target is to increase the overall downlink throughput through user multiplexing. Multiple beams are formed over an array of antennas at a transmit point (TP) to serve multiple users distributed within a cell. Every MIMO layer is assigned to a user while layers are orthogonally separated in the space domain assuming MIMO beamforming precoders are properly selected according to the channels of target users. At the receive side, every user can simply match itself to its intended layer while other MIMO layers are seemed totally muted with no cross-layer interference, provided the precoders are properly designed. Despite the promising throughput gain and the simplicity of detection at user nodes, MU-MIMO as a closed-loop system suffers from some
practical difficulties in terms of channel aging and high overhead to feed back channel state information (CSI) of users to a serving TP. CSI is required to form the best set of precoders for a selected set of paired users. If CSI is not well estimated, cross-layer interference practically limits the potential performance gain of MU-MIMO.
Open-loop user multiplexing is a desired approach to avoid practical limitations of MU-MIMO. Non-orthogonal code- domain multiple-access is an open-loop scheme to pair multiple users over shared time-frequency resources. Sparse code multiple access (SCMA) [5], [6] is a non-orthogonal codebook-based multiple-access technique with near optimal spectral efficiency. In SCMA, incoming bits are directly mapped to multi-dimensional complex codewords selected from predefined codebook sets. Co-transmitted spread data are carried over super-imposed layers.
SCMA is well-matched to user multiplexing as we can allocate code-domain layers to different users without need for CSI knowledge of paired users. In this paper, multi-user SCMA (MU-SCMA) is proposed to improve a network throughput. With a very limited need for channel knowledge in terms of channel quality indicator (CQI), TP simply pairs users together while the transmit downlink power is properly shared among multiplexed layers. Compared to MU-MIMO, this system is more robust against channel variations. In addition, the problem of CSI feedback is totally removed for this open- loop multiple-access scheme.
Since layers are not fully separated in a non-orthogonal multiple access system, a non-linear receiver is required to detect the intended layer of every user. Therefore, further complexity of detection is the cost of the non-orthogonal multiple-access especially when a system is heavily overloaded with a large number of multiplexed layers. Sparsity of SCMA codewords lets us take advantage of the low complexity message passing algorithm (MPA) [7] detector with ML-like performance. MPA performs well even if the system is overloaded with a large number of layers.
Low density spreading (LDS) [7], [8] is a special form of SCMA. In LDS, codewords are built by spreading of modulated QAM symbols using low-density spreading signatures with a few numbers of nonzero elements within a large signature length. Despite the moderate complexity of detection, LDS suffers from poor performance especially for large constellation sizes above QPSK. All CDMA schemes and in particular LDS can be considered as different types of repetition coding in which different variations of a QAM symbol are generated by a spreading signature. Repetition
coding is not able to provide desirable spectral efficiency for a wide range of SNR. To overcome this problem, in SCMA the QAM mapper and linear operation of sparse spreading are merged together to directly map incoming bits to a complex sparse vector called a codeword. This enables SCMA to benefit from shaping gain [9] of multi-dimensional constellations as opposed to simple repetition coding of linear sparse sequences.
Consequently, SCMA substantially improves spectral efficiency of linear sparse sequences through multi- dimensional shaping gain of codebooks while it still provides other benefits in terms of overloading and moderate complexity of detection.
Interference management and robustness of the link quality are concerns in lightly loaded networks. When the traffic demand is low, the resource utilization drops. Within the long- term evolution (LTE) [10] context, as an example of an OFDMA system, that is equivalent to muting of some resource blocks (RB) across the bandwidth of a TP. In this situation, the interference level at a downlink user changes rapidly within every scheduling interval even if fading channels are quite stable with very slow variation. Interference level at an RB rises if most of RBs of neighboring cells are occupied, and drops if corresponding RBs of neighboring cells are empty.
This rapid variation of interference level in time and frequency is not predictable in practice when there is no dynamic cooperation among the neighboring cells. The system has no choice but to adapt itself to the worst case scenario of channel quality. Poor link-adaptation inherently decreases the efficiency of a link.
Spreading over OFDMA tones can potentially improve the quality of link-adaptation procedure due to the interference averaging [11]. By using SCMA spreading technique, interference from different TPs is averaged out over the spread tones. This makes the interference white which has the advantage of better and more robust link-adaptation. In addition, layer multiplexing adds another degree of freedom to the link-adaptation capability of an SCMA system. Number of layers along with codebook sizes, coding rates, and power level of multiplexed layers are the parameters dictating the rate and quality of a link.
This paper evaluates the advantage of SCMA in a downlink wireless network. Two scenarios are considered: i) a fully loaded network with high throughput demand, and ii) a lightly loaded network with a fast variation of interference within each scheduling interval. MU-SCMA is proposed and evaluated in a heavily loaded network for the sake of throughput improvement. The techniques related to MU-SCMA are developed to pair users over shared time-frequency resources.
The impact of interference averaging due to SCMA spreading is also evaluated for a lightly loaded network scenario.
Throughout this paper, ܠ is a vertical vector, ܆ represents a matrix, ே is an all-one vector of size ܰ, and ۷ே depicts an
ܰ ൈ ܰ identity matrix.
The rest of the paper is organized as follows. Section II defines the SCMA system model and structure. Section III is dedicated to the algorithms required to enable MU-SCMA.
This section describes the details of scheduling and user paring algorithms, rate adjustment, detection strategies and power
allocation of the paired users. Numerical results are reported in Section IV. The paper finally concludes in Section V.
II. SYSTEM MODEL AND DESCRIPTION A. Downlink SCMA Model
An SCMA encoder is defined as a mapping from ଶሺܯሻ coded bits to a ܭ-dimensional complex codebook of size ܯ.
The ܭ-dimensional complex codewords of the codebook are sparse vectors with ܰ ൏ ܭ non-zero entries. All the codewords in the codebook contain 0 in the same ܭ െ ܰ dimensions.
An SCMA encoder contains ܷ users each with ܬ௨, ݑ ൌ ͳǡ ǥ ǡ ܷ separate layers. SCMA codewords are multiplexed over ܭ shared orthogonal resources, e.g. OFDMA tones. In a downlink single-input multiple-output (SIMO) channel, the received signal at antenna ݎ of user ݑ can be expressed as
ܡݎݑ
Ͳ ൌ ൫ܐݎݑͲ൯ σܷݑൌͳඥݑȀܬ௨σܬ݆ൌͳݑ ܠ݆ݑ ܖݎݑͲ, (1) where ܬ௨ is the number of layers allocated to user ݑ, ܠ௨ is the
݆th SCMA codeword of user ݑ such that ฮܠ௨ฮଶൌ ܭ, and ௨ is the total transmit power per tone allocated to user ݑ. The power of user ݑ is equally distributed among ܬ௨ layers. The total transmit power is ܲ ൌ σ௨ୀଵ௨ and the total number of multiplexed layers is ܬ ൌ σ௨ୀଵܬ௨. The ܭ ൈ ͳ channel vector of ݎth receive antenna of user ݑ is ܐ௨ in which every element represents the channel of an OFDMA tone. The ambient noise vector of user ݑ at receive antenna ݎ is represented by ܖ௨. For the sake of notation simplification, adjacent OFDMA tones are assumed identical, i.e. ܐ௨ൌ ݄௨.
As SCMA is a non-linear modulator, it is not straightforward to model and extract its capacity. Hence, in the rest of the paper the linear sparse sequence modeling is used to develop the related pairing algorithms for MU-SCMA. In the sequel, the MIMO equivalent model of a linear sparse sequence system is developed.
B. MIMO Equivalent of Linear Sparse Sequence
A linear sparse sequence is simply the spread version of a QAM symbol such that ܠ௨ൌ ܛ௨ݍ௨ where ܛ௨ is the ݆ th signature vector of user ݑ such that ฮܛ௨ฮଶൌ ܭ and ݍ௨ is its corresponding QAM symbol with unit average power. Let
܁௨ൌ ሺܛଵ௨ǡ ǥ ǡ ܛೠ௨ሻ represent the ܭ ൈ ܬ௨ signature matrix of user ݑ, and ܙ௨ൌ ൫ݍଵ௨ǡ ǥ ǡ ݍೠ௨൯. (1) can be rewritten as
ܡݎݑ
Ͳൌ݄௨బσܷݑൌͳඥݑȀܬݑ܁௨ܙ௨ ܖݎݑͲ. (2) Stacking received signal of all ܴ antennas together, the linear sparse sequence model is expressed as a MIMO system
ܡݑ
Ͳ ൌσܷݑൌͳඥݑȀܬݑ۶௨బ௨ܙݑ ܖݑͲ, (3) where ܡ௨ൌ ሺܡଵ௨ǡ ǥ ǡ ܡோ௨ ሻ , ܖ௨ൌ ሺܖଵ௨ ǡ ǥ ǡ ܖோ௨ ሻ and ۶௨బ௨ൌ ܐ௨బ۪܁௨ in which ܐ௨ൌ ሺ݄ଵ௨ǡ ǥ ǡ ݄ோ௨ሻ and ۪ represents Kronecker product. The size of ۶௨బ௨ is ܴܭ ൈ ܬ௨. By multiplexing ܬ layers over ܭ resources, the overloading factor of the system is ܬȀܭ.
Assuming all ܬ layers belong to one user, i.e. ܷ ൌ ͳ, the open-loop capacity of the equivalent MIMO system is
ܥ ൌ ଶሺ۷ ܲȀܬ۶ୌ܀ିଵ۶ሻ, (4) where ܀ is the covariance matrix of noise ܖ. Note that index ݑ is dropped for the simplicity of the notation. This is the upper bound rate of a single-user sparse spreading sequence system with a given channel, signature matrix, and power allocation of layers. This bound is tight for QPSK modulation but deviates from performance of linear sparse sequence for higher constellation sizes where the repetition coding fails. The benefit of SCMA is to recover this performance gap through multi-dimensional modulation.
Assuming ܀ൌ ܰଵ۷ோ, (4) is equivalent to
ܥ ൌ ଶሺ۷ ܲȀܬܰଵ۶ୌ۶ሻ Ǥ (5) Based on the definition of ۶, one can simply show that
۶ୌ۶ ൌ ԡܐԡଶሺ܁ୌ܁ሻ. (6) By replacing (6) into (5), we have
ܥ ൌ ଶ൫۷ ɀȀܬሺ܁ୌ܁ሻ൯, (7) in which ɀ ؔ ԡܐԡଶܲȀܰଵ is the instantaneous SIMO SNR of the user.
According to (7), the rate of a single-user system depends on SNR as well as the number of layers and the signature matrix. Consequently, it can provide further degree of freedom for link-adaptation of an SCMA system. In the case of OFDMA with ܁ ൌ ሺͳሻ , ܬ ൌ ͳ , and ܷ ൌ ͳ , (7) is simply reduced to OFDMA SIMO capacity, i.e. ܥ ൌ ଶሺͳ ɀሻ.
III. DOWNLINK MU-SCMAALGORITHMS
In downlink MU-SCMA, the transmitted layers belong to more than one user. Several algorithms are required to enable MU-SCMA. Paired users are first selected from a pool of users. The user selection criterion and its optimization approach are part of the design parameters. Signals of paired users are transmitted from an antenna with a total power constraint. Therefore, the power has to be split among paired users according to their channel conditions. Following the power allocation, the rate of each user is adjusted to match the target error rate and link quality. Codebook size, coding rate and number of layers are the parameters to adjust the rate of each paired user.
A. User Pairing to Maximize Wiegthed Sum-Rate
Assume a pool of users with instantaneous SINR ɀ௨ൌ ԡܐ௨ԡଶܲȀܰ௨, ݑ ൌ ͳǡ ǥ ǡ ܷ, and average rates ܴ௨. In the absence of user pairing, a proportional fair (PF) scheduler maximizes the weighted rate as follows
ݑכൌ
௨
ݎ௨
ܴ௨ǡ (8)
where ݎ௨ is determined according to the available CQI, e.g.
ݎ௨ൌ ଶሺͳ ɀ௨ሻ for OFDMA.
The target of pairing is to maximize the weighted sum-rate.
Assuming two users, the weighted sum-rate is expressed as ݑଵכǡ ݑଶכ ൌ ௨భǡ௨మǁೠభ
ோೠభǁೠమ
ோೠమ, (9)
in which ݎǁ௨భǣ ൌ ݎǁ௨భሺݑଵǡ ݑଶǢ ሻ is the adjusted rate of user ݑଵ after pairing. Notably, the adjusted rate depends on both paired users and the power sharing strategy. Following the exhaustive search, all ܷሺܷ െ ͳሻ pairing options as well as ܷ single-user options must be checked to find the solution of (9).
The complexity of the exhaustive search increases in the order of ܷଶ, which might not be practically feasible.
A greedy algorithm can be used to reduce the complexity of pairing. In a greedy approach, the first user is picked according to the single-user scheduling criterion of (8) and then another user is paired with the first one. With greedy scheduling, the complexity order of two user pairing is reduced to ܷ െ ͳ. The procedure of the greedy scheduling is listed as below
ݑଵכൌ ௨ೠ
ோೠ, (10)
ݑଶכൌ ௨ஷ௨భכǁೠభכ
ோೠభכǁೠ
ோೠ, (11)
and the pairing result is valid only if the following condition is satisfied
ǁೠభכ
ோೠభכோǁೠమכ
ೠమכ ோೠభכ
ೠభכ. (12)
B. Rate Adjustment and Detection Strategy
Assuming ܷ ൌ ʹ, ଵൌ Ƚܲ, and ଶൌ ሺͳ െ Ƚሻܲ, (3) can be rewritten as follows for two users
ܡ௨ൌ ට
భ۶௨ଵܙଵ ටሺଵିሻ
మ ۶௨ଶܙଶ ܖ௨ǡ ݑ ൌ ͳǡʹǡ (13) in which Ƚ א ሺͲǡͳǤͲሻ represents the power sharing factor.
Without loss of generality, we assume ɀଵ ɀଶ.
The above equation models a MIMO broadcast channel which is not generally degraded [12]. In other words, the assumption of ɀଵ ɀଶ does not necessarily imply that user 1 FDQGHFRGHXVHU¶VGDWDDQGDFKLHYHDKLJKHUUDWHFRPSDUHGWR
this user. For the sake of simplifying the analysis, the model is transformed to an approximated degraded model. The signal of user 1 is treated as interference at user 2 such that the equivalent interference at user 2 is described as
܀ଶൌ ܰଶ۷ܴܭ ȽܲȀܬଵ۶ଶଵ۶ଶଵୌǤ (14) It can be shown that ۶ଶଵ۶ଶଵୌ ൌ ሺܐଶܐଶୌሻ ٔ ሺ܁ଵ܁ଵୌሻ meaning that equivalent interference at user 2 is colored even if the background noise in white. According to (7), the broadcast model of (13) becomes degraded if the interference in (14) is approximated with a white noise as follows
܀ଶൎ ሺܰଶ Ƚܲԡܐଶԡଶሻ۷Ǥ (15) In other words, with the above approximation, if user 2 is able to decode its own data, user 1 can also decode it.
For the sake of simplicity, the intended algorithms are first developed for OFDMA (which is degraded by nature) and then extended to SCMA. For OFDMA, (13) is rewritten as follows
ܡ௨ൌ ܐ௨ξȽܲݍଵ ܐ௨ඥሺͳ െ Ƚሻܲݍଶ ܖ௨. (16)
As ɀଵ ɀଶ, in the degraded OFDMA channel, user 1 is the good quality user with a higher rate compared to user 2 with a lower instantaneous rate.
1) Detection at high-quality user 1
The capacity region of user 1 is shown in Fig. 1 with solid lines. An ideal joint ML detector is feasible at user 1 if
ݎǁଵ ݎǁଶ ଶሺͳ ɀଵሻ, (17) subject to
ݎǁଶ ଶሺͳ ɀଶ̷ଵሻ, (18) and
ݎǁଵ ଶሺͳ ɀଵሻ. (19) Referring to (16) for ݑ ൌ ͳ, ɀଶ̷ଵ represents the effective SINR for the single-user detection of user 2 at user 1 while user 1 is treated as an interferer, i.e.
ɀଶ̷ଵ ൌԡܐభԡమሺଵିሻ
ԡܐభԡమାேభൌሺଵିሻஓభ
ଵାஓభ. (20) Condition (18) guarantees the single-user detection of the low rate user 2 at the good quality user 1. Assuming user 2 is totally decodable at user 1, after successive interference cancellation (SIC), the detection problem of user 1 is reduced to ܡଵൌ ܐଵξȽܲݍଵ ܖଵ. In this case, user 1 is decodable if condition (19) is guaranteed, in which
ɀଵ ൌԡܐభԡమ
ேభ ൌ Ƚɀଵ. (21)
The SIC detection strategy corresponds to point C in the capacity region of Fig. 1 where the maximum achievable rate is provided for user 1.
2) Detection at low-quality user 2
Since user 2 has lower channel quality, it is not able to detect user 1 with a higher rate. Therefore, user 2 has no choice but to treat user 1 as its co-paired interference. In the other hand, the capability of user 1 to detect user 2 does not necessarily mean that user 2 can also detect its own intended data. Consequently, a tighter condition on the rate of user 2 might be required to make the detection of user 2 signal possible for its target user. Referring to (16) for ݑ ൌ ʹ, the SINR for single-user detection of user 2 is expressed as
ɀଶ ൌԡܐʹԡʹሺͳെȽሻܲ
ԡܐʹԡʹȽܲܰʹ ൌሺͳെȽሻɀʹ
ͳȽɀʹǤ (22) Therefore, the signal of user 2 is detectable at user 2 with single-user detection strategy only if
ݎǁଶ ଶሺͳ ɀଶሻ. (23) 3) Optimum operating point
The capacity region of user 1 and 2 are illustrated jointly in Fig. 1. The shaded region corresponds to an area in which every user can detect its intended data stream while the power sharing factor is Ƚ. The shaded area satisfies conditions (17) to (19) as well as (23).
Theoretically, the best point of transmission is either A or B of Fig. 1 depending on the weights of the users. The weighted sum-rate at point B is described as
Fig. 1. Capacity regions at user 1 and 2.
ܹܴܵሺȽሻ ൌ୪୭మሺଵା
ಉಋమ భశሺభషಉሻಋమሻ
ோభ ୪୭మሺଵାሺଵିሻஓమሻ
ோమ . (24) Assuming ܴଵ ܴଶ , the weighted sum-rate at B is maximized only if Ƚ ൌ Ͳ. Under this condition, the scheduling result falls back to the single-user scheduling. Therefore, if the user pairing provides better weighted sum-rate, the only promising scenario of interest is point A.
Assuming the pairing providers gain at point A, the quality of single-user detection of user 2 signal at user 1 is much better than detection of user 2 signal at user 2. It can be shown by comparing ɀଶ̷ଵ and ɀଶ. Referring to (20), (22), and Fig. 1, the detection margin of user 2 is defined as
ȟ ൌஓమ̷భ
ஓమ ൌஓభ
ஓమ ଵାஓమ
ଵାஓభǤ (25)
C. OFDMA Power Sharing Optimization
The goal is to optimize the power sharing factor Ƚ while the two paired users operate at point A of Fig. 1. The weighted sum-rate of the paired users at point A is
ܹܴܵሺȽሻ ൌ୪୭మሺଵାஓభሻ
ோభ ୪୭మሺଵା
ሺభషಉሻಋమ భశಉಋమሻ
ோమ (26) The optimum Ƚ is the solution of డௐௌோಲሺሻ
డ ൌ Ͳ and can be easily derived as
Ƚכൌ ோభஓమିோమஓభ
ሺோమିோభሻஓభஓమ. (27) The optimal solution Ƚכ is valid only if Ƚכא ሺͲǡͳሻ . To facilitate the detection, one may limit Ƚ to a smaller range.
Referring to (25) and (27), the detection margin of users 2 for Ƚ ൌ Ƚכ is reduced to
ȟ ൌஓభ
ஓమ ଵାכஓమ ଵାכஓభൌோభ
ோమǤ (28)
It explains that two paired users are easily separated if the ratio of their long-term rates is large enough.
D. SCMA Power Sharing Optimization
Following the same detection strategy as OFDMA, by referring to (7) and (21), the adjusted rate of the first paired user can be described as
ݎǁଵൌ ଶሺ۷ ஓభ
భ ሺ܁ଵୌ܁ଵሻሻǤ (29)
ݎǁ2= log2(1 +ሺ1 െ Ƚሻɀ2
1 + Ƚɀ2
)
r2
A
B
r1
'
ݎǁ2= log2(1 + (1 െ Ƚ)ɀ2) ݎǁ2= log2(1 +ሺ1 െ Ƚሻɀ1
1 + Ƚɀ1)
C
ݎǁ1+ ݎǁ2= log2(1 + ɀ1)
Region of user 1 Region of user 2 Region of broadcasting
ݎǁ2= log2(1 + ሺ1 െ Ƚሻɀ1) ݎǁ1= log2(1 + Ƚɀ2
1 + ሺ1 െ Ƚሻɀ2) ݎǁ1= log2ሺ1 + Ƚɀ2ሻ ݎǁ1= log2ሺ1 + Ƚɀ1ሻ
Referring to (7), (13), and (15), the adjusted rate of second user can be expressed as
ݎǁଶൌ ଶሺ۷ ሺଵିሻԡܐమԡమ
మሺேమାԡܐమԡమሻሺ܁ଶୌ܁ଶሻሻǡ (30) or equivalently
ݎǁଶൌ ଶሺ۷ ሺଵିሻஓమ
మሺଵାஓమሻሺ܁ଶୌ܁ଶሻሻǤ (31) The weighted sum-rate with weights ݓൌ ͳȀܴ is
ܹܴܵሺȽሻ ൌ ݓଵଶሺ۷ ஓభ
భ ሺ܁ଵୌ܁ଵሻሻ ݓଶଶሺ۷ ሺଵିሻஓమ
మሺଵାஓమሻሺ܁ଶୌ܁ଶሻሻ .
(32)
The Hermitive matrix ܁௨ୌ܁௨ can be decomposed to
܃௨௨܃௨ୌ , and hence ଶሺ۷ ɏ܁௨ୌ܁௨ሻ ൌ σ ଶሺͳ ɏɉ௨ሻ in which ɉ௨ is the ݅th diagonal element ௨. Rewriting (32), we have
ܹܴܵሺȽሻ ൌ ݓଵσ ଶሺͳ ஓభ
భ ɉଵሻ
୫୧୬ሺǡభሻ
ୀଵ
ݓଶσ ଶሺͳ ሺଵିሻஓమ
మሺଵାஓమሻɉଶሻ
୫୧୬ሺǡమሻ
ୀଵ Ǥ
(33)
The optimum power sharing factor is the solution of
డௐௌோಲሺሻ
డ ൌ Ͳ which leads to the following σ ௪భஓభభ
భାஓభభכ ୫୧୬ሺǡభሻ
ୀଵ െ
σ ሺଵାஓ ௪మஓమమሺଵାஓమሻ
మכሻሺమାஓమమାሺమିమሻஓమכሻ ୫୧୬ሺǡమሻ
ୀଵ ൌ ͲǤ
(34)
The solution of the above polynomial is Ƚכ which is valid only if it is real and belongs to the interval ሺͲǡͳǤͲሻ. In the case of multiple solutions, the one that maximizes ܹܴܵሺȽכሻ is selected.
IV. NUMERICAL RESULTS
Simulations are done to evaluate the benefits of SCMA and MU-SCMA in a downlink wireless cellular network. As listed in TABLE I, the common simulation assumptions and parameters follow the 3rd generation partnership project (3GPP) evaluation methodology [13]. The codebooks of SCMA are designed based on the principles reported in [6].
The dimension of SCMA codewords is 4 with 2 non-zero elements in each codeword. The maximum number of SCMA layers is 6. SCMA layers are detected with the near-optimal MPA detector and the detection strategy for MU-SCMA follows the approach described in Section III.
The system-level simulation results are listed in TABLE II comparing OFDMA with SCMA and MU-SCMA in terms of cell aggregate throughput and 5 percentile coverage rate of cell edge users. The traffic model is full buffer with average 10 users per cell in a 10 MHz LTE network. This scenario is equivalent to a heavily loaded network with a high demand for throughput. The scheduler is PF with wideband scheduling meaning that a scheduled user occupies the whole resources within a scheduling interval.
Extracting from the results of TABLE II, the relative throughput and coverage gains of SCMA and MU-SCMA with respect to OFDMA are illustrated in Fig. 2.
TABLE I. SIMULATION ASSUMPTIONS AND PARAMETERS FOR NETWORK
SCENARIOS
Parameter Value Deployment Hexagonal grid, 19 sites, 3 sectors per
site, and 500 m inter-site distance Distance-dependent
path loss
ܮ ൌ ͳʹͺǤͳ ͵Ǥ ଵሺܦሻ, ܦ in km and ܦ ͵ͷ m
Penetration loss 20 dB
Shadowing 8 dB long-normal shadowing TP antenna pattern 3GPP 3D model
Number of users 570 users uniformly distributed across the entire network
System bandwidth 10 MHz at 2 GHz carrier frequency Channel type 1×2 ITU-TU fading channel User speed 3 and 120 km/h
HARQ Incremental redundancy (IR) HARQ with up to 3 retransmissions
Scheduler PF with wideband or subband scheduling
SCMA codeword dimension
4 OFDMA tones SCMA codebook
sizes
4, 8, and 16 SCMA maximum
number of layers
6 with overloading factor of 1.5 SCMA receiver MPA joint detector
TABLE II. SYSTEM SIMULATION RESULTS COMPARING OFDMA,SCMA,
AND MU-SCMA FOR A FULL BUFFER SCENARIO WITH WIDEBAND PF SCHEDULING
Radio Access Mode Throughput [Mbps]
Coverage [kbps]
OFDMA 18.6 574.7
SCMA 19.6 621.8
MU-SCMA 24.0 779.7
0 5 10 15 20 25 30 35 40
SCMA MU-SCMA
Gain over OFDMA [%]
Throughput Gain [%]
Coverage Gain [%]
Fig. 2. Cell throughput and coverage gain of SCMA and MU-SCMA over OFDMA.
According to Fig. 2, SCMA shows 5% throughput and 8%
coverage gain over OFDMA. The major source of the gain is multi-dimensional shaping gain of SCMA codebooks and the flexibility of the link-adaptation associated with SCMA.
However, the major advantage of SCMA over OFDMA appears when the non-orthogonal MU-SCMA technique is implemented. Referring to Fig. 2, the throughput and coverage gains of MU-SCMA over OFDMA are 28% and 36%, respectively. The reported gain here is for users with 3 km/h speed, but the same results are also derived for a network with higher user speeds up to 120 km/h. Therefore, the robustness of open-loop MU-SCMA to channel variation is one of its main advantages over MU-MIMO where the system fails for high speed and moving networks.
Fig. 3. Cell coverage and throughput trade-off for OFDMA and MU-SCMA.
For coverage rate at 700 kbps, the gain of cell throughput is more than 51%.
The metric of a PF scheduler can be modified to establish a trade-off between coverage and throughput of a network. The weight of the PF metric is modified to ݓ௨ൌ ͳȀܴ௨£ where £ is the exponent of the average rate to adjust the outcome of the original weighted sum-rate in (32). Fig. 3 depicts how £ impacts the coverage and throughput rates of OFDMA and MU-SCMA transmission modes. For a given coverage rate at 700 kbps, the throughput gain of MU-SCMA with respect to OFDMA is more than 51%.
The results of the evaluation of a network with 50%
resource utilization are listed in TABLE III to show the advantage of SCMA over OFDMA in terms link-adaptation in a highly variant interference environment. In an OFDMA system, in average 50% of RBs are randomly off within a scheduling interval. Lower resource utilization reduces the average interference level but increases the time and frequency variation of the interference power.
In SCMA the whole bandwidth might be allocated but 50%
of layers are not randomly assigned during the subband PF scheduling. The width of each subband is 5 RBs. Despite OFDMA in which an RB is either on with full power or completely off, the transmit power of an RB in SCMA changes according to its corresponding number of active layers. It alleviates the rapid variation of interference across RBs in the frequency direction.
TABLE III. SIMULATION RESULTS COMPARING OFDMA AND SCMA WITH
50%RESOURCE UTILIZATION AND SUBBAND PFSCHEDULING
Radio Access Mode Throughput [Mbps] Coverage [kbps]
OFDMA 13.0 526.3
SCMA 20.3 (56.2%) 665.7 (26.5%)
According to TABLE III, the throughput and coverage gains of SCMA over OFDMA are 56% and 26%, respectively.
Therefore, SCMA can bring robustness to a lightly-loaded system through interference averaging due to slow variation of transmit power across frequency and the spreading of codewords across multiple OFDMA tones.
V. CONCLUSION
MU-SCMA is introduced to increase the downlink spectral efficiency of 5G wireless cellular networks. SCMA is a non-
orthogonal multiple-access scheme. User multiplexing is UHDOL]HG ZLWKRXW QHHG IRU D IXOO NQRZOHGJH RI XVHUV¶
instantaneous channels. This feature provides an advantage for MU-SCMA over other existing multiplexing techniques such as MU-MIMO in which sensitivity to channel aging and high overhead of channel knowledge feedback are the obstacles for their practical implementation in a real network. High data rate and at the same time the robustness to mobility are two major advantages of MU-SCMA. In addition, compared to MU-MIMO schemes which are based on spatial domain precoding, code-domain multiplexing has a substantial advantage in terms of the transmit side computational complexity. Promising performance gain of MU-SCMA makes it attractive for future wireless and moving networks. In this paper, MU-SCMA is developed for a single-TP and SIMO channel. The extension of MU-SCMA to multiple-TP and MIMO scenarios is a direction for future research activities.
ACKNOWLEDGEMENT
Part of this work has been performed in the framework of the FP7 project ICT-317669 METIS. The authors would like to acknowledge the contributions of their colleagues in METIS for the discussions and the comments.
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400 450 500 550 600 650 700 750 800 850
14 16 18 20 22 24 26
Cell Edge Coverage [kbps]
Cell Throughput [Mbps]
OFDMA MU-SCMA 51.8%
3.0
ɴ=1.0
0.7 2.0
0.8
ɴ=1.0 0.8
2.0 1.5
1.5 0.7
0.9
