The Vault

Pulse shaped OFDM for Cognitive Radio
Research Paper / Feb 2014

1 Abstract— Multicarrier modulation (MCM) schemes offer many advantages including high spectral efficiency and robustness against channel selectivity, and have been adapted in current wireless systems. While OFDM has become the most popular MCM scheme, its high side lobes result in spectral leakage. Filtering is a popular technique used to reduce the out-of-band emission of OFDM. However, to utilize non- contiguous spectrum fragments, filters need to be dynamically designed for each fragment, making the use of filtered OFDM challenging. As an alternative, OFDM-Offset QAM (OFDM- OQAM), a filter bank based multicarrier (FBMC) modulation technique, offers better spectral containment and flexibility for dynamic spectrum allocation. However, it has several disadvantages including high complexity and large latency. In this paper, we propose a transceiver architecture based on transmit and receive windowing to reduce spectral leakage and reject adjacent channel interference. Starting from an MCM framework, we first show the implementation of transmit and receive pulse shaping and present the orthogonality condition. The inter-symbol interference (ISI) resulting from receive windowing with a multi-path channel is characterized and the performance of the presented transceiver architecture is evaluated and compared to other MCM techniques. The results show that pulse shaping (also known as windowing) offers a simple transceiver architecture with acceptable performance and it is well suited for non-contiguous spectrum fragments. Its performance can further be improved by using more advanced receivers. Index Terms— Multicarrier modulation, filterbank multicarrier, OFDM-OQAM, pulse shaping, windowing I. INTRODUCTION Multicarrier modulation (MCM) is based on the idea of splitting a high-rate wideband signal into lower-rate signals where each signal occupies a narrower band [1], [2]. Orthogonal frequency division multiplexing (OFDM) has proved itself as one of the most popular MCM techniques and is currently used in many wireless communication systems such as 3GPP Long Term Evolution (LTE) [3], 802.11 [3], etc. OFDM offers many advantages such as robustness to multipath propagation, simple equalization, a simple transceiver architecture and efficient use of the available bandwidth through overlapping subchnanels. On the other hand, it has several disadvantages such as spectral leakage due to high sidelobes, and high peak-to-average power ratio (PAPR). The demand for higher data rates has been increasing significantly. Several techniques have been studied and proposed to meet this demand. Among these, overlaying small cells over macro cells to allow spectral reuse, opening new bands to wireless communication, and utilizing the bandwidth more efficiently by spectrum sharing via cognitive radio are some of the notable ones [5]. Since wireless systems are evolving towards a “network of networks” architecture where many networks are expected to share the spectrum, spectrally agile waveforms with small out-of-band leakage are very important. To that end, the adjacent channel interference (ACI) created by the spectral leakage of OFDM makes this waveform unsuitable for these networks. As an alternative to OFDM, filter bank multicarrier (FBMC) modulation schemes, specifically OFDM-Offset QAM (OFDM-OQAM), have recently taken great interest [6], [7]. OFDM-OQAM is another MCM technique where data on each subcarrier is shaped with an appropriately designed pulse so that side lobes are significantly lower. A real data symbol is transmitted in each subchannel and on each OFDM-OQAM symbol and consecutive OFDM- OQAM symbols are staggered. Adjacent subchannels overlap to maximize the spectral efficiency, creating inter- carrier interference (ICI); and consecutive OFDM-OQAM symbols interfere with each other due to the long pulse, creating inter-symbol interference (ISI). In an ideal single path AWGN channel, perfect orthogonality can be achieved and ISI/ICI be cancelled. The OFDM-OQAM transmitter and receiver are implemented in an efficient manner by using polyphase filterbanks. Although OFDM-OQAM offers significantly less spectral leakage, its implementation in practical systems poses several challenges due to its complexity, latency, and more complex channel estimation and equalization algorithms in doubly dispersive channels [8]. Therefore, it is desirable to design an OFDM-like, but spectral contained waveform with improved out-of-band emission characteristics. One way to improve the spectral containment of OFDM is filtering the time domain signal at the output of the OFDM modulator. However, in a fragmented spectrum where available sub-bands are not contiguous, filtering becomes challenging since a separate filter needs to be designed and used for each fragment [11]. Another method is to use pulse shaping, also known as windowing. In this technique, the rectangular pulse shape of the OFDM is smoothed to prevent sharp transitions between consecutive OFDM symbols, resulting in lower side lobes [9]-[11]. A mechanism is also required at the receiver to reject the adjacent channel interference. This is because even if the interfering signal in the adjacent band has low out-of-band emission, the spectral leakage from the interfering signal significantly increases after the cyclic prefix (CP) removal if the received filter covers the whole accessible band. Therefore, before the CP is removed, the received signal should be filtered for individual sub-bands. Similar to the transmitter filtering, receive filtering imposes challenges in fragmented spectrum. An alternative method is to use windowing at the receiver. Receive windowing has been Pulse shaped OFDM for Cognitive Radio Erdem Bala, Jialing Li, Rui Yang, InterDigital Communications, Inc., Melville, NY, 11747 2 used to reduce the impact of ICI due to carrier frequency offset or Doppler [13]- [16] and to suppress radio frequency interference (RFI) in Discrete Multitone (DMT) systems [17], [18]. In this paper, we propose a transceiver architecture based on transmit and receive windowing to reduce spectral leakage and reject adjacent channel interference. Starting from an MCM framework as in [9], we first show the implementation of transmit and receive pulse shaping and present the orthogonality condition. In most of the previous work, ISI due to receive windowing in multi-path channels is discarded. In this paper, we also characterize the ISI. The performance of the presented transceiver architecture will be evaluated and compared to other MCM techniques in the full paper. The outline of this paper is as follows: In Section II, the system model is introduced. Section III introduces the transmit and receive pulse shaping, presents an implementation of these techniques and shows the characterization of ISI. Section IV draws conclusions. The current paper is a long abstract and features only some of the key results; the final paper will present more details about the presented work. II. SYSTEM MODEL In the following, ๐‘˜ denotes the subcarrier index, ๐‘› denotes the time sample index, and โ„“๐“ denotes the symbol index. The input data sequence to be transmitted on the ๐‘˜’th subcarrier and โ„“๐“’th symbol is denoted as ๐‘†![โ„“๐“]. The data on each subcarrier is convolved by a filter ๐‘! ๐‘ก = ๐‘(๐‘ก)๐‘’!!!"!!! where ๐‘ ๐‘ก is the prototype filter, and ๐œˆ! is the subcarrier spacing. The total number of subcarriers is ๐‘. The critically sampled discrete-time OFDM signal can then be written as ๐‘ฅ[๐‘›] =  !โ„“๐“!!! !!! !!! ๐‘†! โ„“๐“ ๐‘[๐‘› − โ„“๐“๐œ†]๐‘’!!!"!!(!!โ„“๐“!) (1) where ๐œ† = ๐‘ + ๐‘! with ๐‘! being the CP duration (or guard interval) in samples. The pulse shape ๐‘ ๐‘› is defined as ๐‘ ๐‘› = 1,            ๐‘› = −๐‘! ,… ,0,1,…๐‘ − 10,                                ๐‘œ๐‘กโ„Ž๐‘’๐‘Ÿ๐‘ค๐‘–๐‘ ๐‘’ (2) III. TRANSMIT AND RECEIVE PULSE SHAPING A. Transmit pulse shaping It is known that the rectangular pulse shape used in OFDM results in a frequency domain sinc-function with high tails contributing to spectral leakage to the adjacent bands. By smoothing the edges of the rectangular pulse, the spectral leakage can be reduced. One method to achieve this is to introduce a prefix and a postfix before and after each symbol, respectively, and shape these portions with smooth functions, such as a raised cosine function. A sample is illustrated in Fig. 1a. 0 ≤ ๐›ฝ ≤ 1 is the roll-off factor and controls the length of the extended guard interval ๐›ฝ(๐‘ +๐‘!). The overhead created by the additional guard intervals results in spectral loss; one method to reduce this loss is to allow overlapping of the prefix and postfix of consecutive symbols as shown in Fig. 1b. It is also possible to apply the roll-of portion of the window to the CP without adding an extended guard interval; however this would result in ICI. β(N+NG) (b) (a) CP Data CP Data CP Data CP Data + NG N β(N+NG) Fig. 1. Illustrations of two transmit windowing approaches. The implementation of transmit windowing can be derived from (1) by setting ๐œ† = (1 + ๐›ฝ)๐‘!, where ๐‘! = ๐‘ + ๐‘! , and defining ๐‘› =  ๐‘– 1 + ๐›ฝ ๐‘! +๐‘š,   where ๐‘š = 0,… , 1 + ๐›ฝ ๐‘! − 1, and ๐‘– is an integer. Then, the transmit signal can be written as ๐‘ฅ ๐‘– 1 + ๐›ฝ ๐‘! +๐‘š =  ๐‘†! ๐‘– − 1!!!!!! ๐‘[   1 + ๐›ฝ ๐‘! +๐‘š]๐‘’!!!"!!(   !!! !!!!)+ ๐‘†! ๐‘–!!!!!! ๐‘[๐‘š]๐‘’!!!"!!  ! (3) From (3), the implementation of transmit side windowing can be shown as in Fig. 2. s0[ l ] sk[ l ] sK-1[ l] x[n] S[ l] N-point IFFT x0[ l ] xN-1[ l ] P/S pβNT+NG p0 p(β+1)NT-1 p(2β+1)NT-1 p(β+1)NT Z-1 Z-1 p2βNT-1 + + p2βNT pN-1 pβNT+NG-1 pβNT-1 pN pN+βNT-1 Fig. 2. Implementation of transmit windowing. The spectral agility a MCM scheme can be seen by observing its out-of-band emission. To this end, Fig. 3 illustrates the power spectral density of several MCM schemes in a fragmented band; where two available sub- bands on the sides are utilized by a MCM transmitter while the sub-band in the middle is empty. The filtered OFDM uses a 35-tap RRC filter over the whole band and the roll off of the windowed OFDM (W-OFDM) is 128 samples. As we 3 can see from this figure, the spectral leakage of OFDM and filtered OFDM (F-OFDM) into the middle sub-band is similar since one filter over the whole band cannot improve the out-of-band emission. Windowing, on the other hand, is able to reduce the leakage with low complexity. Fig. 3. Power spectral density of MCM schemes in fragmented spectrum. B. Receive pulse shaping A mechanism is required at the receiver to reject the adjacent channel interference leakage. This is required because even if the interfering signal in the adjacent band has low out-of-band emission, the spectral leakage from the interfering signal significantly increases after the CP removal. Therefore, before the CP is removed, the received signal should be filtered. Similar to the transmitter side filtering, receive filtering imposes challenges in fragmented spectrum. An alternative method is to use windowing at the receiver. In general, if the transmitter adds a prefix and postfix as illustrated in Fig. 1, receive windowing may be applied to the prefix, data, and postfix samples. However, in practical systems, the postfix of one symbol serves as the prefix of the next symbol and therefore applying windowing to the postfix introduces additional ISI from the following symbol and increases latency. Therefore, we choose to apply windowing to the prefix and the data portion only, as shown in Fig. 4. DataCP Fig. 4. Illustration of a sample receive windowing. Defining ๐‘› = ๐‘–๐‘ +๐‘š, ๐‘š = 0, 1… ,๐‘ − 1, ๐‘– as an integer and ๐‘ค[๐‘›] as the receive window where some samples of ๐‘ค[๐‘›] can be zero, in the absence of transmit windowing, the estimate of data transmitted on subcarrier ๐‘˜ can be written as ๐‘†โ„“๐“ ๐‘˜ = ๐‘†! โ„“๐“ ๐‘ค[๐‘–๐‘ +๐‘š]๐‘’!!!(!!!)!!(!"!!)!!!!!   !!! !!! !!! !!! (4) From (4), the orthogonality condition is found to be as ๐‘ค ๐‘–๐‘ +๐‘š = ๐‘๐‘œ๐‘›๐‘ ๐‘ก๐‘Ž๐‘›๐‘ก!!!!! (5) The implementation of receive windowing is illustrated in Fig. 5, where ๐‘!"# is the size of the prefix. S/P w 0 wN+Npre-1 ! + + wNpre-1 ! wNpre ! ][ny N-point FFT ! + wα wα+N ! ! wN wN-1 Fig. 5. Implementation of receive windowing. C. ISI Analysis Receive windowing may introduce ISI since part of the prefix is multiplied with the window coefficients and added to samples in the data portion as shown in Fig. 5. The amount of the ISI depends on the channel delay spread and how much of the prefix is used for windowing. The samples in the prefix not used for windowing serves as a buffer against the multi-path. The power of the ISI due to receive windowing is analyzed as follows. Defining ๐‘ญ as the FFT matrix, and ๐œ“ as the duration of the guard band, the received signal after propagating through an ๐ฟ-path channel can be written as ๐’š๐’ = ๐‘ฏ!"#$%๐’ ๐ŸŽ๐×(๐‘ต!๐) ๐‘ฐ๐๐‘ฐ๐‘ต ๐‘ญ!๐‘บ๐’+  ๐‘ฏ!"! ๐ŸŽ๐×(๐‘ต!๐) ๐‘ฐ๐๐‘ฐ๐‘ต ๐‘ญ!๐‘บ๐’!๐Ÿ+ ๐’ (6) where the channel matrices corresponding to the desired signal and the interference from the previous block are ๐‡!"#$%& =   โ„Ž! 0 โ‹ฏโ‹ฎ โ‹ฑ โ‹ฑโ„Ž!!! โ‹ฏ โ„Ž! โ‹ฏ โ‹ฏ 0โ‹ฑ โ‹ฑ โ‹ฎ0 โ‹ฑ โ‹ฎ0 โ„Ž!!! โ‹ฏโ‹ฎ โ‹ฑ โ‹ฑ0 โ‹ฏ 0 โ„Ž! โ‹ฑ โ‹ฎโ‹ฎ โ‹ฑ 0โ„Ž!!! โ‹ฏ โ„Ž!   , ๐‡!"! =   0 โ‹ฏ 0โ‹ฎ โ‹ฑ โ‹ฑโ‹ฎ โ‹ฑ โ‹ฑ โ„Ž!!! โ‹ฏ โ„Ž!โ‹ฑ โ‹ฑ โ‹ฎโ‹ฑ 0 โ„Ž!!!โ‹ฎ โ‹ฑ โ‹ฑโ‹ฎ โ‹ฑ โ‹ฑ0 โ‹ฏ โ‹ฏ โ‹ฑ โ‹ฑ 0โ‹ฑ โ‹ฑ โ‹ฎโ‹ฏ โ‹ฏ 0 (7) The first term in (6) is the desired signal, the second term is the ISI from the previous symbol due to multipath, and the third term is the noise. After applying the receive 4 window, discarding the guard interval, and performing FFT, it can be shown that that the ISI will be equal to ๐’€!"! =  ๐‘ญ ๐ŸŽ ๐‘ต๐’™๐ ๐‘ฐ๐‘ต ๐‘ฏ!"! ๐ŸŽ๐๐’™ ๐‘ต!๐ ๐‘ฐ๐๐‘ฐ๐‘ต ๐‘ญ!๐‘บ๐’!๐Ÿ = ๐‘ญ ๐ŸŽ(๐‘ต๐’™๐) ๐‘ฐ๐‘ต 0… 0  ๐‘ค!!๐‘” 0 … .    ๐‘ค!!๐‘” ๐œ“ − 1 ! ,       where ๐’ˆ = ๐‘” 0 … .    ๐‘” ๐œ“ − 1 ! =   0 โ‹ฏ 0โ‹ฎ โ‹ฑ โ‹ฑโ‹ฎ โ‹ฑ โ‹ฑ โ„Ž!!! โ‹ฏ โ„Ž!โ‹ฑ โ‹ฑ โ‹ฎโ‹ฑ 0 โ„Ž!!!โ‹ฎ โ‹ฑ โ‹ฑโ‹ฎ โ‹ฑ โ‹ฑ0 โ‹ฏ โ‹ฏ โ‹ฑ โ‹ฑ 0โ‹ฑ โ‹ฑ โ‹ฎโ‹ฏ โ‹ฏ 0 ๐ŸŽ๐×(๐‘ต!๐) ๐‘ฐ๐๐‘ฐ๐‘ต ๐‘ญ!๐‘บ๐’!๐Ÿ (8) From (8), the interference power can be computed and the performance of receive windowing analyzed. We can see that ISI depends on the previous symbol, so it would be possible to cancel this interference with a successive interference cancelation (SIC) based receiver. As an alternative, the statistical information of the interference can be used by an MMSE receiver. IV. SIMULATIONS The performance of the W-OFDM is evaluated and compared to the performance of OFDM, F-OFDM, and OFDM-OQAM when adjacent channel interference exists. For the evaluation, a link level simulation tool compliant with the 3GPP Release 8 LTE specifications is used. After QAM modulation, the transmit signal is generated by using one of the MCM schemes. The generated signal goes through a frequency selective fading channel. At the receiver side, the signal is first processed by the appropriate receiver and then data symbols are demodulated. A spectral hole scenario similar to the one depicted in Fig. 3 is created. The bandwidth of the whole channel is set 10 MHz and divided into 50 resource blocks (RBs) where one RB consists of 12 subcarriers. RBs 13 to 36 are available and are used by the desired transmitter while the remaining RBs are used by the interfering transmitter. There is a guard band of 1 RB on each side of the available band. In this setup, the interference created by the out-of-band emission of the interferer leaks to the desired band from both sides. We assume that a 35-tap root raised cosine (RRC) filter covering the whole channel is used for the F-OFDM. The adjacent channel interference is generated using the same waveform as the desired signal. The frequency offset between the desired and interfering signal is set to 0.5Δf, where Δf is the subcarrier spacing and is equal to 15 kHz. The power difference between the ACI and the desired signal is a parameter denoted as ΔP and is set to 0 or 10 dB. An FFT size of 1024 is assumed. The channel is modeled as Extended Vehicular Channel (EVA) with 5 Hz Doppler [19]. A one-tap frequency domain equalizer is used at the receiver and ideal channel estimation is assumed. The modulation scheme used is 16 QAM. Three types of windowing techniques are evaluated. In the first type (W-OFDM), both transmit and receive windowing are applied, and an extended guard interval (EGI) of 32 samples are added at the transmitter, i.e., effectively a longer CP is used resulting in a slight spectral efficiency loss. In the second type (W-OFDM/CP), extended guard interval is not added and the CP is used for windowing purposes. Finally, in the third type (W- OFDM/Rx), only receive windowing is used. The number of samples used for smoothing is 32 and 64, respectively, for the transmit and receive windowing. The windowing function used is given in (9). ๐‘[๐‘›] = 0.5(1 + ๐‘๐‘œ๐‘  ๐œ‹ 1 + ๐‘›๐›ฝ๐‘! , 0 ≤ ๐‘› < ๐›ฝ๐‘!  1, ๐›ฝ๐‘! ≤ ๐‘› < (๐›ฝ + 1)๐‘!  0.5(1 + ๐‘๐‘œ๐‘  ๐œ‹ ๐‘› − ๐›ฝ + 1 ๐‘!๐›ฝ๐‘! ,๐›ฝ + 1 ๐‘! ≤ ๐‘› ≤ 2๐›ฝ + 1 ๐‘! − 1 (9) Fig. 6. Comparison of various MCM techniques with ΔP ACI = 10dB. Fig. 6 compares the BER performance of the various MCM schemes when ΔP ACI = 10dB. We can see from this figure that OFDM performs the worst because of the significant leakage from the adjacent band. The performance of the F-OFDM is similar to OFDM since F-OFDM cannot utilize the spectral hole due to the filter covering the whole 10 MHz band. The performance of the OFDM-OQAM is significantly better than both OFDM and F-OFDM due to its spectral agility and low out-of-band emission characteristics. Since OFDM-OQAM does not have CP, one-tap equalizer is not optimal and its performance may be further improved by using more complex equalizers [20]. Out of the three W-OFDM types, W-OFDM/CP is the worst since the cyclic prefix is used for windowing purposes; which degrades the effectiveness of the CP against multipath. In this case, one-tap equalizer is not optimal any more. W-OFDM with EGI is the best. A slightly longer EGI may be used to further reduce the OOB emission at the expense of a reduced spectral efficiency. Finally, the performance of W-OFDM/Rx illustrates the effectiveness of windowing for interference rejection. Although receive windowing introduces ISI, the benefit of rejecting ACI significantly outweighs the loss introduced by the additional ISI. Fig. 7 compares the BER performance of the MCM schemes when ΔP ACI = 0 dB. The observations are similar 5 to those made for Fig. 6 except that the performance of OFDM and F-OFDM is better because of the reduced ACI power. OFDM-OQAM and W-OFDM still perform better than OFDM and F-OFDM but the performance gap is smaller. Fig. 7. Comparison of various MCM techniques with ΔP ACI = 0 dB. V. CONCLUSIONS In this paper, a transceiver architecture based on transmit and receive windowing to reduce spectral leakage and reject adjacent channel interference has been presented. This architecture has low complexity and can be used to utilize fragmented spectral bands. 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