- Research
- Open Access
Receiver design combining iteration detection and ICI compensation for SEFDM
- Min Jia†^{1}Email author,
- Zhiying Wu^{1},
- Zhisheng Yin†^{1},
- Qing Guo^{1} and
- Xuemai Gu^{1}
https://doi.org/10.1186/s13638-018-1036-2
© The Author(s) 2018
- Received: 10 October 2017
- Accepted: 20 January 2018
- Published: 5 February 2018
Abstract
With the rapid development of wireless communication, the spectrum resource becomes rare, and research on utilization of limited spectrum resource becomes more popular, especially in fifth generation (5G) mobile communication system. Some efficient frequency division multiplexing systems, such as spectrally efficient frequency division multiplexing (SEFDM) system, can improve spectrum utilization by further compression of the distance between subcarriers with respect to orthogonal frequency division multiplexing (OFDM) carrier structure. This idea of further compressing bands will efficiently solve the problem of scarce spectrum resource in future. However, this kind of systems exist strong self-caused inter-carrier interference (ICI) due to non-orthogonal subcarriers employment, which poses a great challenge to the design of receiver. In this paper, a receiver designed with iterative ICI compensation (IIC) for SEFDM is proposed, which has excellent bit error rate (BER) performance and low complexity. Simulation results show that the BER performance of system under iterative ICI compensation receiver is almost same as traditional combining iterative detection and fixed sphere detection (ID-FSD) scheme with large bandwidth compression factor (BCF). But the complexity of the proposed method is lower than that of ID-FSD.
Keywords
- Non-orthogonal subcarriers
- ICI compensation
- BER performance
- Low complexity
1 Introduction
In multi-carrier transmission systems, orthogonal frequency division multiplexing (OFDM) is always referred to the classical transmission mode with its high spectrum utilization ratio and simple transmission/reception equipment, but fifth generation (5G) requires a transmission system with higher spectrum utilization than OFDM. As an underlying technique, flexible waveforms are required in 5G networks to address the coming challenges. In 5G network, a fundamental requirement of waveform design is to support asynchronous transmission in order to avoid large overhead of synchronization signaling caused by massive terminals. Although OFDM has been used in long-term evolution (LTE), it can hardly meet the above requirements because the orthogonality among subcarriers cannot be maintained in asynchronous transmission.
SEFDM is one of the candidate technologies for 5G system. However, further compression of the distance between sub-carriers makes the performance of bit error rate (BER) much worse than that of OFDM system with traditional detection method. Efficient spectrum utilization is one of the main research points in 5G. Therefore, it is necessary to further research the related problems in efficiency frequency division multiplexing.
Due to the further compression of frequency band, orthogonality between sub-carriers is destroyed, and more complex detection mode is needed to overcome the inter-carrier interference (ICI) and detect the signal [5]. So far, many detection methods for SEFDM system have been proposed such as iterative detection (ID) [6], sphere decoders (SD), truncated singular value decomposition (TSVD), fixed complexity sphere decoder (FSD), combining truncated singular value decomposition and fixed sphere detection (TSVD-FSD) and combining iterative detection and fixed sphere detection (ID-FSD) [7, 8]. All these methods are suitable for SEFDM system [9–12]. However, each detection method has its own disadvantages. For example, the BER performance of ID and SD is worse than that of ID-FSD. But the complexity of ID-FSD is higher than that of ID and FSD. ID-FSD is considered to be the best detection method so far in terms of BER performance.
In this paper, a new receiving method named iterative ICI compensation (IIC) receiver for SEFDM is proposed, which has better BER performance and lower complexity than ID-FSD. The method of iterative ICI compensation receiver is a hybrid one, which combines ID and ICI compensation (IC) receiver.
The rest of this paper is arranged as follows. Section 2 describes the principle of the SEFDM symbol generation and whole frame of traditional SEFDM system. The principle of proposed IC and comparison with other detection methods are depicted in Section 3. Simulation results and conclusion are given in Section 4 and Section 5, respectively.
2 Principle of symbol generation and system model
In the transmitter, complex symbol is generated by symbol mapping and then the SEFDM symbol is generated by band compression algorithm. Specific steps for the process are as follows.
2.1 Symbol mapping
The purpose of symbol mapping is to generate constellation mapping complex symbols, which are mapped into complex symbols by a group of symbols through different modulation schemes by 0, 1. Suppose that number of modulation phase is m, number of transmitted information symbols is n, and the number of complex symbols after mapping is e. After grouping the information 0, 1 binary symbols, each group of symbols is mapped to a complex symbol. Number of binary symbols is h, number of modulation phases of each group is m, and the number of complex symbols after mapping is e, where h= log _{2}m, \(e = \frac {n}{h}\).
2.2 Non-orthogonal processing of subcarriers
where α is the bandwidth compression factor, α=Δf×T; Δf is the subcarrier spacing; T is the SEFDM symbol interval; N is the number of subcarriers; s_{l,n} is the nth subcarrier in the lth SEFDM symbol.
In other words, the element in the matrix is \({\varphi _{k,n}} = \frac {1}{{\sqrt N }}{e^{j\frac {{2\pi \alpha nk}}{N}}}\), where 0≤n<N, 0≤k<N.
3 Detection methods for SEFDM system
So far, many detection methods for SEFDM system have been proposed such as ID, SD, TSVD, FSD, TSVD-FSD, and ID-FSD [7]. All these methods are suitable for SEFDM system.However, each detection method has its own disadvantages. For example, the BER performance of ID and SD is worse than that of ID-FSD. But the complexity of ID-FSD is higher than that of ID and FSD. ID-FSD is considered to be the best detection method so far in terms of BER performance.
In this paper, an ICI compensation detection is proposed, which has the same BER performance as ID with appropriate number of iterations. In addition, a method that named iterative ICI compensation combining ID and IC is proposed, which has the same BER performance as ID-FSD but has much lower complexity.
where S denotes the N-dimensional vector of transmitted symbols, Z represents the N-dimensional vector of Gaussian noise, C is an N×N correlation matrix that describes that the interference between the sub-carriers and R is an N-dimensional vector of distorted symbols after demodulating the received SEFDM symbols using a DFT operation.
3.1 Iterative detection
where R is the is the symbol matrix received by the receiver; S_{ n } is an N-dimensional vector of recovered symbols after n iterations, S_{ n − 1 } is an N-dimensional vector of estimated symbols after n−1 iteration, e is an N×N identify matrix.
ID aims to eliminate the ISI step by step. In (8), S_{ n − 1 } can be seen as an estimate value of S and named \(\overset {\frown }{\mathbf {S}}\)
Equation (9) shows the principle of the process in ID.
In ID, some symbols in Zone A should be detected after each iteration and replace the initial ones. However, these symbols will be detected again in the next iteration since Zone A becomes larger. It leads to the high complexity in ID. So, a simplified ID algorithm which only uses (8) to get the result may be more accepted in engineering implementation.
From (8) we can get the complexity of ID: the number of complex multiplication operations in per iteration is N^{2}; the number of complex addition operations in the first iteration is 2N^{2} and the number of complex addition operations in the rest each iteration is N^{2}. The reason of the phenomenon is that the value of the factor (C−e) has been calculated in the first iteration, which includes N^{2} complex addition operations. Additionally, N is the length of S.
3.2 ICI compensation
The specific operation process is as follows. In the receiver, \(\frac {{{\mathrm {1 - }}\alpha }}{\alpha }N\) zeros are added at the end of R, and followed by the DFT of length \(\frac {N}{\alpha }\). After the DFT processing, a \(\frac {N}{\alpha }\) points data is acquired. Then, \(\frac {{{\mathrm {1 - }}\alpha }}{\alpha }N\) points are removed at the end. The remaining N- point data is an estimate of the matrix S in transmitter. The matrix IC is made to add at the end of matrix R instead of adding zeros and followed by a DFT operation of length \(\frac {N}{\alpha }\), which means the first iteration is accomplished. After the processing, the data \(\hat {\mathbf {S}}\) is much closer to the real data S. Then, another iteration may be done according to the requirement of the system.
The complexity of IC is calculated based on its principle. firstly, a block matrix of the K×K IDFT matrix named I is acquired. Then, the operation of I×S^{′} is done to get the IC matrix. After that, the IC matrix is added at the end of R instead of adding zeros and followed with a DFT operation. Finally, the result is acquired after removing the (K−N) data at the end.
As the size of matrix I is small, the amount of computation of I×S^{′} is not large. The number of complex multiplication that I×S^{′} brings in one iteration is (K−N)N, and the number of complex addition is (K−N)(N−1). Then, a DFT operation is needed. Generally, the number K is an integer multiple of 2, which can replace DFT with FFT and make the operation more efficient. So, finally, the number of complex multiplication operations in per iteration is \(K\log _{2}^{K} + (K - N)N\); the number of complex addition operations in one iteration is \(K\log _{2}^{K} + (K - N)(N - 1)\).
It should be noticed that the matrix IC is generated by I×S^{′} and S^{′} is made up of useful data after the DFT operation other than the ignored data.
3.3 ID-FSD detection
where ||∙|| donates the Euclidean norm. The initial radius equals the distance between the sphere center and the initial constrained estimate \(\bar {\mathbf {S}}\). Due to the ill conditioning of SEFDM system, these initial estimates may deviate greatly from the optimal points. Therefore, ID is employed to calculate an improved initial radius.
The elements of C and Cholesky decomposition of C are stored in this block, where c_{m,n} are the elements of C and are used for calculating the initial radius in Eq. (13). l_{m,n} denotes the elements of the upper triangular matrix and are used for calculating squared Euclidean norm in Eq. (16).
Actually, it’s too complex to consider all of the situations when deciding the value of each dimension in FSD. Therefore, a simplified FSD is implemented in the paper. The simplified method decides an exact value instead of a range from the last dimension to the first dimension. It makes the complexity much lower. However, this method performs well only when the size of the system is small.
3.4 IIC detection
The IIC combines ID and IC detection. Before performing the IC operation, an ID operation is done, which can provide a more accurate initial data for IC detection. When combined with ID, the number of iterations in IC can be reduced drastically, even to only once, which result in the lower complexity.
4 Simulation results
Complexity comparison
ID | FSD | IC | |
---|---|---|---|
Multiplications | N ^{2} | N^{3}+N^{2}+NM | \(K\log _{2}^{K} + (K - N)N\) |
Additions | N ^{2} | N^{3}+N^{2}−N +NM−M | \(K\log _{2}^{K} + (K - N)(N - 1)\) |
Simulation parameters
Detector | FFT size | Subcarrier number | α |
---|---|---|---|
ID | 8 | 7,6 | 7/8,6/8 |
FSD | 8 | 7,6 | 7/8,6/8 |
IC | 8 | 7,6 | 7/8,6/8 |
ID-FSD | 8 | 7,6 | 7/8,6/8 |
IIC | 8 | 7,6 | 7/8,6/8 |
Simulation parameters
Detector | FFT size | Subcarrier number | α |
---|---|---|---|
ID | 16 | 15,14 | 15/16,14/16 |
FSD | 16 | 15,14 | 15/16,14/16 |
IC | 16 | 15,14 | 15/16,14/16 |
ID-FSD | 16 | 15,14 | 15/16,14/16 |
IIC | 16 | 15,14 | 15/16,14/16 |
Figures 8 and 9 illustrate that BER performance of ID is almost same as that of IC. However, the computational complexity of IC is much lower than that of ID.
It can be seen from these figures that in case of small α, more iterations are required to converge the BER curve, and increase the number of subcarriers means the increase of ICI strength, which makes the performance of BER worse.
5 Conclusions
SEFDM yields higher spectral efficiency than OFDM by employing non-orthogonal sub-carriers. The deliberate collapse of orthogonality property in SEFDM systems necessitates more complicated detectors. A new detector named ICI compensation is proposed in this paper, which has better BER performance than iterative detection. Finally, a hybrid detector named iterative ICI compensation is proposed and achieves better BER performance and lower complexity than ID-FSD. However, the IIC method has the similar performance as ID-FSD only when the value of α is large.
Declarations
Acknowledgements
This work was supported by National Natural Science Foundations of China (No.61671183, 61771163 and 91438205) and the Open Fund of Shanghai Key Laboratory of Integrated Administration Technologies for Information Security (AGK201706).
Authors’ contributions
ZYW wrote the majority of the text and performed the design and implementation of the algorithm. QG and XMG contributed text to earlier versions of the manuscript and participated in the theoretical analysis. MJ and ZSY commented on and approved the manuscript. ZYW and ZSY initiated the research on the detection of IC. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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