Other meanings of Maximal-ratio combining
Wireless Communications
Maximal-ratio combining (MRC) is a signal processing technique used in wireless communications to combine multiple received signals from diversity antennas or paths in a way that maximizes the output signal-to-noise ratio (SNR). It is a form of diversity combining that weights each branch by its complex conjugate of the channel gain, scaled by the noise variance, and then sums them. MRC is optimal in the sense that it achieves the maximum possible SNR improvement among linear combiners when the noise is Gaussian and independent across branches.
Maximal-ratio combining operates by coherently summing the received signals from multiple branches, each weighted by a factor proportional to the complex conjugate of the channel gain divided by the noise power in that branch. For a system with L branches, the combined signal is given by r = Σi=1L (hi*/σi2) yi, where hi is the channel coefficient, σi2 is the noise variance, and yi is the received signal on branch i. This weighting maximizes the output SNR, which becomes the sum of the individual branch SNRs.1
The technique assumes that the channel state information (CSI) is known at the receiver, which is typically estimated via pilot symbols. In practice, MRC is implemented in baseband after down-conversion and channel estimation. It is widely used in systems with multiple receive antennas, such as in MIMO (multiple-input multiple-output) communications, and in RAKE receivers for CDMA (code-division multiple access) to combine multipath components.2
MRC provides the best performance among linear combining techniques, achieving a diversity order equal to the number of branches L. This means that the bit error rate (BER) decays as SNR-L in Rayleigh fading. In contrast, equal-gain combining (EGC) and selection combining (SC) have lower complexity but yield inferior performance: EGC achieves the same diversity order but with a small SNR penalty (about 1 dB), while SC achieves a diversity order of only 1.3
In the presence of correlated fading or non-Gaussian noise, MRC may not be optimal, and techniques like optimum combining (which accounts for interference) may be preferred. However, MRC remains a benchmark for performance comparison in many studies. Its simplicity and optimality under ideal conditions make it a fundamental building block in wireless system design.
MRC is employed in a variety of modern wireless systems. In 5G NR (New Radio), MRC is used in uplink reception at the base station with multiple antennas, and in downlink with user equipment having multiple receive antennas. It is also a key component in massive MIMO systems, where the large number of antennas allows near-optimal MRC processing with simple linear receivers.4
In Wi-Fi (IEEE 802.11n/ac/ax), MRC is used in the receiver to combine signals from multiple antennas, improving range and throughput. In satellite communications, MRC is used in ground stations to combine signals from multiple antennas to mitigate rain fade. Additionally, MRC is used in underwater acoustic communications and in optical wireless links to combat fading.5
The concept of maximal-ratio combining was first introduced by Leonard R. Kahn in 1954 in the context of frequency-shift keying (FSK) reception, where he proposed a ratio-squarer combiner. Later, Brennan (1959) provided a comprehensive analysis of linear diversity combining techniques, including MRC, and established its optimality in terms of SNR.6
Kahn's work was motivated by the need to improve the reliability of radio communications in fading channels. The technique was initially implemented in analog form, but with the advent of digital signal processing, it became easier to implement in digital receivers. Over the decades, MRC has been extended to various scenarios, including frequency-selective channels, multi-user systems, and cooperative communications.7
One lesser-known aspect is that MRC can be implemented in the frequency domain for OFDM systems, where each subcarrier is combined separately. Another is that MRC is closely related to the matched filter, as the weighting is essentially a matched filter for each branch.
In cooperative communications, MRC is used at the destination to combine signals from multiple relays, but the relays themselves may use different combining strategies. Also, MRC is optimal only when the noise is white and Gaussian; in the presence of co-channel interference, a modified version called optimum combining (OC) that whitens the interference is superior. Furthermore, MRC can be used in conjunction with error correction coding, where soft information from each branch is combined before decoding.
An edge case is when the channel gains are not perfectly known; then, MRC degrades, and robust combining techniques may be needed. Additionally, in massive MIMO, MRC is asymptotically optimal as the number of antennas grows, but with finite antennas, other linear receivers like zero-forcing (ZF) or minimum mean square error (MMSE) may offer better performance in interference-limited scenarios.
This article focuses on the wireless communications sense of maximal-ratio combining.
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