Assignment of Walsh Codes: Reverse Link

The IS-2000 reverse link (for RC3, RC4, RC5, and RC6) is fundamentally different from that of IS-95. On the IS-95 reverse link, only one channel is active at a time (i.e., either the access channel or the traffic channel). Therefore, there is no need to distinguish individual channels transmitted by a mobile since each mobile can only

transmit one channel at a time. In IS-95, a mobile is distinguished from other mobiles by its long PN code.

In IS-2000, a mobile can transmit multiple channels simultaneously. So the base station not only has to distinguish among different mobiles, but also has to distin- guish among different channels transmitted by a specific mobile. In IS-2000, the base station still discriminates the mobiles by their individual long PN codes, but after a mobile is identified using its long PN code, the base station demodulates the channels (transmitted by that mobile) using their assigned Walsh codes2_{. Note that}

this arrangement is analogous to the forward link where, to a mobile, different base stations are first identified by their short PN codes. After a mobile identifies a spe- cific base station, the mobile then demodulates the channels (transmitted by that base station) using their assigned Walsh codes. What enables the operation of the IS-2000 reverse link is that the mobile now transmits an R-PICH, which allows the base station to perform coherent detection of the mobile’s signal and to lock onto a mobile’s identifying PN code.

In IS-2000, the base station does not dynamically assign Walsh codes for a mobile to use. Rather, the IS-2000 standard defines the Walsh code each reverse link channel must use. Table 9.2 shows these predefined Walsh codes and their lengths on the reverse link [1].

To ensure orthogonality, the preassignment of these Walsh codes also meet the constraints described in the previous section. For example, a mobile would some- times transmit both the R-FCH and the R-DCCH simultaneously. As shown in Figure 9.5, the Walsh code preassigned to the R-FCH ([0000111100001111]) is not directly or indirectly related to the Walsh code preassigned to the R-DCCH ([0000000011111111]). In addition, if the system chooses [01] to channelize R-SCH 1, then it can choose either [0011] or [00111100] to channelize R-SCH 2. If it chooses [0011] to channelize R-SCH 1, then it cannot choose [00111100] to chan- nelize R-SCH 2; in fact, in this case the mobile cannot have an additional R-SCH (i.e., R-SCH 2) because the standard does not have preassigned any usable Walsh code. Figure 9.5 shows the location of these Walsh codes on the recursive tree.

Table 9.2 Walsh Codes Used on the Reverse Link for Both SR1 (RC3 and RC4)3

and SR3 (RC5 and RC6)

Channel Walsh Code Walsh Code Length

R-SCH 1 w2 4 =[0011] or w1 2 =[01] 4, or 2 R-SCH 2 w6 8_{=[00111100] or w} 2 4_{=[0011] 8 or 4} R-FCH w4 16 =[0000111100001111] 16 R-DCCH w8 16 =[0000000011111111] 16 R-EACH w2 8_{=[00110011] 8} R-CCCH w2 8 =[00110011] 8

2. IS-2000 calls Walsh codes used on the reverse link Walsh covers.

3. Walsh code lengths for RC1 and RC2 are not shown because Walsh codes are not used for channelization in these radio configurations.

At this point, readers may ask that given a predefined Walsh code, how does the system vary the transmission rate on the reverse link. To change the transmission rate, the mobile uses the same Walsh code but repeats it in a given bit. Figure 9.6 illustrates this operation. Suppose that an R-SCH is operating at 614.4 Kbps1_{and is}

using Walsh code [01]. This gives a final chip rate of 1.2288 Mcps (= 614.4 Kbps× 2). Now the system would like to change the rate from 614.4 Kbps down to 153.6 Kbps1_{(by a factor of four). What the mobile would do then is to repeat Walsh code}

[01] four times during a bit, thus still attaining a final chip rate 1.2288 Mcps. Note that repeating a Walsh code does not cause any orthogonality problems because the

9.3 Code Management 149 Level 0 Level 1 0 0 0 0 1 0000 0011 0101 0110 00000000 00001111 00110011 00111100 01010101 01011010 01100110 01101001 Level 2 Level 3 W4 W8 W2 Level 4 W16 0000000011111111 0000111100001111 R-SCH1 or R-SCH2 R-SCH1 R-SCH2 R-EACH or R-CCCH R-DCCH R-FCH

Figure 9.5 Location of reverse link Walsh codes on the recursive tree.

614.4 Kbps 1.2288 Mcps 153.6 Kbps 1.2288 Mcps 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 chip 1 bit 1 bit 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 chip usew₁2

repeatw four times₁2

standard has already predefined the Walsh codes in such a way that they are not related directly and indirectly (by branches), and repeating a Walsh code is equiva- lent to traversing down the recursive tree along the branches.

9.4

Turbo Codes

Turbo codes are relatively new in the family of error-correcting codes. They were first proposed in 1993 [5, 6] and constitute a new way of implementing concate- nated codes. IS-2000 makes use of turbo codes because of their ability to achieve low error rates at very-small signal-to-noise ratios (SNR) or Eb/N0. Recall that

M W R

E_b N

∝ ( / )

( / ₀) (9.3)

where M is the number of simultaneous users [3]. Equation (9.3) states that, in gen- eral, the capacity of a CDMA system is directly proportional to the processing gain (W/R) and inversely proportional to the required Eb/N0. Therefore, to the extent that

the required Eb/N0can be reduced, the capacity of a CDMA system can be increased

(subject to the availability of orthogonal codes, of course).

A turbo encoder has some important and distinguishing characteristics:

• _{A turbo encoder typically contains two convolutional encoders. These convo-}

lutional encoders are sometimes referred to as constituent encoders. The con- stituent encoders are usually identical to each other.

• _{Each constituent encoder operates as a recursive systematic convolutional}

(RSC) encoder. In producing coded bits, an RSC encoder not only linearly combines shifted bits at different stages in the register, but also feeds back these shifted bits to the beginning of the register.

• _{Whereas the first constituent encoder codes the message bits as they enter the}

turbo encoder, the second constituent encoder codes a permuted version of the message bits.

Figure 9.7 shows an example of a turbo encoder with its two constituent encod- ers arranged in a parallel fashion. In this example, each constituent encoder operates at rate 1/2 and produces two coded bits for every input bit. Turbo codes imple- mented by turbo encoders shown in Figure 9.7 are also known as parallel concate- nated convolutional codes (PCCC) because they are generated by concatenating two convolutional codes in parallel.

Figure 9.7 shows that the message bits mi(to be encoded) also form parts of the

output bits. Because each constituent encoder is of rate 1/2, Encoder 1 operates on miand produces coded bits x′iand x″i. Encoder 2 operates on a permuted version of mi, or mi, and produces coded bits y′iand y″i. The interleaver rearranges the bits mito

produce miin such a way that miappear completely different from mi. The inter-

leaver typically operates on a block of input bits at a time. In addition, a puncturing function selectively deletes the coded bits (produced by constituent encoders) to arrive at a desired rate for the whole turbo encoder. In the example shown in Figure

9.7, each constituent encoder operates at rate 1/2 and produces two coded bits for every input bit. If there is no puncturing, then the entire turbo encoder operates at rate 1/5 because a total of five bits (including the input bit itself) are produced for every input bit.

The turbo encoder shown in Figure 9.7 happens to be the one used by IS-2000. In fact, both the forward link and the reverse link use the same turbo encoder. By using puncturing, the turbo encoder used in IS-2000 can operate at rates 1/2, 1/3, and 1/4. For example, to achieve rate 1/3, the turbo encoder only outputs mi, x′i, and y′iand lets the puncturing function completely punctures out x″iand y″i. In terms of

the interleaver, the interleaver permutes one frame of bits at a time.

The interleaver is a key to turbo codes’ good error-correcting performance. Because of the interleaver, the two constituent encoders essentially operate on the same set of bits but in different order. Therefore, at the receiver, erroneous bit sequences that appear correct to one decoder would more likely be rejected by the other decoder [7]. As the previous sentence implies, at the receiver the turbo decoder consists of two convolutional decoders. The decoding of turbo codes is beyond the scope of this book. It suffices to say that the two convolutional decoders work together by exchanging soft decisions between themselves and iteratively arrive at the (hard) decisions on what the correct message bits should be. See [8, 9] for good discussions of turbo decoding.

The reason why turbo codes are used in 3G systems is their ability to correct errors at a low SNR. They have been shown to achieve very-low error rates (i.e., around 10–5_{) but require only an SNR of less than 1 dB above the Shannon’s limit.}

The cost of such a superior error performance is equally obvious. Turbo coding and decoding are computationally more intensive than conventional convolutional cod- ing and decoding. Delays resulting from such computations render turbo codes unusable in voice applications. This is the reason why, in IS-2000, turbo codes are only used for supplemental channels (forward and reverse) for data applications

9.4 Turbo Codes 151 Constituent encoder 1 (rate 1/2) Puncture mi Interleaver xi' x''i Constituent encoder 2 (rate 1/2) Puncture yi' y''i mi ( Turbo encoded bits

where delays can be tolerated. Research has shown that in IS-2000 turbo codes can achieve gains of 1.3 to 1.5 dB at an FER of 1% [10].

9.5

Transmit Diversity

IS-2000 has made much effort to improve the forward link. One reason is that field experience with IS-95 has shown that in many instances the system is forward link limited [11]. Another reason is that many high-rate data applications sup- ported by 3G require higher throughput on the forward link. One enhancement made to improve the forward link is the enhanced forward link power control (see Chapter 7); IS-2000 can now power control the forward link at a rate of 800-times- per-second.

Another enhancement IS-2000 made is transmit diversity, which typically uses two transmit antennas. Transmission through two antennas achieves spatial diver- sity when antennas are spaced sufficiently apart (by several wavelengths). This way two transmitted signals undergo independent fading and are uncorrelated, and the probability that both signals undergo fading at the same time is small. IS-2000 pro- visions two transmit diversity schemes: orthogonal transmit diversity (OTD) and space time spreading (STS). In OTD, the base station splits the symbol stream into multiple streams and transmits them through multiple antennas. In STS, the base station duplicates multiple copies of the symbol stream and transmits them through multiple antennas.