Base Station

effort of theQ-point IFFT required for OFDMA is small.

For M > 4, the time domain implementation can be considered as inappropriate be-cause it requires a significantly higher number of complex multiplications than the implementation in frequency domain. Regarding today’s markets for available Digital Signal Processors (DSPs), it can be seen that DSPs providing several hundred millions of complex multiplications per second are already available. Thus, the computational power required for OFDMA and B-IFDMA modulation in future mobile terminals is already on the market. However, as computational power is always a source of costs, a low complexity solution as provided for B-IFDMA with M <4 can be still regarded as an interesting option in order to make low cost mobile terminals possible.

complexity of the channel estimation algorithm depends on the number of pilots within a subcarrier set and, thus, on the B-IFDMA signal parameters, cf. Section 4.2.6. In the following, for the complexity of the channel estimation, as a worst case it is assumed that channel estimation has to be performed for every subcarrier in each subcarrier set.

As discussed in Section 4.2.6, this would be the case for B-IFDMA with L= 1. Thus, the computational effort for channel estimation results inK·Qcomplex multiplications per base station.

For frequency domain equalization, the received signal has to be multiplied with the inverse of a matrix, cf. (2.31) and (2.32). As the matrix to be inverted is a diagonal matrix, cf. Section 2.3.5, the matrix inversion can be performed by an inversion of the diagonal elements of the matrix. Thus, the multiplication of the received signal with the equalizer matrix, cf. (2.33), can be implemented by a division of the received signal at every subcarrier by the respective diagonal element. Thus, the required computational effort for frequency domain equalization is given by K·Q complex divisions per base station.

Thus, in total, the computational effort for the B-IFDMA base station receiver imple-mented in frequency domain is given by

MUL^(f)_B−IFDMA,Rx = 1

2N ·ld(N) +K·Q+K· 1

2Q·ld(Q) (4.26) complex multiplications and

DIV_B−IFDMA,Rx^(f) =K ·Q (4.27)

complex divisions per base station per modulated data symbol vector.

In order to obtain the computational effort for the B-IFDMA base station receiver with demodulation implemented in time domain, the computational effort of the N -point FFT in (4.26) has to be replaced by the effort required for K demodulators implemented in time domain according to (3.28). As the output of the demodulator is a signal in time domain and equalization is performed in frequency domain, an additional Q-point DFT is required for each of the K users. Thus, the computational effort of the respective base station receiver is given by

MUL^(t)_B−IFDMA,Rx = K·N

L + 2K· 1

2Q·ld(Q) +K·Q (4.28) complex multiplications and

DIV_B−IFDMA,Rx^(t) =K ·Q (4.29)

complex divisions per base station and per modulated data symbol vector.

For OFDMA, compared to (4.26), the DFT pre-coding does not have to be reversed at the receiver. Thus, for OFDMA, the computational effort for the OFDMA base station receiver implemented in frequency domain is given by

MUL^(f)_OFDMA,Rx = 1

2N·ld(N) +K ·Q (4.30)

complex multiplications and

DIV_OFDMA,Rx^(f) =K·Q (4.31)

complex divisions per base station and per modulated data symbol vector. Similar as for the OFDMA modulation, in general, there is also no efficient time domain implementation for OFDMA demodulation.

Since, as explained in Section 4.3.1, B-EFDMA can be regarded as IDFT pre-coded B-IFDMA, the computational effort of a base station receiver for B-EFDMA using the time domain demodulation from Section 3.2.4 is given by the computational complexity of the B-IFDMA receiver, where the IDFT after frequency domain equalization, cf.

Figure 2.4 in Section 2.3.5, is omitted and, thus, is given by MUL^(t)_B−EFDMA,Rx = K·N

L +K· 1

2Q·ld(Q) +K·Q (4.32) complex multiplications and

DIV_B−EFDMA,Rx^(t) =K·Q (4.33)

complex divisions per base station per modulated data vector.

In Figure 4.22, the respective numbers of complex multiplications are depicted for Q = 64. The system parameters are chosen according to Table 4.2. The required number of complex divisions is the same for all schemes that are regarded throughout this section and independent from the B-IFDMA signal parameters. It is given by K · Q = N = 1024 complex divisions per base station per modulated data vector.

As in Section 4.3.1, from the required numbers of multiplications per modulated data vector, the required numbers of complex multiplications per second can be calculated.

It is given by the multiplication of the number of complex multiplications per modu-lated data vector with 1/(T +TCP) ≈ 34722. In Figure 4.22, the required number of complex multiplications per second is given on the vertical axis on the right. Figure 4.22 shows that, in general, for B-IFDMA, the computational effort at the base station is slightly higher than for OFDMA, because for B-IFDMA the DFT pre-coding has to

be reversed at the receiver side. Again, the implementation in time domain shows a computational complexity that increases with an increasing number M of subcarriers per block whereas the computational complexity for the implementation in frequency domain is independent of M. However, at the base station receiver, the demodula-tion in time domain requires a significantly higher computademodula-tional effort compared to frequency domain demodulation for all numbers M. The reason is that in case of time domain demodulation one demodulator is required for each user whereas for fre-quency domain modulation an N-point DFT together with the subcarrier demapping performs user separation jointly for all users. Thus, at the base station receiver, for uplink transmission, the implementation in frequency domain is clearly preferable.

Figure 4.22: Computational complexity in terms of required complex multiplications per base station and per modulated data symbol dependent on the number M of subcarriers per block.