orthogonal multicarrier cdma and its detection on frequency-selective channels

1 Multi- Carrier Spread-Spectrum and Related Topics 1

Orthogonal Multicarrier CDMA and its Detection on Frequency-Selective Channels*

W T SARI Juniper Networks, 4-14 rue Ferns, 75014 Paris, France

hsnn'8ieee.org

Abstract. Multicarrier code-division multiple access (MC-CDMA) fust appeared in the literature in 1993. It combines conventional code-division multiple access (CDMA) and orthogonal frequency-division multiplexing (OFDM), and has several variants that depend on how this combination is done. Although there have been a significant number of publications on MC-CDMA since its introduction, the literature is still very fragmented, and the terminologies used by different authors are inconsistent. In addition, there are also a number of confusions concerning the detection of MC- CDMA signals on frequency-selective channels. As an attempt to achieve this goal, this paper gives a comprehensive review of MC-CDMA, descriks its different variants, and reviews the receiver techniques for orthogonal MC-CDMA. It also discusses the relative merits of MC-CDMA and of multicanier timedivision multiple access (MC-TDMA) and orthogonal frequency-division multiple access (OFDMA) which arc the two other multiple access techniques usable in conjunction with multicarrier transmission.

1 INTRODUCTION Multicarrier code-division multiple access (MC-

CDMA) combines the multicarrier transmission technique known as orthogonal frequency-division multiplexing (OFDM) and code-division multiple access (CDMA). The first has been popular in digital audio and video broad- casting, and more recently in wireless local area networks (Wireless LANs), as well as in broadband fixed wireless access. The second is particularly popular in mobile cellular systems. Both OFDM and CDMA have some attrac- tive features, and MC-CDMA attempts to combine them.

Since its introduction in 1993 [1]-[5], there have been a large number of papers on MC-CDMA, each one essentially describing or analyzing a particular variant. One of the difficulties today is that virtually each author has a different terminology, and the terminologies used neither are consistent nor clearly describe the particular technique at hand. We therefore feel a need for a unified presenta- tion of MC-CDMA and a clarification of the detection problem where there seems to be some confusions and inconsistencies. This paper focuses on orthogonal MC- CDMA and attempts to fulfill these goals. It also discusses the performance of this multiple access technique

Parts of this paper were presented at the Third International Work- shop on Multi-Carrier Spread Specmum & Related Topics (MCSS 200 I), September 2001. Oberpfaffenhofen. Germany.

and gives a qualitative comparison with multicanier timedivision multiple access (MC-TDMA) and orthogonal frequency-division multiple access (OFDMA) which are the two other multiple access techniques suitable to multicarrier systems. MC-TDMA and OFDMA were recently adopted for several future standards.

In a multicarrier system, there are obviously different ways of using CDMA. Since multicarrier transmission gives the frequency dimension in addition to the time dimension (which is the only dimension available in single- carrier systems), transmission of the chips corresponding to a given symbol can be done using both dimensions. In the early literature, MC-CDMA was used to describe the variant in which spreading is performed in the frequency- domain only [l] - [3]. The MC-CDMA which spreads a given symbol in the time domain was called multicarrier direct-sequence code-division multiple access (MC-DS- CDMA) in the literature [4]. We can also mention.multitone CDMA (MT-CDMA) in which signal spreading follows the generation of the OFDM signal [ 5 ] . We will not discuss this technique in which the spectral overlap of adjacent carriers is N times that in other variants of MC- CDMA. Finally, spread-spectrum multicarrier multiple access (SS-MC-MA) refers to a multiple access scheme where different user signals are transmitted on different carriers, and code-division multiplexing (CDM) is usid on each carrier [6] . In other words, SS-MC-MA is a simple

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combination of OFDMA and CDM, which means that it is not a variant of MC-CDMA. This technique will therefore nut be included in our discussion.

The purpose of this paper is to give B general and unified framework for MC-CDMA. discuss its detection, and compare it to other multiple access techniques in multicarrier transmission. First, in the next section, we recall conventional CDMA. Next, in Section 3, we give the principle and a general description of MC-CDMA. Section 4 discusses the detection problem on frequency-selective channels and clarifies why detection techniques based on diversity combining are not suitable for MC-CDMA. Sec- tion 5 discusses the relative merits of MC-CDMA. OFDMA, and MC-TDMA. Finally, we give a summary of the results and our conclusions in Section 6 .

2 CONVENTIONAL CDMA CDMA is based on direct-sequence (DS) spectral

spreading, and therefore i t is also often referred to as DS- CDMA. The principle of CDMA is to spread user signals through multiplication by a chip sequence whose rate Iflc is N times that of the symbol rate Ins. That is, TC = T f l . This operation expands the signal bandwidth by a factor of N, but the expanded bandwidth can accommodate a mulcitude of users by assigning one or several spreading sequences to each of them [7], [8]. There are two basic variants of CDMA. One of them employs orthogonal spreading sequences such as Walsh-Hadamard (WH) sequences and is referred to as Orthogonal CDMA (OCDMA). This technique requires very precise timing synchronization on the upstream channel. The other employs non-orthogonal spreading sequences such as pseudo-noise (PN) sequences and requires joint detection or interference cancellation at the receiver to compensate for the interference between signals carried by different spreading sequences.

In the present article, we will focus on OCDMA. It is well known that there exist only N orthogonal binary sequences of length N . The theoretical user capacity of OCDMA is identical to that of TDMA, because on a channel whose bandwidth is N times the bandwidth of individual user signals, both TDMA and OCDMA can accommodate N users [9]. [lo]. TDMA accommodates these signals by transmitting the symbols serially, and OCDMA accommodates them by transmitting a symbol from each user in parallel. OCDM.4 is simply described by an orthogonal transformation of the input signal, in the same way as orthogonal frequency-division multiple access (OFDMA) [ l l ] is described by the Discrete Fourier Transform (DFT). These transformations do not change the number of users that can be accommodated on an additive white Gaussian noise (AWGN) channel, but different multiple access schemes have different behaviors in the presence of channel impairments.

3 PRINCXPLE OF MULTICARRIER CDMA In an MC-CDMA system, transmission of the chips

associated to a given symbol can be done in many different ways. Consider an MC-CDMA system with N carriers and also N chips per symbol. The first type of MC-CDMA transmits the N chips simultaneously by assigning each chip to a separate carrier [ I ] - [3]. Signal spreading in this scheme is performed purely in the frequency domain. The receiver extracts the transmitted symbol by correlating the N signal samples at the DFT output with the sequence used for signal spreading. In other words, this type of MC-CDMA system is the dual of conventional CDMA in the sense conventional CDMA spreads the signal in the time domain and this system spreads it in the frequency domain.

In a second variant of MC-CDMA. signal spreading is performed in the time domain [4], exactly as in conventional CDMA. To do this, the input symbol stream is first converted into a parallel form such that the first symbol of each N-symbol block is transmitted on the first carrier, the second symbol is transmitted on the second carrier, and so on. Signal spreading is then simultaneously applied to all of these symbols using the same spreading sequence, and this is followed by an inverse DFT that operates at the chip rate. The first inverse DFT per symbol bloc transmits the first chips of the N parallel symbols; the second DFT transmits the second chips, and so on. In this scheme, signal detection employs N correlators each operating on a different carrier. The correlator correlates the received N samples per symbol period with the locally generated chip sequence to remove spectral spreading and detect the transmitted symbols. This scheme is referred to as MC- DS-CDMA in the literature, and the term MC-CDMA is often reserved for MC-CDMA with pure frequency- domain spreading. Since CDMA and DS-CDMA are syn- onymous in single-carrier systems. it is unfortunate that MC-CDMA and MC-DS-CDMA are used to designate two different techniques in multicarrier systems. In the rest of the article, we only use the terminology of MC- CDMA no matter how spreading is performed.

With respect to single-user transmission, multiple access systems have some form of inherent diversity, as transmission of the composite signal needs more bandwidth than the individual signals composing it. In timedivision multiple access (TDMA) and in conventional (single-carrier) CDMA. this diversity is purely in the frequency domain, because the symbol duration is not in- creased with respect to single-user transmission. (In fact, TDMA reduces time diversity, since the symbol duration in an N-user TDMA system is reduced by a factor of N.) The pure frequency diversity also holds for MC-CDMA with frequency-domain spreading. In contrast, the dive;- sity is purely in the time domain in the second variant of

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MC-CDMA where signal spreading is performed in the time domain, separately on each carrier. This is easily seen by realizinE that the serial-to-parallel (SP) conver- sion that precedes the inverse DFT operator expands the symbol duration by a factor of N and that all chips associated to a given data symbol are transmitted at the same carrier frequency.

The previous examples are just the two extremes. It is also possible to create some form of diversity both in the time domain and in the frequency domain. The maximum diversity occurs when each chip of a given symbol is transmitted at a different carrier and in a different chip period. This creates an order-N diversity both in the time domain and in the frequency domain. A simple way to do this is as follows: Consider a symbol block (a,, u2, ......., UN) at the S P converter output. Suppose that the kth WH sequence (wk, , wk2, ....., wLN) is assigned to the user at hand. Rather than simultaneously sending to the inverse DFT input all of the N chips associated to one symbol, or serially transmitting all these chips at the same carrier, we can use a transmission scheme described by the following matrix representation:

1 ' I w l l ' N ' " I 2 " N - l W & 1 ... ... a2'vw

a1wur ... ...

The rnth column of this matrix represents the samples simultaneously transmitted on the N carriers during the rnth chip period and the nth row represents the signal samples serially transmitted on the nth carrier. Note that each symbol in this N-symbol block appears once per row and per column of this matrix, indicating that transmission of a symbol spans all carrier frequencies and chip periods. What we- have represented here is the symbol block transmitted by user k. Other user signals have identical representations that are obtained simply by substituting the appropriate user index for the integer k. Different user signals are separated at the receiver due to the orthogonality of the WH spreading sequences used.

Figure 1 shows a simplified block diagram of the signal processing used for each user signal in MC-CDMA before the modulator. The input data symbols which are generated at the symbol frequency I n s , are passed to a serial-to-parallel ( S P ) converter which generates a block of N parallel symbols (u,, uz, ......, UN).

In this single-index representation, the symbol indices correspond to the position of the symbols in the length-N block. The time index and the user index, which are not relevant to this discussion. are dropped for simplicity. Each symbol block has a duration of NTs seconds. but during this interval, N successive inverse DFTs are performed, which means that the inverse DFT operation is

carried out at the symbol frequency I n s . The box labeled chip distribution performs the operation described by the A matrix in (1) and defines the particular MC-CDMA scheme at hand. Specifically, it maps the N' chips associated to the N symbols of the block (N chips per symbol) onto the N parallel inputs of the N inverse DFTs performed during that block. After the inverse DFT, a parallel-to-serial (P/S) converter, that is driven by a clock of frequency N f f . Hz, generates signal samples at N times the symbol rate.

Figure 1: Basic signal processing in a,MC-CDMA transmirter.

4 DETECTION AND PERFORMANCE

As mentioned earlier, we focus here on orthogonal MC-CDMA. This means that the spreading sequences are orthogonal and that user signals are perfectly synchronized. In such a system, user signals remain orthogonaI at the receiver if they are transmitted over an ideal (distortion-free) channel. But orthogonality is destroyed if the channel frequency response is not flat or its phase response is not linear. In this case, the correlator that correlates the received signal with a given sequence yields not only the useful signal but also interference terms from other sequences. Restoring signal orthogonality at the receiver is in fact a pure channel equalization problem, and all techniques previously used for channel equalization are applicable here.

Detectors for MC-CDMA can be grouped into two basic categories: Single-user detectors and multiuser detectors. In the first category, the receiver has knowledge of the spreading sequence employed by the user of interest only, which means that it has no knowledge of the spreading sequences employed by other users. Interfer- ence' from other users is assimilated to' additive channel noise and no attempt is made to compensate for it. .

In the second category, the receiver has knowledge of spreading sequences employed by other users and exploits this knowledge for signal detection. In multiuser detectors based on interference cancellation (IC), the interference affecting each user is explicitly synthesized and sub- tracted from the received signal before sending it to a threshold detector and make symbol decisions.

The two basic forms of IC detectors are parallelher- ference cancellation (PIC) and serial interference cancel-

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lation (SIC). In PIC detectors, a preliminary decision is made simultaneously on all user signals, and these preliminary decisions Are used to estimate the interference affecting the received user signals, subtract the interference, and pass the resulting signals to a set of threshold detectors to make more reliable decisions. This procedure can be reiterated improving the decision reliability from iteration to iteration.

PIC detectors in CDMA and MC-CDMA are analogous to intersymbol interference (ISI) cancellation proposed in the 1970s for channel equalization. This was a generalization of decision-feedback equalizers, where interference is cancelled from both future and past symbols. The other basic form of IC detectors (SIC detection) consists of first making preliminary symbol decisions for the strong signals that are not too much affected by interference and using these decisions to estimate and subtract their interference on other signals, and so forth, until a f irst set of decisions is available for all signals. As in PIC detectors, the process is reiterated to improve receiver decisions until the desired performance is achieved.

1.1 DETECTORS BASED ON CHANNEL EQUALIZATION

Since our focus here is on orthogonal MC-CDMA and the detection problem for this class of signals is a pure channel equalization problem, multiuser detection is not necessary. Indeed, once the channel is equalized. there is no need for the detector to know the spreading sequences of other users, because there is no interference from other users at the threshold detector input. Assume that (HI, H2, ....., HN) designates the frequency response of the channel, i.e.. H, is the complex channel response at frequency fn, for r~ = I. 2, ....., N. The channel is perfectly equalized if the DFT output (q, x2, ...., xN) is passed to a multiplier bank whose coefficients (G/, G2, ....., GN) are given by

This is the frequency-domain version of the channel equalization technique that is commonly referred to as zero-forcing (ZF) equalization in the literature [12]. This criterion perfectly equalizes the channel (and entirely suppresses multiuser interference in orthogonal MC- CDMA), but it significantly enhances the additive noise at frequencies with high channel attenuation.

Another criterion, which trades off the effect of interference with that of additive noise, is the minimum mean- square error (MMSE) criterion [12]. The optimum coefficients of the multiplier bank under the MMSE criterion are given by

, n = 1 , 2 ,....., N (3) G,, = H,' P,l2 + Y

where y denotes the inverse of the signal-to-noise ratio (SNR). Channel equalization will not be perfect in this case, but the combined effect of multi-user interference and of additive noise will be minimized.

4.2 DETECTORS BASED ON DIVERSITY COMBINING

In the literature, there have also been some attempts to use detection techniques inspired from space diversity combining such as equal-gain combining (ECG) and maximum-ratio combining (MRC) [ 131. The reasoning behind the application of diversity combining techniques to MC-CDMA detection is that the N chips of each symbol can be regarded as N replicas of this symbol, and that these replicas should be combined to have a better estimate of the transmitted symbol. It is not a surprise that these attempts did not give any useful results, because as we will show here, this approach is not appropriate for the detection of MC-CDMA signals. Not only this type of combining does not help equalize the channel, but also it may actually increase signal distortion and degrade the bit error rate (BER) performance.

To describe detection techniques based on diversity combining, consider an MC-CDMA system with pure frequency-domain spreading, and again let HI, Hz, ......., HN designate the channel frequency response at the N carrier frequencies. Suppose that ak denotes the symbol to be transmitted by user k at the considered instant. This symbol is multiplied by a spreading sequence (wkl, WU, ....., WW), and the resulting N signal samples (ukwh, n = 1, 2, ....., N) are transmitted at the N carrier frequencies, re- spectively. On the receiver side, the received and de- modulated signal is first passed to a DFT operator, and the DFT output is sent to a correlator that correlates the DFT output samples with a locally generated despreadmg sequence. Equal-gain combining consists of passing the N parallel samples at the correlator output to a bank of complex multipliers whose coefficients are

(4)

Note that the modulus of all G,'s is unity. which is in line with the name of this combining technique. Further- more, for each index n, the product of the gain G, with the channel frequency response H,, is real-valued.

Refemng back to channel equalization, equal-gain combining in the case at hand actually corresponds to Qe unequalized system. First, it is clear that equal-gain combining leaves the channel amplitude response unchanged.

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Second, although it does equalize the channel phase response in some sense, this is not analogous to phase equalization in single-carrier systems. Indeed, phase equalization in single-carrier systems partially equalizes the channel and reduces intersymbol interference. But in multicanier systems, phase equalization only gives the reference carrier phase to each sample at the threshold detector input, and is therefore analogous to the carrier recovery function in single-carrier systems. In other words, symbol detection based on equal-gain combining does not counteract frequency selectivity of the channel, and an MC-CDMA system with such a detector can be indeed assimilated to an unequalized MC-CDMA system.

Next, let us examine maximum-ratio combining. The optimum coefficients of the multiplier bank in this case are given by Cr, = f i n for all n, and the frequency response of the overall channel including the combiner is given by

G , H , = I H ~ ~ * , n = 1,2 ,......, N. ( 5 )

As previously, the combined frequency response is real-valued, which means that the channel is phase- equalized. After the combiner that sums the respective outputs of the N multipliers in the multiplier bank, we have an equivalent channel gain

n=l

This combining technique actually performs frequency-domain matched filtering and therefore maximizes SNR at the threshold detector input. But matched filtering, which is optimum for narrowband channels with a flat amplitude response and linear phase response, is not appropriate to use on frequency-selective channels. The rea- son is that while it maximizes SNR, matched filtering actually increases channel distortion and multiuser interference. Equation (6) indicates that in the dB scale, maximum ratio combining doubles the depth of notches in the channel frequency response. This significantly deterio- rates performance with respect to unequalized systems. There is nothing surprising to this result, because the real problem here is to equalize the channel in order to restore orthogonality of the transmitted sequences and suppress interference between different user signals.

4.3 PERFORMANCE OF VARIOUS DETECTORS

(LOS) wireless indoor channel used by the Broadband Radio Access Networks (BRAN) group of the ETSI for wireless local area networks (LANs) at 5.2 GHz. The spreading factor N used in the simulations is 64, and MC- CDMA is used at full load, i.e., all of the 64 spreading sequences are used.

The results are given in Figure 2, which also shows the performance of QPSK on an ideal additive white Gaussian noise (AWGN) channel as well as the matched filter bound (MFB) corresponding to the channel used. The MFB maximizes the channel SNR and assumes that the interference is perfectly cancelled.

. \ I

Figure 2: Performance of different types of derectors on u BRAN channel.

The results indicate that the MRC detector is unusable in these conditions, as it leads to a BER floor in excess of 10‘. The ECG detector improves performance considera- bly as compared to the MRC detector, but the degradation with respect to the AWGN channel remains very large. Finally, we observe that the two detectors based on linear channel equalization (ZF and MMSE detectors) lead to substantially better performance, with some slight advan- tage to the MMSE equalizer. (The difference between MMSE and ZF detectors is higher on non-LOS channels with higher channel dispersion.) These results confirm our earlier conjecture that signal detection in MC-CDMA is a pure channel equalization problem, and that detectors based on equal-gain or maximum-ratio diversity combining are not an appropriate solution to it.

5 FURTHER DISCUSSION

The three basic multiple access techniques in multicarrier systems are multicanier time-division multiple access (MC--TDMA), orthogonal frequency-division miltiple access (OFDMA) [l 11, and MC-CDMA, which is the topic of this paper. MC-TDh4A is used in the ETSI HIPERLAN2 and IEEE 802.11a standards [15]. [16] for high-speed wireless local area networks (LAN’s). As in single-carrier TDMA systems, the base station in this scheme allocates time slots to different user terminals, and

We now give some simulation results that illustrate the relative bit error rate (BER) performance of the orthogonal MC-CDMA detectors presented in the previous sub- sections. These simulation results, borrowed from [14], were obtained using an uncoded quaternary phase-shift keying (QPSK) modulation and the Type-D HIF’ERLAN2 channel model [15]. This model represents a line-of-sight

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each user terminal transmits only when a time slot is allo- cated to it. The only difference from conventional TDMA is that the transmitted signal is rnulticamer. For conven- ience, the time slot is usually chosen so as to coincide with the length of the inverse DFT that defines the OFDM symbol. or with a multiple of it. MC-TDMA has the prop- erties of OFDM with respect to multipath propagation.

OFDMA consists of assigning a different set of camers to different users. It has appeared in the literature under a variety of names including Synchronized Discrete MultiTone (DMT), Multi-User OFDM, OFDMEDMA, and others. The name OFDMA was coined in [ I I]. where this technique was proposed for the return channel on hy- brid fiberkoax (HFC) networks, which suffers from narrowband ingress noise. It was shown in [ I I ] that OFDMA is the best multiple access technique for channels with narrowband interference. Both TDMA and CDMA break on this type of channel when the power level of the interference exceeds some threshold f17j. In contrast, the interference only affects a restricted number of carriers in OFDMA, and all other camers remain usable. Another interesting feature of OFDMA is that it increases coverage in cellular systems by allocating a power level that is a function of the u m distance on the downstream and con- centrating the available user terminal power on a few carriers on the upstream. OFDMA is today used in the DVB- RCT specifications for terrestrial interactive TV networks [ 181 and it also appears in the IEEE 802.16a specifications [ 191 for broadband wireless access networks in licensed and license-exempt frequency bands between 2 and I 1 GHz.

Comparison of MC-CDMA and MC-TDMA closely resembles that of CDMA and TDMA in single-carrier systems. An interesting feature of MC-CDMA in cellular applications is that i t suppresses the need for frequency planning, since the same channels can be reused in adjacent cells. This gives some flexibility in network planning, but does not mean higher network capacity. If we concentrate on a single-cell (or a cable network) and use orthogonal spreading sequences in MC-CDMA. the maximum capacity will be the same for MC-CDMA and MC-TDMA, and their performance will be essentially the same at full load.

Performance of MC-CDMA improves as the number of users is reduced, but the same type of improvement is also achievable in MC-TDMA by adapting the modulation and coding functions to the average traffic in the network. Specifically, MC-TDMA can use lower channel code rates and a lower-level modulation when the channel load is reduced. Adaptive modulation and coding technique actually appears today in several new standards (or draft standards) including the IEEE 802.1 l a 1161. Finally, MC-CDMA shares the interesting feature of OFDMA that it can allocate a transmit power to each spreading se-

quence that is a function of the user distance to the base station.

6 SUMMARY AND CONCLUSIONS

We have given a comprehensive review of MC- CDMA and described different variants of this multiple access technique from a unified framework. Next, we have clarified the fact that detection of orthogonal MC- CDMA signals on frequency-selective channels is a pure channel equalization problem, and that detectors inspired from diversity combining are inappropriate for this purpose. Indeed, the detector based on equal-gain combining corresponds to the unequalized system, and the detector based on maximum-ratio combining corresponds to the matched filter. The latter actually doubles the frequency selectivity of the channel transfer function and significantly degrades system performance. We have also briefly discussed the relative merits of MC-TDMA and OFDMA, which are the other two multiple access techniques suitable for multicamer transmission.

ACKNOWLEDGMENT The author would like to thank Dr. Rodolphe Le

Gouable from France Telecom R&D, Rennes, for permis- sion to reproduce Figure 2 from his Ph.D. Thesis.

Manuscript received on Apri l 9, 2002.

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