A Flexible ASIC for Time-Domain Decision-Directed Channel Estimation in MIMO-OFDM Systems

Orthogonal frequency division multiplexing (OFDM) and spatial multiplexing over multiple-input multiple-output (MIMO) transmissions schemes are adopted by several recent wireless communication standards such as 3GPP Long Term Evolution (LTE) or IEEE 802.11n and beyond. Due to the concept of coherent detection in MIMO-OFDM receivers the channel estimation (CE) is a crucial and computational intensive part of the overall system and has a significant impact an the communication performance in terms of frame error rate and thus influence directly the maximal achievable throughtput. Traditionally, pilot-aided channel estimation (PACE) is applied where the channel is estimated at predefined pilot positions. The complete channel over all subcarriers is obtained via interpolation. Iterative channel estimation can be used to improve the estimates which delivers promising SNR gains [1]. In the case of iterative channel estimation algorithms, a priori knowledge from the detector or the decoder is used to improve the channel estimates iteratively.

However, the gain in terms of algorithmic performance is payed for in terms of high latencies since each block that participates in the iterations has to complete its processing before the next one can start using the improved input. An alternative that does not increase the latency but still provides significant benefits is the channel tracking approach. This approach [2, 3] provides channel estimation updates for time instance \(n+U_x\) based on the detector or decoder decisions for time instance n, as shown in Fig. 1.

Especially, fast fading channels are interesting scenarios for such a solution. An algorithmic investigation for a communication system similar to LTE is performed in [4] using the simplified frequency domain (FD) SAGE (space-alternating generalized expectation-maximization) algorithm, which calculates updates of the channel impulse response (CIR) estimates for M-QAM constellations. The authors of [3] present a modification that provides a gain of 2 dB for 64-QAM. This modification requires a non trivial matrix inversion. Fortunately, this matrix inversion can be avoided by iteratively processing each tap of the CIR in the time domain, as proposed by the time-domain (TD) SAGE algorithm presented in [5].

Furthermore, the authors of [6] present an analysis of the TD-SAGE algorithm in the context of LTE-Advanced. The results show that it has the potential to double the system throughput at high user mobility due to a better channel estimate and therefore, a lower frame error rate. Apart from that the authors present simulation results about the impact on the system performance of usage of variable number of feedback symbols from the decoder to the channel estimation block. These results show interesting trade-offs between the computational complexity and the algorithmic performance for the TD-SAGE algorithm. Therefore, the number of feedback symbols seems to be interesting parameter for a trade-off analysis between energy dissipation and algorithmic performance of a dedicated VLSI architecture.

Contributions: This chapter introduces an extension of the first ASIC implementation of the TD-SAGE algorithm which is presented in [7]. The TD-SAGE algorithm is transformed to a novel variant, further reducing the computational complexity, to what is termed the tap alternating (TA) SAGE. Apart from that this work discusses two options to further reduce the computational complexity with the penalty of a loss in algorithmic performance. Either reducing the number of feedback symbols as discussed in [6] or reducing the frequency of updating the channel estimate. A suitable VLSI architecture is presented and area, timing and power numbers are provided. The support for a variable number of feedback symbols introduces a modification to the state machine that has an impact on the critical path. Therefore the implementation results for a architectures with and without variable feedback support are presented. This work evaluates the hardware costs of channel tracking in a MIMO-OFDM system.

Outline of the Chapter: The remainder of the chapter is organized as follows. In Sect. 2 the system setup is introduced. Section 3 presents the implemented, modified algorithm followed by Sect. 5 deriving the ASIC architecture and details about the processing units and the memory are given. Finally Sect. 6 discusses post-layout implementation results.

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The system considered in this chapter is a MIMO-OFDM system using \(N_\mathrm {T}=2\) transmit antennas and \(N_\mathrm {R}=2\) receive antennas, with \(N_\mathrm {K} = 512\) sub-carriers and a cyclic prefix length of \(N_\mathrm {L}=32\). First, information bits \(\{b\}\) are encoded using a convolutional encoder with the generator polynomial \([133_o 171_o]\). These code bits \(\{c\}\) are interleaved by a random interleaver, mapped to complex symbols using a 4-, 16- or 64-QAM modulation and then multiplexed over \(N_\mathrm {T}\) spatial streams, each corresponding to a transmit antenna. Each symbol stream is expressed as a vector \(\varvec{t}_{i}[n] = \left[ t_{i}[n,0],\ldots , t_{i}[n,N_\mathrm {K} - 1]\right] ^T \in \mathbb {C}^{N_\mathrm {K}\times 1}\), where \(t_i[n,k]\) is the complex symbol at time n on sub-carrier k transmitted over the ith antenna. Each of the spatial FD streams is processed by an OFDM modulator which outputs the final TD vector \(\varvec{s}_i\) transmitted by the ith transmit antenna.

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The channel model used in this chapter is a frequency-selective Rayleigh fading channel with a power delay profile according to the typical urban COST259 model. It is time variant with the correlation according to Jake’s model with a normalized Doppler frequency of \(f_d = 1.4468\cdot 10^{-5}\), a sub-carrier spacing of 15 kHz, a user velocity \(v=50\,\mathrm{km/h}\) and a carrier frequency \(f_\mathrm {c} = 2.4\,\mathrm{GHz}\).

The frame structure of the system setup used throughout this chapter is shown in Fig. 1. The first OFDM symbol of a frame is a preamble following an orthogonal preamble scheme over the transmit antennas as proposed in [8]. The subsequent OFDM symbols are only consisting of data symbol vectors across all sub-carriers.

The receiver model considered throughout this chapter is depicted in Fig. 2. Each received data symbol vector is iteratively processed by a soft-in soft-out (SISO) detector and a SISO decoder. A data symbol vector is defined as the vector over all receive antennas at the kth sub-carrier. Detection is performed by a max-log MAP SISO sphere detector (SD) with QR decomposition [9], while the channel decoder is a BCJR decoder providing soft information of the coded bits \(\{c\}\). For the simulation results each processing block is executed twice, corresponding to one complete iteration between the detector and the decoder is performed.

The channel estimation provides the required estimate of the channel frequency response to the detector. As depicted in Fig. 2 the CE is split into two parts. First, the PACE processing block calculates an initial CIR estimate based on the preamble. This initial estimate is used to decode the second OFDM symbol of the frame. Second, the DD-CE block uses the decoder decisions of time n in order to provide an updated estimate at time \(n + U_x\) for the detection of the next OFDM symbol. Thus, the third OFDM symbol is detected and decoded based on the updated channel estimate. The update frequency (\(U_x\)) can vary depending on the considered Doppler frequency.

There is an option to adjust the computational complexity of calculation of an update of the CIR. It was presented in [6]. The idea is to reduce the feedback from the decoder and therefore reduce the number of computations. Either the full feedback is used, meaning that all modulation symbols of the previous OFDM symbol are used to calculate the CIR estimate or only every second, third and so on symbol is used in the calculation.

The \(\varvec{H}_{i,j}\) from (1) can be expressed as the DFT of the CIR: \(\varvec{H}_{i,j} = \text {DFT}(\varvec{h}_{i,j})\), where \(\varvec{h}_{i,j}\) is the CIR between the ith transmit antenna and the jth receive antenna. Only the calculation of the CIR estimate \(\hat{\varvec{h}}_{i,j}=( \hat{h}_{i,j}[0], ..., \hat{h}_{i,j}[N_\mathrm {L}-1] )^T\) will be investigated in the remainder of this chapter.

The description of the TD-SAGE algorithm in [5] is modified in this chapter to remove redundant calculations for an efficient VLSI implementation.

The iterations are done for each receive antenna independently. The whole processing of the algorithm is done on the TD samples and can be split into four steps that have to be executed for each receive antenna. For these steps a new variable is introduced. The residual \(\epsilon _\mathrm {j}^{(m)}\) is the vector of the values that are remaining after subtracting the reconstruction of the observation given the current CIR estimate from the real observation \(\varvec{y}_j\), which is basically the current estimation error. Then, the steps of the modified SAGE algorithm are the following:

A variable feedback from the decoder was evaluated in [6]. There the authors explained that they use for a reduced feedback either every second, fourth symbol and so on. In the time domain this means that only the first \(N_{K_F} = N_K / F_b\) time-domain samples are used to calculate an update of the CIR estimate. The variable \(F_b\) is defined to be a power of two, where \(F_b\) greater 8 is not considered. This can be directly realized using the formulars (5)–(10) with the first elements of the vectors \( \varvec{z}\), \(\varvec{s}_i\) and \(\varvec{\epsilon }_j\) respectively.

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Figure 3 shows the block error rate (BLER) for the investigated modulation schemes 4-,16- and 64-QAM using a floating-point implementation. A block is defined as one code word which is spread over one OFDM symbol. The simulations for 4-, 16- and 64-QAM were performed with \(N_i=3\) iterations. The number of estimated taps is \(N_L=32\) which equals the length of the cyclic prefix. This is a worst case assumption for the presented OFDM system which is used throughout this work. Besides the floating-point simulations the results for a fixed-point implementation are shown in Fig. 3. The degradation due to the fixed-point arithmetic is negligible.

For the following evaluation the modulation 4-QAM was chosen exemplary and the number of internal iteration is \(N_i=1\). In Fig. 1 the update frequency is given by \(U_x\). In the following two different options to reduce the computational complexity by a factor of four are evaluated for two different exemplary operation points. The plot depicted in Fig. 4 shows the algorithmic performance for 4-QAM and a mobile device speed of \(v=50\, \mathrm{km/h}\) and an \(U_x=1\) and \(U_x=4\). The loss in algorithmic performance is about 1 dB at a BLER of 1 %. Additionally the BLER for a reduced feedback from the decoder is plotted. There \(F_b\) equals 4 which means that every 4th symbol from decoder is used to calculate the update of the CIR estimate. In this case leads to the same computational complexity than using the full feedback but updating the CIR estimate only every 4th OFDM symbol. From an algorithmic perspective it can be concluded from Fig. 4 that for the given mobile speed and the same computational complexity it is a better choice to update the CIR estimate every 4th OFDM symbol using the full decoder feedback.

Figure 5 shows a BLER plot with the same parameters of \(U_x\) and \(F_b\) but evaluated at a mobile device speed of \(v=100\,\mathrm{km/h}\). The loss in terms of algorithmic performance is in this case for an \(U_x=4\) about 7 dB at a BLER of 10 % using the full decoder feedback, compared to updating the CIR estimate every OFDM symbol. Apart from that it also shows a clear error floor at a BLER of \(3\cdot 10^{-2}\). The second option using only one 4th of the decoder feedback for the calculations shows at \(v=100\,\mathrm{km/h}\) a loss of 2 dB at a BLER of 10 %. The plot depicted in Fig. 5 also shows that at the given speed it is better to use a fourth of the decoder feedback every OFDM symbol instead, when the computational complexity should be kept constant.

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In this chapter we present to the best of our knowledge the first ASIC implementation of a decision directed channel estimation for MIMO-OFDM for M-QAM. The architecture is described and formulas for the calculation of the run-time of the algorithm depending on its parameters on the architecture are presented. The implementation is characterized in terms of area-time trade-offs and power dissipation.

It was shown, that the additional hardware costs of a channel tracking algorithm like the TA-SAGE are high compared to traditional PACE as presented in [11] but it is possible and therefore worth further investigations.

Future work will include the influence of using latched based SCMs as presented in [10] and the evaluation of mixing macro cell memories (e.g. for the residual and the tap memory) with the SCMs approach for the TX memory. Furthermore, this architecture will be compared with simplified algorithms as for example in [12].