Figure 10.5 OFDM receiver structure

~

unit by the channel transfer function H_ i at the corresponding frequencies.1 To learn

~

the current channel state, i.e. H_ i, some special training procedures are typically used. Note also that since the guard interval creates a sort of overhead reducing the data transmission rate, it is often reasonable to increase Mc, making the guard interval a small fraction of OFDM symbol duration.

When data are transmitted with PSK and subchannel signals are processed separately, i.e. the ith component of DDFT (10.32) is used independently of the others to demodulate the modulation symbol bi, the equalization above may be simplified to just compensation of the channel phase shift, since subcarrier amplitude is redundant for a decision. If joined subchannel processing is necessary,~however, e.g. in the case of MC-based CDMA considered below, the amplitudes of H_ i are of serious importance, and the ultimate equalizing may appear preferable.

Summarizing, we may present the OFDM receiver structure in the form of Figure 10.5. The sampler provides samples Y_ l, from which the prefix ones are then discarded. The

sample sequence is then transformed into a parallel form. The DDFT unit outputs DFT

~

spectral components Y_ i, which are data symbols bi distorted by noise and channel effects.

Therefore they, after equalizing (just multiplying by an appropriate weight coefficients wi ),

^

may serve to elaborate data symbol estimates bi in the same manner as for BPSK, QPSK, QAM or other modulation mode.

10.2.3 Multicarrier CDMA

The MC modulation scheme is easily adaptable to the multiuser environment to provide code division multiplexing. Unlike DS CDMA, where an appropriate signature shaping in the time domain provides separation of user signals, in multicarrier CDMA (MC-CDMA) signatures are formed in the frequency domain, by controlling the amplitudes and phases of subcarriers in a user-specific manner. One way of explaining MC-CDMA is linking DS CDMA with MC transmission. Let us refer back to Figure 10.3 and imagine that instead of the source fast bit stream we have the kth user data symbol

1 Such evening of the channel transfer function is known as zero-forcing equalizing and was mentioned earlier in Section 6.12.

stream spread by the kth user DS signature of length (spreading factor) N. By this we have N DS chips of duration D per kth user data symbol of duration Tp. Let us demultiplex this fast DS spread stream into Mc ¼ N slow streams, unfolding every data symbol into Mc ¼ N parallel chips of long duration D0 ¼ Tp ¼ ND. Each of these parallel slow chip streams is further transmitted in an MC (OFDM) manner, so that each user has his specific law of modulating subcarriers.

Let us describe the same more directly. Let bk be a current data symbol of the kth user. Let ak ¼ (ak, 0, ak, 1, . . . , ak, N 1) be the kth user signature vector, now used in the frequency domain. To form the MC-CDMA signal N components of vector bkak manipulate in parallel amplitudes and phases of Mc ¼ N subcarriers f1, f2, . . . , fN during the pulse of duration Tp. Summation of all manipulated subcarriers produces the ith MC-CDMA symbol of duration Tp transmitted by the kth user. Certainly, with F ¼ 1/Tp implementing MC-CDMA is more feasible in a typical OFDM DFT-based form, but the direct way of generating the MC-CDMA signal shown in Figure 10.6 for the case of real (e.g. BPSK) alphabets of data symbols and signatures is more transparent as an illustration of the idea. Its generalization to complex alphabets is straightforward. In the OFDM implementation the IDFT unit replaces the multi-channel structure of Figure 10.6.

In synchronous non-oversaturated systems, like mobile radio downlink, any set of K N orthogonal signature vectors (Walsh functions etc.) might provide MAI-free separation of OFDM MC-CDMA user signals, since the orthogonality of the DFT spectra guarantees the orthogonality of OFDM symbols. Selection of signatures in asynchronous systems (e.g. mobile radio uplinks) is not that straightforward, although some minimax signature ensembles characteristic of asynchronous DS CDMA (see Section 7.5) may be of interest for MC-CDMA, too [105–107]. There is one more complication related to designing MC-CDMA signatures which is especially topical for mobile uplinks: the real envelope of the MC-CDMA signal, in contrast to that of DS CDMA, has significant variations, making the peak-factor perceptibly greater than

Figure 10.6 Generation of kth user MC-CDMA signal

one. This issue is to be taken into consideration and, all other factors being the same, of the many candidates the signature set providing the smallest peak-factor should be preferred.

Figure 10.7 presents a generic (non-DFT-based) structure of the kth user’s MC-CDMA receiver. It consists of N ¼ Mc channels, each tuned to its own frequency and realized as a complex correlator processing the observation complex envelope Y_ (t). To counter flat fading within each frequency subchannel, the complex value zk, i from the ith

correlator output is weighted by a complex coefficient wi and multiplied by the conjugated signature symbol ak, i. The last operation is nothing but despreading in the frequency domain. Summation of such products over all subchannels produces the statistic zk to be used in estimating the kth user’s current data symbol bk. Again, in a

DFT realization the DDFT unit replaces the set of correlators.

Let us briefly touch upon the issue of choosing weight coefficients wi , i ¼ 1, 2, . . . , N. In the scenario of MC-CDMA this task is somewhat more complicated than in conventional MC transmission, due to the necessity of controlling MAI level. Suppose that all user signals pass through the same channel, as is the case, e.g., for a mobile downlink.

Since subcarrier spacing F is no smaller than the channel coherence bandwidth, values

~

of the channel transfer function H_ i, i ¼ 1, 2, . . . , N at the subcarrier frequencies may

disperse independently in a wide range. Normalizing the channel transfer function as

Ak. Then the powers Pk, Pnk, Pl created by the useful signal, noise and the lth MAI, respectively, at the kth user output are calculated as:

Figure 10.7 Generic scheme of MC-CDMA receiver

where 2 is noise subchannel power. It is seen now that even if signatures are originally orthonormal:

N 1

X

al;iak;i ¼ kl

i¼0

the frequency selectivity over the subchannels may destroy orthogonality, amplifying some and suppressing other subcarriers. As a result MAI emerges so that not all

Pl, l 6¼k are zeros. To preserve signature orthogonality at the receiving end indepen-

~

dently of the channel current state one should select wi ¼ 1/H_ i, i ¼ 1, 2, . . . , N, i.e. realize zero-forcing equalizing entirely compensating for the channel effects. This, however, is a mismatched processing whenever the channel amplitude transfer function is non-uniform, so that the penalty for complete suppression of MAI is loss in SNR q2k, zf corresponding to zero-forcing combining:

It is seen from (10.33) that when~ nonuniformity of the channel amplitude frequency distortion is remarkable (some H_ i are close to zero), SNR loss, i.e. the penalty for radical elimination of MAI, may appear intolerable, and it is more reasonable to seek for a compromise between the levels of unsuppressed MAI and noise. One of the approaches of this sort leads to MMSE equalization, the idea of which is similar to that discussed in the previous section applied to multiuser detection. Details of this technique, as well as further insight into the spread spectrum MC philosophy, can be found in [105,106] and the numerous references listed there.

In conclusion, we again stress that no hard barrier exists between DS and MC CDMA. They are just parallel technical ways of getting the same result: the spread spectrum signature. The latter may always be synthesized either as a superposition of harmonics in the frequency domain (MC) or by direct shaping in the time domain (DS).

10.2.4 Applications

The penetration of the MC technique into digital telecommunication is presently very wide. Among examples of its practical application are the standards of digital audio and video broadcasting DAB, DVB-T etc. The positive experience accumulated to date