# CDMA tutorial, part 2: time division and multicarrier CDMA

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*This series is excerpted from "Mobile Broadband Multimedia Networks: Techniques, Models and Tools for 4G."
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Part 1 introduces CDMA and Wideband CDMA (WCDMA). Also see our OFDM tutorial. The many papers noted in this series are listed in the references section.*

**2.3.3 Time division CDMA**

Joint Detection (JD) is an advantageous detection scheme for time slotted CDMA systems, which leads to air interface concepts known as Joint Detection-Code Division Multiple Access (JDCDMA) [Klei96], [LuBa00]. Also TD-CDMA, the air interface for the TDD bands of UMTS and IMT-2000 [HKKO00], utilizes JD as an option, which allows the total elimination of intracell multiple access interference and intersymbol interference. It is expected that in many applications of TD-CDMA, for instance web browsing, the downlink has to support much higher data rates than the uplink. Therefore, in TD-CDMA the downlink tends to be the bottleneck, and it would be desirable to enhance the performance especially of this link. In what follows, we will show how such an enhancement can be achieved by a non-obvious and inexpensive combination of conventional JD-CDMA with the scheme Joint Transmission (JT) recently proposed in [MBWL00], [MBLP00], [BMWT00], [MTWB01]. As a prerequisite of this combination, the channel impulse responses valid in the downlink have to be known at the Base Station (BS). In the case of TDD systems, this knowledge is at least approximately available from the uplink channel estimation. The combination of JT with multiple transmit antennas at the BS is especially favorable. With JD it is easily possible to make optimum use of multiple receive antennas [StBl96], [BKNS94]. JT offers a solution dual to the one exploited in JD to make optimum use of multiple transmit antennas. In order to keep the presentation as concise as possible, the reader is assumed to be familiar with the contents of [Klei96], [LuBa00], [HKKO00], [MBWL00], [MBLP00], [BMWT00] and with the notations introduced in those publications.

Let us consider a conventional JD-CDMA downlink where the BS supports *K* MT *k *= 1 *. . . K*.
The *K *partial data vectors __d__* ^{(k)}*,

*k*= 1

*. . . K*, to be transmitted by the BS to the individual MTs

*k*= 1

*. . . K*can be stacked to form the total data vector:

Generally, both the BS and the MTs dispose of more than one antenna. By means of a modulator matrix **M **that is a priori constituted by the utilized CDMA codes and – if multiple transmit antennas are employed at the BS – also by the antenna weights [LuBa00], the total transmit signal

is generated. The channel impulse responses between the individual antennas of the BS and MT *k*, can be represented by the partial channel matrix __H__* ^{(k) }*[LuBa00]. Then, the desired signal impinging at MT

*k*is given by

where ** s **in the middle term of (2.33) is substituted by (2.32) in order to obtain the right-hand term of (2.33). At MT

*k*, with

__e__*of (2.33) and following the zero forcing algorithm to perform JD, the estimate*

^{(k) }

of **d **of (2.31) can be obtained [Klei96], [LuBa00], where the matrix in brackets is a posteriori determined at MT

*k*. Of course, at MT

*k*only the estimate

of the partial data vector __d__* ^{(k) }*pertaining to MT

*k*is of interest, where stands for a matrix

__D__*consisting of lines*

^{(k) }*i*through

*j*of the matrix in brackets. Nevertheless, the matrix utilized in conventional JD allows data that is not useful to a particular MT to be detected there, which is unnecessary. This feature of conventional JD-CDMA can be considered as an unnecessary restriction when generating the transmit signal

**. Generating**

__s__**according to (2.32) would have the effect that also irrelevant data could be detected by JD at MT**

__s__*k*. Therefore,

**should rather be generated under the sole consideration of the data of interest to this MT, being**

__s__

__d__*. This rationale would offer additional degrees of freedom when designing*

^{(k)}**, which for instance could be exploited to minimize the required transmission energy and, consequently, the interference to MTs not belonging to the ensemble of the**

__s__*K*MTs

*k*= 1

*. . . K*.