Dear Talha, Thank you for your answer. Why do you think that LTE requires equalization only in the uplink , is it probably because the uplink is not well controlled by the base station compared to the downlink?. Thanks. @AlDmour.

Dear Adam, I think equalization is needed to combat Intersymbole Interference (ISI), which is a self interference (which is probably what you referred to as "spurious influence"), and has nothing to do with interference from other sources. Please correct me if I am mistaken. Hence, I cam't see the role of frequency hopping in combating ISI.

Basically, as we are have large symbols in LTE (Narrow band sub-channels of about 10KHz) the need for equalization is less than in GSM (200KHz). Part of this large symbol is used to account for ISI. The remaining question is do we actually have to use equalization in LTE and if so how we compare the complexity of equalizers in LTE to GSM?. Thanks. @AlDmour.

Well, I do not fully agree. In non-OFDM systems such as GSM and UMTS, equalization is used to combat ISI, and also to utilize the energy from several echoes and thus achieve a diversity gain. However, that is not true for OFDM/OFDMA/SC-FDMA systems. Equalization is not required to combat ISI in those systems, because the symbols are very long in time, and we can afford a long guard interval in-between the symbols. The ISI can be completely eliminated in OFDM systems as long as the guard interval is longer than the time spreading between the echoes, which normally is the case.

Actually, equalization is not needed at all in OFDM systems where DPSK modulation is applied to each sub-carrier, for example in the digital-audio-broadcasting system DAB/Eureka; such systems are not sensitive to phase shift and minor amplitude changes caused by fading. An error-correcting code is enough to deal with frequency selective fading (different phase shift and amplitude shift of each sub-carrier), The error-correction can cope with a certain portion of sub-carreirs that are completely cancelled out by fading and noise. On the other hand, OFDM systems using for example QAM modulation are sensitive to fading, and need a simple equalization scheme.

I wrote large portions of the Wikipedia OFDM article, where I tried to show the low computational complexity required for the equalization and fourier transform calculation, by giving numerical examples. In OFDM and SC-FDMA, equalization is done in the frequency domain, which requires much less multiplications per second than the time-domain equalization used in for example wideband CDMA systems, in severe multi-path propagation situations.

Ok, good, this means that equalization can be used in OFDM and SC-OFDM depending on the modulation applied to the subcarrier (@Magnus). In other words, equalization is not totally avoided in OFDM systems. In any case the equalization should be simpler in OFDM-LTE than that of GSM because of the long symbol duration with long enough guard interval between symbols enough for the symbol tail to die before interfering with next symbol. On the other hand, @Talha is raising a good reason for having the equalizer on the LTE uplink which is SC-FDMA. This means that the uplink equalizer for the uplink should be a complex one, and probably more complex than that of the GSM. Thank you both. May be it is good to assume so far that both are the cases, we will have simple equalizer based on modulation type on the DL and a more complex equalizer on the UL in all cases. What do you think?. Thanks. @AlDmour.

Yes. But if equalization is carried out in the SC-FDE uplink, it can still be done in the frequency domain which is not computationally complex. We may calculate the spectrum of the signal (the frequency domain representation) by a first FFT calculation (an inverse Fourier transform) applied on the received time-domain signal. Only one complex-valued multiplication per FFT coefficient and symbol is then required for equalization. A second FFT follows the equalization.

@Ismat: GSM is a narrowband system of 200kHz wide channels, which is hard to compare with LTE. But yes, if the principles of GSM were applied to a 20MHz wide channel (same as in LTE) allowing bit rates in the same order as in LTE, and severe multi-path propagation was assumed, the GSM time-domain equalization would require several orders of magnitude higher number of multiplications per second than the LTE FFT calculations and frequency-domain equalization altogether.

@Talha: Have I understood you correctly? You explain that frequency-domain equalization would be enough in first-release LTE, but in LTE-A, it must be supplemented with linear time-domain equalization for interference rejection, and also with non-linear time-domain equalization to compensate for non-linear amplifiers in the transmitter.

But then SC-FDE (frequency-domain equalization) would be an inappropriate name for the LTE-A uplink modulation scheme? And if the single-carrier behaviour is lost, SC-FDMA would also be an inappropriate term? Why have they not replaced the SC-FDE scheme by OFDMA in the LTE-A uplink to skip one FFT calculation in the mobile unit? And if complex time-domain equalization is required, why not replace the modulation by CDMA to eliminate all FFT calculations? If the base-station has infinite computational capacity, equalization using a conventional Rake receiver plus MIMO interference rejection would be enough.

@ Magnus Eriksson ... You understood right ... Why are we not using OFDMA in the uplink despite the fact that we'd not be needing equalizer at receiver? It is because, OFDMA has high peak to average power ratio (PAPR). Meaning that your mobile phone power amplifier will dissipate lot of power when transmitting. Hence, it is not power efficient technique. However, OFDMA is used in downlink of LTE-A. The reason is BS has infinite power so it can afford; also, OFDMA does not require equalizer, the receiver in downlink is MS, hence receiver architecture will be simpler.

To my knowledge, CDMA can be a good solution when you have single bandwidth, e.g. 5 MHz. It is because the spreading sequence works accordingly. But in the LTE/LTE-A, we have 1.4, 3, 5, 10, 20 MHz bandwidths. Supposing spreading sequence for each of them will be cumbersome.

Recently, some time domain equalization techniques have been proposed in SC-FDMA context. In which , frequency domain MMSE equalization is performed together with time domain ML detection. But i havent read them in detail.

Let me know if i miss something here.

HTH

@Talha. You give clarifying answers to all my questions.

So the non-MIMO SC-FDMA transmitter of first-release LTE may use a class C (on-off) non-linear amplifier. The amplifier would be followed by a passive pass-band resonance filter the turns the square wave into a constant amplitude phase-modulated sine wave signal. Class C amplifiers are very efficient from energy consumption point of view because transistors that only go on and off emit very little heat energy. The emitted radio energy would be higher than the emitted heat energy.

But the MIMO SC-FDMA transmitters used in the LTE-A uplink produce several SC-FDMA signals per transmitter signal which all together shows higher PAPR and need one class AB amplifier, which consumes more energy (or would several class C amplifiers be possible, one per MIMO signal?). And OFDMA shows even more PAPR, and requires a class AB or class A amplifier that is even less efficient from energy consumption point of view than in MIMO SC-FDMA? The average energy concumption of a class AB amplifier is proportional to its emitted peak power. That is why SC-FDMA still is used in the LTE-A uplink?

Is the computational complexity of the time-domain equalization feasible? Does the interference rejection require sample-by-sample time-domain equalization (before IFFT), or does it carry out symbol-by-symbol equalization (of the fourier coefficients after the IFFT)? In the first case it would suffer from extremely high computational complexity, in the second not so much, for a given time-spreading of the multi-path propagation.

Would the non-linear equalization be taken care of on a sample by sample bases? I suppose the required memory is short (only a few samples), so it would still not be extremely computationally complex.

Would you consider non-linear equalization necessary in LTE-A or just a way to improve its performance?

@Ismat: Thank you for formulating such interesting questions and for the inivitation to join.

//ME

Interesting discussion @Magnus and Talha. It brings lots new dimensions to a seemingly direct question to answer. I want here to summarise and elaborate on some of the points discussed above as follows:

* There is a need for equalization in GSM (Time Division Multiple Access -TDMA technique) compared to basic LTE (OFDM based technique). This is because GSM has a high symbol rate leading to problems with multipath causing inter-symbol interference. I like to add that this is one of the tempting factors of OFDM techniques; i.e. simpler transceiver design. In other words, an equalizer is a must for GSM but not for LTE.

* Nevertheless, other factors in LTE necessitate resorting to equalization, especially on the UL as it is uses the single carrier FDM (@Talha) to reduce the necessary overhead (power overhead) due to high peak power to average ratio of OFDM thereby reducing power requirements of the mobile unit running on battery. To reduce the complexity of such equalizer, frequency domain equalization is done rather than time domain equalization.

* The resort to multi antennas in UL in newer LTE standards necessitates the resort to equalization (@Talha). MIMO with space (time) block codes will put pressure on detecting symbols as it results in symbol repetition (as a result of space-time coding). Hence, either we contend with lower gains (as a result of spacial multiplexing only) or we opt to use more symbol repetition (space-time coding) which motivates more ISI, hence, equalization is needed.

* The type of modulation is another factor in LTE (@Magnus) which may necessitate the resort to equalization. For simple DPSK, equalization might not be necessary while going up using higher QAM modulations necessitate the resort to equalization to combat phase and amplitude perturbations resulting from ISI. Or, let me put the other way, we will use higher order QAMs whenever S/N ratio (including multipath effect) is higher the a threshold for the given QAM, but combining QAM with equalization means that we can run it at lower S/N ratio (i.e. we run higher QAM at worse multipath and noise conditions) leading to -higher data rates overall.

Thank you Talha/Magnus for the contribution, please feel free to correct any of the conclusions I made above out of your points. Thanks. @AlDmour

I like to comment also on the point raised regarding the use of multi antennas in SC-FDM and the suggested alternative of WCDMA. First, I don't think that the use of multi-antennas in UL will totally remove the SC-FDM PAPER gain as each antenna signal will use the single carrier with its own PAPR gain (correct me if not). Hence, assuming simply that we are sending a SISO signal at rate R, sending the same signal using MIMO 2x2 using spatial multiplexing needs that the rate at each antenna be R/2. Sending at a lower rate (half) means that less power will be transmitted at the S/N ratio. Or otherwise, MIMO will enable increasing the data rate for the same power.(and bandwidth). Thanks. @AlDmour.

Also, there was a suggestion above, if we are loosing the PAPR gain, why not resorting to WCDMA. Basically, we headed from WCDMA to OFDMA for capacity reasons resulting from compacting narrowband channels (like in GSM) using simple transceiver (no need for equalization). Also, equalization in WCDMA is not a must (Rake receiver is optional) compared to GSM. Thanks. @AlDmour.

@Magnus .... i have very limited knowledge of electronics, especially amplifiers. I may not be able to answer your question properly. Recently, i published a paper in Globecom 2013 in which i dealt with Class C amplifier. At the output of IFFT amplifier, OFDMA waveform is very fluctuating thanks to additions and multiplications operations of IFFT. So high peaks in the waveform drives the amplifier into saturation region but we want our amplifier to be work in linear region where output and input has linear relation (imagine ohm's curve of I and V). But once your amplifier is driven into saturation region, it starts producing harmonics meaning that your input power is dissipated into unwanted harmonics. This means you have reduced your transmitted power. Hence, S/N is reduced at receiver and BER is increased. But in SC-FDMA and together with QPSK, our amplifier remains in linear region. Not sure how Class AB will act in such case.

@ismat ... you summarised everything right. and i second with what you have said about MIMO and OFDMA/WCDMA.