**5. Other MIMO techniques for WOC**

16 Will-be-set-by-IN-TECH

of users (*L* = 4) would outweigh the number of branches concerned (*P* = 3). Then, an additional branch must be considered in order to fulfil the condition *P* ≥ *L* required by LS detectors. Thus, branch 2 must be chosen, since this is another one illuminated by user 6, in addition to branch 3. However, branch 2 is also affected by emissions from user 2, which additionally illuminates branch 6. Finally, the detection of the data coming from only user 3

A simple algorithm can be developed to find the minimum number of branches required for the detection of a certain user's data. Let *uj* be a vector that includes the users' indexes that

branch, and *bl* a vector that includes the indexes of the branches illuminated by a certain user *l*. The algorithm for obtaining the minimum set of branches required to demodulate the data

Fig. 8 compares the performance of the original LS detector, which uses all the *P*max = 6 branches to demodulate the data corresponding to the different users, and a reduced version of this which only uses the minimum set of *P*min branches obtained by using the previous algorithm. The modulation mode was 16-QAM for every subcarrier. The results have been shown versus the total SNR because they are easier to visualise as compared with maximum SNR results where the greater overlapping of the curves hinders its analysis enormously. However, here we are concerned with comparing BER performance of reduced and original

In the graphs, total SNR refers, as in section 4.2, to the sum of the SNRs at each branch for

reduction is applied by using fewer branches during demodulation or not. Therefore, reduced and original LS detectors are compared fairly, contrasting their performances with the same total SNR. Surprisingly, we can see how the reduced LS detector outperforms, although with less than 1 dB gain, the original one for all the users (the unique exception being *l* = 2 for SNRtotal > 23 dB). This can be explained by the fact that, when using all the receiving branches, the residual interference due to the remaining users at each branch impairs the multi-user detector performance, especially when some branches do not receive any signal contribution from the corresponding user. Thus, for example, in the case of the first user, it seems evident that a better performance would be obtained by "switching off" all the receiving branches except the fifth. Therefore, the results show that not only better performance is achieved with the reduced LS detector but also a significant reduction in the complexity of the detection process. Except for users 3 and 4 with slight receiver reductions from 6 to 5 branches, the remaining users can operate perfectly by using only half or fewer of

th receiving branch, *nj* the total number of users illuminating that

th user and not comparing the different performances between users.

*<sup>j</sup>* where *P* = *P*max = 6 irrespective of whether complexity

requires processing the signals received at all the branches except the fifth.

�th user can be described as follows:

7. *x contains the branches to consider for demodulating l*�*th user's data*

*<sup>j</sup>*=<sup>1</sup> SNR(*l*)

significantly illuminate the *j*

1. *Find j so that minimises nj: l*� ∈ *uj*

from the *l*

2. *Set x* = *j* 3. *Set x*� = *x*

4. ∀*j* ∈ *x, repeat 5* 5. ∀*l* ∈ *uj*, *x* = *x* ∪ *bl* 6. *If x* �= *x*� *go back to 3*

LS detectors for each *l*

the corresponding user: ∑*<sup>P</sup>*

the total receiving branches.

As we have seen, the main limitation of LS-based multi-user detection is its high complexity, since it is implemented on a subcarrier-to-subcarrier basis. This complexity can be reduced significantly as described in section 4.3, without forgetting the beneficial capacity of OFDM for accommodating the system throughput to the channel characteristics and number of simultaneous users [9]. However, despite the complexity of the detection process for a particular user being only proportional to the number *P* of receiving branches, obtaining the weight matrix grows exponentially with this number. Therefore, this multi-user technique is only appropriate for scenarios with a reduced number *L* of users (since *P* must always meet the requirement *P* ≥ *L*).

When we are interested in scenarios with large numbers of users, multi-carrier code-division multiple access (MC-CDMA) is a more practical solution [2]. The lower complexity of MC-CDMA to accommodate larger numbers of users implies a compensation payment. Now, the total throughput provided by the OFDM system is shared among all the simultaneous users. This is accomplished by their corresponding orthogonal codes, which avoid any collision between the user's transmissions at a certain subcarrier in a specific instant in time. That is, never there are two users occupying the same frequency-time resource. This can be compared with the multi-user detection techniques presented in this chapter, where the system takes advantage of the spatial diversity provided by the MIMO channel to separate all the users' signals that are continuously being transmitted using all the available bandwidth.

#### 18 Will-be-set-by-IN-TECH 410 Optical Communication

Outside the OFDM context, there are other multiple works addressing MIMO techniques for indoor wireless optical communications, which are generally applied in conjunction with conventional optical modulation schemes (on-off keying, pulse-position modulation, etc.). The main idea of an important group of them relies on creating many nearly-ideal and independent channels between a specific user and receiver by using multibeam transmitters and angle-diversity receivers [1, 14]. Imaging receivers have also been proposed to greatly increase the number of receiving channels at a reduced cost [6, 16], hence providing higher data rates [3, 29]. Sometimes, the distinctive spatial nature of the channel, which is unique, between a specific transmitter and the receiver is exploited to carry additional information as in optical spatial modulation [22].
