Interleaved block subcarrier allocation and power combination for frequency symbol spreading multiuser diversity OFDMA

In a FSS-OFDMA, the OFDM symbol is spread, and the subcarriers are assigned for each user in the frequency band. As the principal subcarrier allocation for each user, localized and interleaved allocations have been proposed, and the interleaved allocation is improved for the BER performance to avoid continuous deep faded subcarrier channels. Also, in the independent channel fluctuation for each user, the MUDiv gain is obtained by the individual and block subcarrier allocations. However, they have a trade-off problem between the BER performance and the computational complexity. To solve this problem, the interleaved block subcarrier allocation has been proposed. On the other hand, the interleaved block is only evaluated for the individual subcarrier and is not evaluated for the several subcarriers. Moreover, the power combination between the subcarrier and the channel is also improved for the BER performance, but the individual and block subcarrier allocations are only evaluated. Therefore, in this paper, we propose the interleaved block subcarrier allocation and the power combination for a FSS-MUDiv/OFDMA.

the WHT and the DFT in the frequency band [6][7][8][9]. And then, in a FSS-OFDMA, the subcarrier allocation for each user is very important [10]. As the principal subcarrier allocation for each user, localized and interleaved allocations have been proposed. In the localized allocation, the subcarriers for each user are assigned continuously in the frequency band. This is a simple allocation. However, when continuous deep faded subcarrier channels occurred, the BER performance is deteriorated due to a burst error. On the other hand, in the interleaved allocation, the subcarriers for each user are assigned alternately in the frequency band [11][12][13]. In this case, the BER performance is improved compared with the localize allocation since a burst error is prevented by avoiding continuous deep faded subcarrier channels.

Related research status, problems, and this paper's contribution
In Table 1, the related research states, problems, and this paper fs contribution are summarized. In a wireless propagation channel, the channel fluctuation occurred due to a multipath fading at the frequency band [14]. And then, since the propagation channel for each user is independent, the channel fluctuation for each user is also independent. By using this characteristic, the MUDiv gain is obtained by assigning the subcarrier based on the CSI for each user [15]. In this paper, the subcarriers for each user are assigned based on the following condition that the number of subcarriers for each user is equal, and the BER performance is improved in all users. In this case, the individual and block subcarrier allocations have been proposed [16,17]. The individual subcarrier allocation obtains the good BER performance compared with the block subcarrier allocation. However, large computational complexity is required. On the other hand, in the block subcarrier allocation, the block consists of the continuous several subcarriers, and the computational complexity is reduced. However, its BER performance is deteriorated compared with the individual subcarrier allocation. As a result, since they have a trade-off problem, we have proposed the following method to solve this problem [18][19][20]. As mentioned in Sect. 1.1, a burst error occurred due to a deep faded subcarrier channel. In [18], deep faded subcarrier channels are avoided by using cooperative communications, but several relay nodes are required. On the other hand, in [19,20], the subcarriers for each user are assigned by the interleaved allocation as the same [11][12][13], and the MUDiv gain is obtained. In this case, deep faded subcarrier channels are avoided without cooperative communications. However, in [19], large computational complexity is required. Also, in [20], the interleaved block is only evaluated for the individual subcarrier, and its flexibility is not evaluated for the several subcarriers. Moreover, the power combination between the subcarrier and the channel has been proposed [21,22]. It improves also the BER performance, but the individual and block subcarrier allocations are only evaluated. As the other method to solve a deep faded subcarrier channel, WF is also effective, but the adaptive threshold is required [23,24]. Therefore, in this paper, we propose the interleaved block subcarrier allocation and the power combination for a FSS-MUDiv/OFDMA. The proposed method is the new FSS-OFDMA with the interleaved subcarrier allocation, and the utilization for the conventional FSS-OFDMA with the interleaved subcarrier allocation is introduced in the existing standards [9,12,13]. And then, since the proposed method is achieved by changing the subcarrier allocation method from the conventional method, authors think that the proposed method is compatible with existing standards.

Notation and this paper's organization
In Table 2, we define the notation for the symbols. And then, the rest of this paper is organized as follows. In Sect. 2, we present the system model for a FSS-MUDiv/ OFDMA. Then, in Sect. 3, we indicate the methods for the conventional individual and block subcarrier allocations, and the proposed interleaved block subcarrier allocation and power combination. And then, we discuss the system performance for the conventional and proposed methods by using the computer simulation in Sect. 4. Finally, we give the conclusion in Sect. 5.

System model
In this section, we indicate the system model for a FSS-MUDiv/OFDMA. Here, in Fig. 1, the block diagram of the proposed system is shown.

WHT and DFT
In a FSS-OFDM, the OFDM symbol is spread. In this paper, WHT and DFT are utilized as the spreading technique. WHT and DFT are expressed as the (Ñ c ×Ñ c ) matrix. Firstly, the WHT matrix is defined by where ω kÑ c = exp(−j2π k/Ñ c ) , and j = √ −1.

Channel model
Firstly, the CIR for the uth user is constituted by where L−1 l=0 E[|h u,l |] 2 = 1 . And then, the CIR is converted to the CR by the FFT operation as  Figure 1a shows the block diagram of the proposed system for the transmitter. Firstly, the original binary data signals are coded by the convolutional code with an interleaving. Next, after the S/P conversion, the parallel signals are modulated to x u (k, i) between the kth subcarrier and the ith symbol for the uth user. Here, its matrix form for the ith symbol is defined by

Transmitter and receiver
In a FSS-OFDM, the ith OFDM symbol for Eq. (5) is spread by using s u (k, i) between the kth subcarrier and the ith symbol for the uth user as Here, if Ñ c = WÑ c , the OFDM symbols are spread by the WHT. Also, if Ñ c = FÑ c , the OFDM symbols are spread by the DFT. After the symbol spreading, the spreading signals are mapped to the frequency band as where γ u (k) is the selection parameter as shown in Eq. (15). The mapping operation is indicated in Sect. 3. In the mapped signal, GI is inserted after the N c points IFFT operation. Finally, after the P/S conversion, the time domain signal for the uth user is sent to the receiver as Figure 1b shows the block diagram of the proposed system for the receiver. Firstly, the time domain signal is given by where w(t) is AWGN with a single side power spectral density of N 0 . Next, after the S/P conversion and the GI elimination, the time domain signal is converted to the frequency domain signal by the N c points FFT operation as where w(k, i) is AWGN with zero-mean and variance 2N 0 /N c . Here, we assume . And then, the frequency domain signals are detected by using the weight ω(k) for the ZF or the MMSE and are demapped as Observing Eq. (11), the demapped signals for the uth user are obtained in γ u (k) = 1 , and its matrix form is expressed as

Methods
In this section, we indicate the methods for the conventional individual and block subcarrier allocations, and the proposed interleaved block subcarrier allocation and power combination. In this paper, as shown in Sect. 2, since . Moreover, we assume also that the subcarriers for each user are not assigned in the same frequency band, and the number of subcarriers for each user is equal as Ñ c . Additionally, Figs. 2, 4, and 5 show the example of the conventional and proposed subcarrier allocations for N c = 8 and N u = 2 , and Fig. 3 shows the flowchart of the proposed interleaved subcarrier allocation and power combination.

Individual and block subcarrier allocations
As shown in Figs. 2, 4, and 5, in wireless communications, since the propagation channel for each user is independent, the channel fluctuation for each user is also independent at the frequency domain. By using this characteristic, the subcarriers for each user are assigned to obtain the MUDiv gain in the frequency band as (10)  where γ u (k) is the selection parameter as . In this case, at the example of Fig. 2a, J B for B = 1 is given by This means that the subcarriers for the 0th user are assigned in k = 1 , 5, 6, and 7, and the subcarriers for the 1st user are assigned in k = 0 , 2, 3, and 4. As a result, the subcarriers for each user are assigned fairly. And then, the MUDiv gain is obtained since the subcarriers for each use are assigned in the good channel condition. The individual subcarrier allocation for B = 1 gives the good BER performance, but large computational complexity is required compared with B > 1 . To solve this problem, the block subcarrier allocation for B > 1 is also considered. In the block subcarrier allocation, the block consists of several adjacent subcarriers as (14) γ u (k) = 1 for allocation 0 for no allocation, In this case, at the example of Fig. 2b, c, J B for B = 2 and 4 is given by These mean that the subcarriers for the 0th user are assigned in k = 4 to 7, and the subcarriers for the 1st user are assigned in k = 0 to 3. From Eqs. (14) and (16), the block subcarrier allocation for B > 1 is assigned for the subcarriers of each user, and the MUDiv gain is also obtained. Moreover, the computational complexity for B > 1 is reduced compared with B = 1.

Interleaved block subcarrier allocation
As shown in Sect. 3.1, the MUDiv gain is obtained by using the individual and block subcarrier allocations. However, the MUDiv gain for B > 1 is to be small since the possibility for the selection of the deep faded subcarrier channel is to be high compared with B = 1 . Therefore, in the conventional individual and block subcarrier allocations, a trade-off problem is occurred between the MUDiv gain and the computational complexity. Therefore, we propose the interleaved block subcarrier allocation, and its flowchart is indicated in Fig. 3. In the interleaved block subcarrier allocation, the subcarriers for each user are assigned alternately to avoid a deep faded channel, and the block consists of the interleaved subcarrier channel to obtain the MUDiv gain as wherẽ H max I,u (k) is the subcarrier block channel which sorts the power of H I,u (k) as (17), the interleaved block subcarrier allocation is only achieved in B = B max . And then, in this paper, B max equals to Ñ c . In this case, at the example of Fig. 4a, K I for I = 1 is given by (16) This means that the subcarriers for the 0th user are assigned in k = 1 , 3, 5, and 7, and the subcarriers for the 1st user are assigned in k = 0 , 2, 4, and 6. Therefore, in the proposed method, the subcarriers for each user are assigned alternately with the MUDiv gain in the frequency band. Moreover, in this paper, we consider also the case of I > 1 . This is achieved by using Eq. (18), and the interleaved block consists of several subcarriers. And then, the subcarriers for each user are assigned as shown in Fig. 4b. In this case, K I for I = 2 is given by This means that the subcarriers for the 0th user are assigned in k = 2 , 3, 6, and 7, and the subcarriers for the 1st user are assigned in k = 0 , 1, 4, and 5. Therefore, in the proposed method, the subcarriers of each user for I > 1 are also assigned.

Interleaved block subcarrier allocation and power combination
In a FSS-OFDM, the OFDM symbols are spread as shown in Eq. (6). In this case, the power of each subcarrier is different in the frequency band as shown in Fig. 5. Moreover, as the above mentioned, the channel is also fluctuated in the frequency band. By using these characteristics, the power combination between the subcarrier and the channel has been proposed. In this paper, we propose the interleaved block subcarrier allocation and the power combination, and its flowchart is indicated in Fig. 3. As shown in Sects. 3.1 and 3.2, when the subcarriers for each user are assigned, the utilized frequency is also determined by Eq. (17). Here, the assigned channel responses are defined by the matrix form as where H sel u (k) = H u (k)γ u (k) for γ u (k) = 1 . Next, the selected channel response matrix for Eq. (19) and the spread signal matrix of the ith symbol for Eq. (6) are sorted based on these powers as

Computational complexity for conventional and proposed subcarrier block allocations
In this Section, we indicate the computational complexity for the conventional and proposed block subcarrier allocations. Firstly, the computational complexity for the individual and block subcarrier allocations for Eq. (14) is given by Next, the interleaved block subcarrier allocation for Eq. (17) is only achieved in B = B max , and ⌊N c /B max ⌋ equals to N u . Therefore, the computational complexity for the interleaved block subcarrier allocation is given by Finally, the power combination for Eq. (22) is achieved after the utilized frequency selection for each user based on Eq. (17). Therefore, the computational complexity for the power combination is given by (1) = H 1 (6).

(23)
In Sect. 4, we will compare these computational complexities by using the computer simulation parameter of Table 3.

Results and discussion
In this section, we discuss the system performance for the conventional and proposed methods by using the computer simulation. Table 3 shows the computer simulation parameters. In this simulation, we assume FSS-MUDiv/OFDMA systems for N u = 4 . And then, in the propagation channel, the symbol duration is 10 µs , the GI length is 2 µs , and the path model is 15 path Rayleigh fading at Doppler frequency of 5 Hz. Moreover,    Table 4. Firstly, at the transmitter as shown in Fig. 1a, the original data signals are coded by the convolutional code for (R, K) = (1/2, 7) with the bit interleaving. After the S/P conversion, the parallel signals are modulated by 16QAM and are spread per the OFDM symbol by the WHT or the DFT. The spread signals for each user are assigned in the frequency band. Here, in the proposed method, the subcarriers for each user are assigned by the interleaved block subcarrier allocation and the power combination. And then, the mapped signals are converted to the time domain signal by the IFFT operation. Finally, after the GI insertion and the P/S conversion, the time domain signal is sent to the receiver via the propagation channel. Next, at the receiver as shown in Fig. 1b, after the S/P conversion and the GI elimination, the time domain signal is converted to the frequency domain signal by the FFT operation. The frequency domain signals are detected by the ZF or the MMSE. Here, we assume the perfect channel estimation. Moreover, the detected signals are demapped and are despread by the WHT or the IDFT. Finally, after the 16QAM demodulation, the demodulated signals are decoded by the Viterbi soft decoding algorithm with the deinterleaving and are returned to the binary signals.   Figure 6 shows the BER of the various B for the individual and block subcarrier allocations, the interleaved block subcarrier allocation, and the power combination with the DFT, the ZF, and the MMSE, without the coding at E b /N 0 = 25 dB. Here, we define that "Blo" is the individual and block subcarrier allocations, "Int" is the interleaved block subcarrier allocation, and "Pow" is the power combination. And then, Table 5 shows the computational complexity for the individual and block subcarrier allocations, the interleaved block subcarrier allocation, and the power combination. In Table 5, they are calculated from Eqs. (23) to (25) by using the parameter of Table 3.

Results
In the ZF case, the block subcarrier allocation for B = 4 and the interleaved block subcarrier allocation for I = 1 show the same BER performance. Next, in the MMSE case, the block subcarrier allocation for B = 4 and the power combination for I = 1 show the same BER performance. Moreover, the block subcarrier allocation for B = 8 and the interleaved block subcarrier allocation for I = 1 show the same BER performance. Also, in all methods, the MMSE shows the good BER performance compared with the ZF.

Discussion
In the ZF case, the computational complexity for the interleaved block subcarrier allocation is reduced to 256/1,048,576 = 0.0002 times compared with the block subcarrier allocation for B = 4 , and they show the same BER performance. Next, in the MMSE case, the computational complexity for the power combination is reduced to 11,776/1,048,576 = 0.0112 times compared with the block subcarrier allocation for B = 4 , and they also show the same BER performance. Moreover, the computational complexity for the interleaved block subcarrier allocation is reduced to 256/65,536 = 0.0039 times compared with the block subcarrier allocation for B = 8 , and they also show the same BER performance. Additionally, the method for the MMSE obtains the good BER performance compared with the ZF since the detected error is reduced by using the noise power and the spreading technique. Therefore, since the proposed method reduces the computational complexity for the subcarrier allocation dramatically and obtains the good BER performance, it solves the trade-off problem for the conventional method. Figure 7 shows the BER of the various I for the interleaved block subcarrier allocation and the power combination with the WHT, the DFT, the ZF, and the MMSE, without the coding at E b /N 0 = 25 dB. Here, the interleaved block subcarrier allocation for I = 32 equals to the block subcarrier allocation for B = 32.

Results
When I is small, the interleaved block subcarrier allocation for the ZF and the MMSE, and the power combination for the ZF show the good BER performance. On the other hand, they show the floor in B ≥ 4 . Next, the power combination for the MMSE shows the good BER performance in I = 1 and I = 32 , and they show the same BER performance. Also, in all methods, the MMSE shows the good BER performance compared with the ZF same as the case of Fig. 6. Finally, since the interleaved block subcarrier allocation and the power combination for the WHT and the DFT show the same BER performance.

Discussion
The interleaved block subcarrier allocation and the power combination for I = 1 achieve the good BER performance in the ZF and MMSE cases. This means that they are effect when the one chunk length for interleaved block subcarrier allocation (I) is small. And then, they have large effect for the avoiding of continuous deep faded subcarrier channels. Moreover, since their methods with the WHT for the biphase code and the DFT for the polyphase code show the same BER performance, they give the same effect for the BER performance. Additionally, the method for the MMSE obtains the good BER performance compared with the ZF as shown in Section 4.1.2. The advantage of the WHT is the simple processing by the biphase code, and the advantage of the DFT is the low PAPR by the polyphase code [7]. As a result, if the fast processing is required, WHT is better. Also, if the low PAPR is required, DFT is better. Therefore, the proposed method for the WHT and the DFT is effective in a small I. Figures 8 and 9 show the BER of the various E b /N 0 for the interleaved block subcarrier allocation, the power combination, and the WF, with the DFT and the ZF, without the coding. For the WF method, we assume only the simple method in a MUDiv-OFDMA without the spreading technique. In this case, the method for the ZF and the MMSE shows the same BER performance [25]. Therefore, we show only the ZF case in Fig. 9. The modulated signal between the kth subcarrier and the ith symbol for the uth user after the WF is defined by  Fig. 11, the interleaved block subcarrier allocation for I = 1 is also shown to compare the power combination.

Results
From the ZF case of Fig. 8, the interleaved block subcarrier allocation for I = 1 shows about 4.5 dB gain compared with I = 2 in the BER of 1.5 × 10 −5 . And then, the interleaved block subcarrier allocation for I = 2 shows about 5.5 dB gain compared with I = 32 in the BER of 8 × 10 −5 . The power combination shows also the same trend,

Discussion
From the ZF case of Fig. 8, the interleaved block allocation and the power combination show the good BER performance in a small I at various E b /N 0 . This reason is discussed in Sect. 4.2.2. However, they show the same BER performance. This means that the influence of the detected error due to the ZF is strong compared with the diversity gain for the power combination. Next, from Fig. 9, the WF for T wf = −20 dB and W wf = 5 shows the good BER performance compared with the interleaved block subcarrier allocation for I = 32 by assigning the adaptive threshold and power. This is because WF is achieved based on the interleaved block subcarrier allocation for I = 32 without the spreading. On the other hand, it shows the bad BER performance compared with the interleaved block subcarrier allocation for I = 1 . This means that the proposed method is mitigated for a deep faded subcarrier channel compared with the WF method. Therefore, the proposed method is effective compared with the WF method.
From the MMSE case of Figs. 10 and 11, the interleaved block allocation and the power combination also show the good BER performance in a small I at various E b /N 0 same as the ZF case. And then, from Fig. 11, since the power combination shows the good BER performance compared with the interleaved block subcarrier allocation, the diversity gain for the power combination is obtained in the MMSE case. Therefore, in the proposed method, MMSE is effective to obtain the diversity gain for the power combination. Moreover, the power combination for I = 2 and the interleaved block subcarrier allocation for I = 1 show the same BER performance. In this case, the computational complexity for the interleaved block subcarrier allocation is reduced to 256/11776 = 0.0217 times compared with the power combination from Table 5. Additionally, the method for the MMSE obtains the good BER performance compared with the ZF as shown in Sects. 4.1.2 and 4.2.2. Therefore, the interleaved block subcarrier allocation for I = 1 is effective for the BER and the computational complexity in the MMSE case without the coding. Figures 12 and 13 show the BER of the various E b /N 0 for the interleaved block subcarrier allocation and the power combination with the DFT, the MMSE, and the coding.

Results
From Fig. 12, the interleaved block subcarrier allocation for I = 1 shows about 1 dB gain compared with I = 2 and shows about 4 dB gain compared with I ≥ 4 in the BER of 1 × 10 −7 . Moreover, since the interleaved block subcarrier allocation for I = 2 shows about 3 dB gain compared with I ≥ 4 . Next, from Fig. 13, the power combination for I = 1 , 2, and 32 shows the same performance in the BER of 1 × 10 −7 . Moreover, they show about 3 to 4 dB gain compared with I = 4 , 8, and 16. Also, the interleaved block subcarrier allocation for I = 1 also shows the good BER performance same as the power combination for I = 4.

Discussion
From Figs. 12 and 13, in the coding case, since the interleaved block subcarrier allocation and power combination for I = 2 show the good BER performance, they are effective as I = 1 . Therefore, the proposed method for I = 2 is also effective by obtaining the coding gain. Moreover, since the interleaved block subcarrier allocation for I = 1 shows also the good BER performance, it is effective as the uncoding case. Figures 14 and 15 show the BER of the various E b /N ici for the interleaved block subcarrier allocation and the power combination with the DFT and the MMSE, without the coding at E b /N 0 = 25 dB.

Discussion
From Figs. 14 and 15, the interleaved block subcarrier allocation and the power combination for I = 1 and 2 show the good BER performance. Therefore, the proposed method is effective to reduce the influence of the ICI by using the interleaved allocation and the MUDiv gain same as the E b /N 0 case.

Conclusion
In this paper, we have proposed the interleaved block subcarrier allocation and the power combination for a FSS-MUDiv/OFDMA. In the individual and block subcarrier allocations, the MUDiv gain is obtained by using the independent channel fluctuation for each user, but they have a trade-off problem between the BER performance and the computational complexity. To solve this problem, in the proposed method, the interleaved block subcarrier allocation which consists of the interleaved block for the individual and several subcarriers is achieved. Moreover, the power combination between the selected interleaved subcarrier and channel is also achieved. From the computer simulation results, the proposed method reduces the computational complexity and shows the good BER performance. Especially, in the proposed method, the interleaved block subcarrier allocation for I = 1 and 2 is effective for the ZF and the MMSE cases with and without the coding.