INSTALACIONES ELECTRICAS 10.1 Generalidades

A multiuser communication scenario of an uplink synchronous CDMA with a pair of collaborating BPSK modulated users kl, l ∈ {1, 2} within kthgroup sharing the common spreading sequence ckand the base-station receiver system employing the former scheme is shown in Figure 4.23.

Figure 4.23: System model of BECD without Relays for uplink of CDMA

During the first period, the users transmit signals skl(j) using the common sequence ckusing

their own data bkl. At the same time, the pairing users i 6= l ∈ {1, 2} receive and decode the

transmitted signals. The received signals rki(j) at the first period j can be written as:

rki(j)= p Pkl/Lgkskl(j) + G X u=1,u6=k L X l=1 p Pul/Lgulksul(j) + v(j), (4.58)

where Pklis the power and L the number of partners per group is used for normalization, skl(j) =

probabilities and with period Tb. The sequence ck consists of antipodal chips each with period

Tc and normalized power over the symbol period

RT_b

0 ck(t)

2_{dt = 1. The spreading factor is}

N = Tb/Tc, gkand gulk are Rayleigh fading inter-user channel (the two way inter-user channels are

assumed symmetric [7]) and channels from users within 1 ≤ u ≤ G, u 6= k groups, respectively which remain constant over the two symbol period), and v is the AWGN with two sided power spectral density N0/2. The second term in (4.65) can also be seen as multiuser interference term

with non-zero variance when non-orthogonal sequences are used [5].

The detection of partner’s data bkl at each pairing user node ki, i ∈ {1, 2} is performed by

first obtaining the soft estimates of the signals by despreading the received signal with sequence ck, given by zkl(j) =

RT b

0 rki(j)c T

k; 1 ≤ k ≤ G; where cT denotes a transpose of vector c. Full

duplex capability is assumed available at user terminals as in [7] for simplicity, however the use of additional relays as in [80] can also be used easily for a more practical half duplex operation. The data estimate ˆbklis obtained as ˆbkl = sgn

h

<zkl(j)g∗k

i

; where sgn[.], <{.} and∗denote sign, real and complex conjugation operation, respectively. The estimated data ˆbklis then spread using

the group spreading sequence ckto form transmitted signals in the second period as follows:

s0_ki(j + 1) = λˆbklck, (4.59)

where λ ∈ {1, −1} is a factor that is dependent on the specific transmission scheme. The received composite signal at the base-station receiver from all users’ transmissions during the first period r(j) and from that of the partnering users’ in the second period r(j + 1) can be written as:

r(j)= G X k=1 L X l=1 p Pkl/Lgklskl(j) + v(j), r(j + 1)= G X k=1 L X i6=l p Pki/Lgkis0ki(j + 1) + v(j + 1), (4.60)

where gklis the Rayleigh fading uplink channel of klth user and assumed constant over the two

symbol period. The structure of the signal s0_ki(j + 1) transmitted during the second period is the same as skl(j), but the data are originated from the kith, i 6= l pairing user terminal with klth

user’s estimated data in the jthperiod ˆbkland transmitted in the next (j + 1)thperiod via its uplink

channel gki.

Assuming average noise variances of all users’ and the base-station receivers are equal, the relative SNR gain in dB of inter-user channels βkcompared to the respective uplink channels can

be expressed as βk= E|gk|2 E|g_kl|2 = E|gk|2 E|gki|2 , (4.61)

where E{.} is the expectation operator. Having introduced with basic signal and channel models, we describe the operation of collaborative transmit diversity schemes next.

Two schemes for the collaborative diversity are presented next. The first scheme is an uncoded scheme where the signals from users sharing the same sequence ckare received as a simple super-

position and the signals are jointly detected and decoded. The second scheme employs distributed space-time coding of users’ data and corresponding detection and decoding at the receiver. 4.5.3.1 Signal Superposition Based BECD

Under this scheme, In the first period, the users transmit their own data {bkl, bki}. During the

second period (j + 1), the cooperating users simply forward the detected data the partners in the previous period ˆbkl and ˆbki to the base-station receiver using the same spreading sequence

ck. Based on the above system model, a signalling structure of the proposed scheme with two

partnering users and spanned over two consecutive symbol period {j, j + 1} can be shown in a matrix form Bkbelow.

Bk =   bk1 bk2 ˆ bk2 ˆbk1  ,

where the rows and columns indicate time periods and signals from users {k1, k2}, respectively. It should be noted that the estimated data {ˆbkl, ˆbki} may not be identical to the transmitted data of

the originating users due to the decoding errors in partners’ receivers.

The base-station receiver first obtains soft estimates of composite data signals for decoding the symbols. This is achieved by first performing CDMA despreading of {r(j), r(j + 1)} using the kthgroup’s spreading sequence ckto obtain the soft data signals {zk(j), zk(j + 1)} shown as

follows: zk(j) = Z T b 0 rk(j)cTk; 1 ≤ k ≤ G zk(j + 1) = Z T b 0 rk(j + 1)cTk. (4.62)

Since {zk(j), zk(j + 1)} consist copies of data signals of both collaborators {bkl, bki} via different

uplink channels {gkl, gki}, either joint ML detection and decoding or space-time decoding is per-

formed to extract the final estimates of users’ data. It is noted that, the latter scheme is particularly more appealing in terms of detection complexity, as the users’ data signals are detected separately due to the orthogonal design of space-time codes [73]. Although, the use of error correction tech- niques such as CRC codes as in [80, 76] can also be used, we do not consider any form of error correction here. This is because we are more interested in the effects of the channels on the diver- sity gain of the scheme to gain insight in to the problem and possible incorporation of coding for future study.

After the soft despread signals {zk(j), zk(j + 1)} are obtained, the receiver performs joint de-

rics of {zk(j), zk(j +1)} for each combination of possible data vectors along with uplink channels

in the first period {gk1, gk2} and second period {gk2, gk1} are used. The receiver obtains the final

estimates of users’ data ˆbk1, ˆbk2from the list of possible data vectors bq = {b1q, b2q, .., bLq}, 1 ≤

q ≤ Q and the one that minimizes the sum distance measure is selected as the transmitted data {ˆb_k1, ˆbk2} = arg min bq∈B h  z_k(j) − L X l=1 gklblq   2 +z_k(j + 1) − L X i=1 gkiblq   2i , (4.63)

where B is the list of all possible Q = 2Lvectors of symbols for BPSK user data signals.

4.5.3.2 Space-Time Coding Based BECD

The transmission scheme we propose here is based on the simple Alamouti space-time codes [73] and is presented in matrix form as follows:

Bk=   bk1 bk2 −ˆb_k2 ˆbk1  ,

where the rows and columns indicate time periods and transmitted signals from users {1, 2}, re- spectively. The received signals are given in (4.67), where uplink channels of users are assumed constant over the two symbol period. The final error performance of both schemes depend on how accurate the estimates ˆbklare, which in turn are dependent on the relative SNR gain of the

inter-user channels βk. The above described transmission and detection processes are performed

at all pairing 1 ≤ k ≤ G users’ terminals.

At the receiver, despreading is first performed as given earlier in (4.62). The signals {zk(j), zk(j+

1)} are processed here following the combining method in [73], which ensures that the data sig- nals of users ˆbkl, l ∈ {1, 2} are detected separately and the copies are maximum ratio combined

by the following process:

ˆ_{bk1 = sgn}h_<zk(j)g∗ k1+ z ∗ k(j + 1)gk2 i ˆ bk2 = sgn h <zk(j)g∗k2− z ∗ k(j + 1)gk1 i . (4.64)

It is expected that under sufficiently high βk, this scheme achieves full diversity gain and ap-

proaches that of the Alamouti scheme.